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BEGIN:VEVENT
SUMMARY:Hong Wang (IAS)
DTSTART;VALUE=DATE-TIME:20200421T220000Z
DTEND;VALUE=DATE-TIME:20200421T230000Z
DTSTAMP;VALUE=DATE-TIME:20240423T101436Z
UID:UCLAAnalysisSeminar/1
DESCRIPTION:Title: Distinct distances for well-separated sets\nby Hong Wang (
IAS) as part of UCLA analysis and PDE seminar\n\nLecture held in https://u
cla.zoom.us/j/9264073849.\n\nAbstract\nGiven a set E of dimension s>1\, Fa
lconer conjectured that its distance set \\Delta(E)=\\{|x-y|: x\, y\\in E\
\} should have positive Lebesgue measure. Orponen\, Shmerkin and Keleti-Sh
merkin proved the conjecture for tightly spaced sets\, for example\, AD-re
gular sets.\n\nIn this talk\, we are going to discuss the opposite type: w
ell-separated sets. This is joint work with Larry Guth and Noam Solomon.\n
LOCATION:https://researchseminars.org/talk/UCLAAnalysisSeminar/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ioannis Angelopoulos (Caltech)
DTSTART;VALUE=DATE-TIME:20200421T230000Z
DTEND;VALUE=DATE-TIME:20200422T000000Z
DTSTAMP;VALUE=DATE-TIME:20240423T101436Z
UID:UCLAAnalysisSeminar/2
DESCRIPTION:Title: Semi-global constructions of vacuum spacetimes\nby Ioannis
Angelopoulos (Caltech) as part of UCLA analysis and PDE seminar\n\nLectur
e held in https://ucla.zoom.us/j/9264073849.\n\nAbstract\nI will describe
some techniques for constructing semi-global solutions to the characterist
ic initial value problem for the vacuum Einstein equations with different
types of data\, and will also mention some applications as well as some op
en problems in the area.\n
LOCATION:https://researchseminars.org/talk/UCLAAnalysisSeminar/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Joni Teravainen (Oxford)
DTSTART;VALUE=DATE-TIME:20200428T170000Z
DTEND;VALUE=DATE-TIME:20200428T180000Z
DTSTAMP;VALUE=DATE-TIME:20240423T101436Z
UID:UCLAAnalysisSeminar/3
DESCRIPTION:Title: Higher order uniformity of the Möbius function\nby Joni T
eravainen (Oxford) as part of UCLA analysis and PDE seminar\n\nLecture hel
d in https://ucla.zoom.us/j/9264073849.\n\nAbstract\nRecently\, Matomäki\
, Radziwiłł and Tao showed that the Möbius function is discorrelated wi
th linear exponential phases on almost all short intervals. I will discuss
joint work where we generalize this result to a much wider class of phase
functions\, showing that the Möbius function does not correlate with pol
ynomial phases or more generally with nilsequences. I will also discuss ap
plications to superpolynomial word complexity for the Liouville sequence a
nd to counting polynomial patterns weighted by the Möbius function.\n
LOCATION:https://researchseminars.org/talk/UCLAAnalysisSeminar/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Beltran (U. Madison Wisconsin)
DTSTART;VALUE=DATE-TIME:20200505T220000Z
DTEND;VALUE=DATE-TIME:20200505T230000Z
DTSTAMP;VALUE=DATE-TIME:20240423T101436Z
UID:UCLAAnalysisSeminar/4
DESCRIPTION:Title: Regularity of the centered fractional maximal function\nby
David Beltran (U. Madison Wisconsin) as part of UCLA analysis and PDE sem
inar\n\nLecture held in https://caltech.zoom.us/j/747242458.\n\nAbstract\n
I will report some recent progress regarding the boundedness of the map $f
\\mapsto |\\nabla M_\\beta f|$ from the endpoint space $W^{1\,1}(\\mathbb
{R}^d)$ to $L^{d/(d-\\beta)}(\\mathbb{R}^d)$\, where $M_\\beta$ denotes th
e fractional version of the centered Hardy--Littlewood maximal function. A
key step in our analysis is a pointwise relation between the centered and
non-centered fractional maximal functions at the derivative level\, which
allows to exploit the known techniques in the non-centered case.\n\nThis
is joint work with José Madrid.\n
LOCATION:https://researchseminars.org/talk/UCLAAnalysisSeminar/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Luca Spolaor (UCSD)
DTSTART;VALUE=DATE-TIME:20200505T230000Z
DTEND;VALUE=DATE-TIME:20200506T000000Z
DTSTAMP;VALUE=DATE-TIME:20240423T101436Z
UID:UCLAAnalysisSeminar/5
DESCRIPTION:Title: Regularity of the free boundary for the two-phase Bernoulli pr
oblem\nby Luca Spolaor (UCSD) as part of UCLA analysis and PDE seminar
\n\nLecture held in https://caltech.zoom.us/j/747242458.\n\nAbstract\nI wi
ll describe a recent result obtained in collaboration with G. De Philippis
and B. Velichkov concerning the regularity of the free boundaries in the
two phase Bernoulli problems. The novelty of our work is the analysis of t
he free boundary at branch points\, where we show that it is given by the
union of two C1 graphs. This completes the work started by Alt\, Caffarell
i\, and Friedman in the 80’s.\n
LOCATION:https://researchseminars.org/talk/UCLAAnalysisSeminar/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dmitry Khavinson (U. South Florida)
DTSTART;VALUE=DATE-TIME:20200519T230000Z
DTEND;VALUE=DATE-TIME:20200520T000000Z
DTSTAMP;VALUE=DATE-TIME:20240423T101436Z
UID:UCLAAnalysisSeminar/6
DESCRIPTION:Title: Classical Potential Theory from the High Ground of Linear Holo
morphic PDE\nby Dmitry Khavinson (U. South Florida) as part of UCLA an
alysis and PDE seminar\n\nLecture held in https://ucla.zoom.us/j/926407384
9.\n\nAbstract\n"Between two truths of the real domain\, the easiest and s
hortest path quite often passes through the complex domain."\n\n
P. Painleve\, 1900.\n\n\nAbstract: \n\nNew
ton noticed that the gravitational potential of a spherical mass with cons
tant density equals\, outside the ball\, the potential of the point-mass
at the center. Rephrasing\, the gravitational potential of the ball with
constant mass density continues as a harmonic function inside the ball exc
ept for the center. Fairly recently\, it was noted that the latter stateme
nt holds for any polynomial\, or even for entire densities.\n\nIf a harmon
ic in a spherical shell function vanishes on one piece of a line through t
he center piercing the shell\, then it must vanish on the second piece of
that line. Yet\, the similar statement fails for tori.\n\nIf we solve the
Dirichlet problem in an ellipse with entire data\, the solution will alway
s be an entire harmonic function. Yet\, if we do that in a domain bounded
by the curve x^4 + y^4 =1\, with the data as simple as x^2+y^2\, the solut
ion will have infinitely many singularities outside the curve. \nWhere and
why do eigenfunctions of the Laplacian in domains bounded by algebraic cu
rves start having singularities?\n\nWe shall discuss these and some other
questions under the unified umbrella of analytic continuation of solution
s to analytic pde in C^n.\n
LOCATION:https://researchseminars.org/talk/UCLAAnalysisSeminar/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kirsti Biggs (Chalmers U. Technology)
DTSTART;VALUE=DATE-TIME:20200526T170000Z
DTEND;VALUE=DATE-TIME:20200526T180000Z
DTSTAMP;VALUE=DATE-TIME:20240423T101436Z
UID:UCLAAnalysisSeminar/7
DESCRIPTION:Title: Ellipsephic efficient congruencing for the moment curve\nb
y Kirsti Biggs (Chalmers U. Technology) as part of UCLA analysis and PDE s
eminar\n\nLecture held in https://ucla.zoom.us/j/9264073849.\n\nAbstract\n
An ellipsephic set is a subset of the natural numbers whose elements have
digital restrictions in some fixed prime base. Such sets have a fractal st
ructure and can be viewed as p-adic Cantor sets. The particular ellipsephi
c sets that interest us have certain additive properties - for example\, t
he set of integers whose digits are squares forms a key motivating example
\, because there are few representations of an integer as the sum of two s
quares.\n\n\nWe obtain discrete restriction estimates for the moment curve
over ellipsephic sets—in number theoretic terms\, we bound the number o
f ellipsephic solutions to a Vinogradov system of equations—using Wooley
’s nested efficient congruencing method. These results generalise previo
us work of the speaker\, on the quadratic case of this problem\, to the mo
ment curve of arbitrary degree.\n
LOCATION:https://researchseminars.org/talk/UCLAAnalysisSeminar/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mihailis Kolountzakis (U. Crete)
DTSTART;VALUE=DATE-TIME:20200602T160000Z
DTEND;VALUE=DATE-TIME:20200602T165000Z
DTSTAMP;VALUE=DATE-TIME:20240423T101436Z
UID:UCLAAnalysisSeminar/8
DESCRIPTION:Title: Orthogonal Fourier analysis on domains: methods\, results and
open problems\nby Mihailis Kolountzakis (U. Crete) as part of UCLA ana
lysis and PDE seminar\n\nLecture held in https://caltech.zoom.us/j/7472424
58.\n\nAbstract\nWe all know how to do Fourier Analysis on an interval\, o
n {\\mathbb R}^d\, or other groups. But what if our functions live on a su
bset of Euclidean space\, let's say on a regular hexagon in the plane? Can
we use our beloved exponentials\, functions of the form e_\\lambda(x) = \
\exp(2\\pi i \\lambda\\cdot x) to analyze the functions defined on our dom
ain? In other words\, can we select a set of frequencies \\lambda such tha
t the corresponding exponentials form an orthogonal basis for L^2 of our d
omain? It turns out that the existence of such an orthogonal basis depends
heavily on the domain. So the answer is yes\, we can find an orthogonal b
asis of exponentials for the hexagon\, but if we ask the same question for
a disk\, the answer turns out to be no.\n\nFuglede conjectured in the 197
0s that the existence of such an exponential basis is equivalent to the do
main being able to tile space by translations (the hexagon\, that we menti
oned\, indeed can tile\, while the disk cannot). In this talk we will trac
k this conjecture and the mathematics created by the attempts to settle it
and its variants. We will see some of its rich connections to geometry\,
number theory and harmonic analysis and some of the spectacular recent suc
cesses in our efforts to understand exponential bases. We will emphasize s
everal problems that are still open.\n
LOCATION:https://researchseminars.org/talk/UCLAAnalysisSeminar/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yakov Shlapentokh-Rothman (Princeton)
DTSTART;VALUE=DATE-TIME:20200602T170000Z
DTEND;VALUE=DATE-TIME:20200602T180000Z
DTSTAMP;VALUE=DATE-TIME:20240423T101436Z
UID:UCLAAnalysisSeminar/9
DESCRIPTION:Title: Naked Singularities for the Einstein Vacuum Equations: The Ext
erior Solution\nby Yakov Shlapentokh-Rothman (Princeton) as part of UC
LA analysis and PDE seminar\n\nLecture held in https://caltech.zoom.us/j/7
47242458.\nAbstract: TBA\n\nWe will start by recalling the weak cosmic cen
sorship conjecture. Then we will review Christodoulou's construction of na
ked singularities for the spherically symmetric Einstein-scalar field syst
em. Finally\, we will discuss joint work with Igor Rodnianski which constr
ucts spacetimes corresponding to the exterior region of a naked singularit
y for the Einstein vacuum equations.\n
LOCATION:https://researchseminars.org/talk/UCLAAnalysisSeminar/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kevin Hughes (U. Bristol)
DTSTART;VALUE=DATE-TIME:20200519T220000Z
DTEND;VALUE=DATE-TIME:20200519T230000Z
DTSTAMP;VALUE=DATE-TIME:20240423T101436Z
UID:UCLAAnalysisSeminar/10
DESCRIPTION:Title: Discrete restriction estimates\nby Kevin Hughes (U. Brist
ol) as part of UCLA analysis and PDE seminar\n\nLecture held in https://uc
la.zoom.us/j/9264073849.\n\nAbstract\nWe will discuss Wooley's Efficient C
ongruencing approach to discrete restriction estimates for translation-dil
ation invariant systems of equations. Then we will discuss recent estimate
s for the curve (X\,X^3) which lie just outside of this framework as well
as that of Decoupling.\n
LOCATION:https://researchseminars.org/talk/UCLAAnalysisSeminar/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Stefan Steinerberger (U. Washington)
DTSTART;VALUE=DATE-TIME:20201006T220000Z
DTEND;VALUE=DATE-TIME:20201006T230000Z
DTSTAMP;VALUE=DATE-TIME:20240423T101436Z
UID:UCLAAnalysisSeminar/11
DESCRIPTION:Title: Roots of polynomials under repeated differentiation: a nonloc
al evolution equation with infinitely many conservation laws (and some uni
versality phenomena)\nby Stefan Steinerberger (U. Washington) as part
of UCLA analysis and PDE seminar\n\n\nAbstract\nSuppose you have a polynom
ial of degree $p_n$ whose $n$ real roots are roughly distributed like a Ga
ussian (or some other nice distribution) and you differentiate $t\\cdot n$
times where $0< t<1$. What's the distribution of the $(1-t)n$ roots of th
at $(t\\cdot n)$-th derivative? How does it depend on $t$? We identify a
relatively simple nonlocal evolution equation (the nonlocality is given by
a Hilbert transform)\; it has two nice closed-form solutions\, a shrinkin
g semicircle and a family of Marchenko-Pastur distributions (this sounds l
ike random matrix theory and we make some remarks in that direction). More
over\, the underlying evolution satisfies an infinite number of conservati
on laws that one can write down explicitly. This suggests a lot of questio
ns: Sean O'Rourke and I proposed an analogous equation for complex-valued
polynomials. Motivated by some numerical simulations\, Jeremy Hoskins and
I conjectured that $t=1$\, just before the polynomial disappears\, the sh
ape of the remaining roots is a semicircle and we prove that for a class o
f random polynomials. I promise lots of open problems and pretty pictures
.\n
LOCATION:https://researchseminars.org/talk/UCLAAnalysisSeminar/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bjoern Bringmann (UCLA)
DTSTART;VALUE=DATE-TIME:20201006T230000Z
DTEND;VALUE=DATE-TIME:20201007T000000Z
DTSTAMP;VALUE=DATE-TIME:20240423T101436Z
UID:UCLAAnalysisSeminar/12
DESCRIPTION:Title: Invariant Gibbs measures for the three-dimensional wave equat
ion with a Hartree nonlinearity\nby Bjoern Bringmann (UCLA) as part of
UCLA analysis and PDE seminar\n\n\nAbstract\nIn this talk\, we discuss th
e construction and invariance of the Gibbs measure for a three-\ndimension
al wave equation with a Hartree-nonlinearity.\n\nIn the first part of the
talk\, we construct the Gibbs measure and examine its properties. We discu
ss the mutual singularity of the Gibbs measure and the so-called Gaussian
free field. In contrast\, the Gibbs measure for one or two-dimensional wav
e equations is absolutely continuous with respect to the Gaussian free fie
ld.\n\nIn the second part of the talk\, we discuss the probabilistic well-
posedness of the corresponding nonlinear wave equation\, which is needed i
n the proof of invariance. At the moment\, this is the only theorem provin
g the invariance of any singular Gibbs measure under a dispersive equation
.\n
LOCATION:https://researchseminars.org/talk/UCLAAnalysisSeminar/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Khang Huynh (UCLA)
DTSTART;VALUE=DATE-TIME:20201020T220000Z
DTEND;VALUE=DATE-TIME:20201020T230000Z
DTSTAMP;VALUE=DATE-TIME:20240423T101436Z
UID:UCLAAnalysisSeminar/13
DESCRIPTION:Title: A geometric trapping approach to global regularity for 2D Nav
ier-Stokes on manifolds\nby Khang Huynh (UCLA) as part of UCLA analysi
s and PDE seminar\n\n\nAbstract\nWe use frequency decomposition techniques
to give a direct proof of global existence and regularity for the Navier-
Stokes equations on two-dimensional Riemannian manifolds without boundary.
Our techniques are inspired by an approach of Mattingly and Sinai which w
as developed in the context of periodic boundary conditions on a flat back
ground\, and which is based on a maximum principle for Fourier coefficient
s. The extension to general manifolds requires several new ideas\, connect
ed to the less favorable spectral localization properties in our setting.
Our arguments make use of frequency projection operators\, multilinear est
imates that originated in the study of the non-linear Schrodinger equation
\, and ideas from microlocal analysis.\n\nThis is joint work with Aynur Bu
lut.\n
LOCATION:https://researchseminars.org/talk/UCLAAnalysisSeminar/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jaemin Park (Georgia Tech)
DTSTART;VALUE=DATE-TIME:20201013T210000Z
DTEND;VALUE=DATE-TIME:20201013T220000Z
DTSTAMP;VALUE=DATE-TIME:20240423T101436Z
UID:UCLAAnalysisSeminar/14
DESCRIPTION:Title: Radial symmetry in stationary/uniformly-rotating solutions to
2D Euler equation\nby Jaemin Park (Georgia Tech) as part of UCLA anal
ysis and PDE seminar\n\n\nAbstract\nIn this talk\, I will discuss whether
all stationary/uniformly-rotating solutions of 2D Euler equation must be r
adially symmetric\, if the vorticity is compactly supported. For a station
ary solution that is either smooth or of patch type\, we prove that if the
vorticity does not change sign\, it must be radially symmetric up to a tr
anslation. It turns out that the fixed-sign condition is necessary for rad
ial symmetry result: indeed\, we are able to find non-radial sign changing
stationary solution with compact support. We have also obtained some shar
p criteria on symmetry for uniformly-rotating solutions for 2D Euler equat
ion and the SQG equation. The symmetry results are mainly obtained by calc
ulus of variations and elliptic equation techniques\, and the construction
of non-radial solution is obtained from bifurcation theory. Part of this
talk is based on joint work with Javier Gomez-Serrano\, Jia Shi and Yao Ya
o\n
LOCATION:https://researchseminars.org/talk/UCLAAnalysisSeminar/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Thomas Bloom (Cambridge)
DTSTART;VALUE=DATE-TIME:20201103T180000Z
DTEND;VALUE=DATE-TIME:20201103T190000Z
DTSTAMP;VALUE=DATE-TIME:20240423T101436Z
UID:UCLAAnalysisSeminar/15
DESCRIPTION:Title: Spectral structure and arithmetic progressions\nby Thomas
Bloom (Cambridge) as part of UCLA analysis and PDE seminar\n\n\nAbstract\
nHow much additive structure can we guarantee in sets of integers\, knowin
g only their density? The study of which density thresholds are sufficient
to guarantee the existence of various kinds of additive structures is an
old and fascinating subject with connections to analytic number theory\, a
dditive combinatorics\, and harmonic analysis.\n\nIn this talk we will dis
cuss recent progress on perhaps the most well-known of these thresholds: h
ow large do we need a set of integers to be to guarantee the existence of
a three-term arithmetic progression? In recent joint work with Olof Sisask
we broke through the logarithmic density barrier for this problem\, estab
lishing in particular that if a set is dense enough such that the sum of r
eciprocals diverges\, then it must contain a three-term arithmetic progres
sion\, establishing the first case of an infamous conjecture of Erdos.\n\n
We will give an introduction to this problem and sketch some of the recent
ideas that have made this progress possible. We will pay particular atten
tion to the ways we exploit 'spectral structure' - understanding combinato
rially sets of large Fourier coefficients\, which we hope will have furthe
r applications in number theory and harmonic analysis.\n
LOCATION:https://researchseminars.org/talk/UCLAAnalysisSeminar/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yao Yao (Georgia Tech)
DTSTART;VALUE=DATE-TIME:20201118T000000Z
DTEND;VALUE=DATE-TIME:20201118T010000Z
DTSTAMP;VALUE=DATE-TIME:20240423T101436Z
UID:UCLAAnalysisSeminar/16
DESCRIPTION:Title: Two results on the interaction energy\nby Yao Yao (Georgi
a Tech) as part of UCLA analysis and PDE seminar\n\n\nAbstract\nFor any no
nnegative density $f$ and radially decreasing interaction potential $W$\,
the celebrated Riesz rearrangement inequality shows the interaction energy
$E[f] = \\int f(x)f(y)W(x-y) dxdy$ satisfies $E[f] \\leq E[f^*]$\, where
$f^*$ is the radially decreasing rearrangement of $f$. It is a natural que
stion to look for a quantitative version of this inequality: if its two si
des almost agree\, how close must $f$ be to a translation of $f^*$? Previo
usly the stability estimate was only known for characteristic functions. I
will discuss a recent work with Xukai Yan\, where we found a simple proof
of stability estimates for general densities. \n\nI will also discuss ano
ther work with Matias Delgadino and Xukai Yan\, where we constructed an in
terpolation curve between any two radially decreasing densities with the s
ame mass\, and show that the interaction energy is convex along this inter
polation. As an application\, this leads to uniqueness of steady states in
aggregation-diffusion equations with any attractive interaction potential
for diffusion power $m\\geq 2$\, where the threshold is sharp.\n
LOCATION:https://researchseminars.org/talk/UCLAAnalysisSeminar/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jared Speck (Vanderbilt)
DTSTART;VALUE=DATE-TIME:20201020T230000Z
DTEND;VALUE=DATE-TIME:20201021T000000Z
DTSTAMP;VALUE=DATE-TIME:20240423T101436Z
UID:UCLAAnalysisSeminar/17
DESCRIPTION:Title: Stable big bang formation in general relativity: the complete
sub-critical regime\nby Jared Speck (Vanderbilt) as part of UCLA anal
ysis and PDE seminar\n\n\nAbstract\nThe celebrated theorems of Hawking and
Penrose show that under appropriate assumptions on the matter model\, a l
arge\, open set of initial data for Einstein's equations lead to geodesica
lly incomplete solutions. However\, these theorems are "soft" in that they
do not yield any information\nabout the nature of the incompleteness\, le
aving open the possibilities that \n\ni) it is tied to the blowup of some
invariant quantity (such as curvature) or \n\nii) it is due to a more sini
ster phenomenon\, such as\nincompleteness due to lack of information for h
ow to uniquely continue the solution (this is roughly\nknown as the format
ion of a Cauchy horizon). \n\nDespite the "general ambiguity" in the mathe
matical physics literature\, there are heuristic results\, going back 50 y
ears\, suggesting that whenever a certain "sub-criticality" condition hold
s\, the Hawking-Penrose incompleteness is caused by the formation of a Big
Bang singularity\, that is\, curvature blowup along an entire spacelike h
ypersurface. In\nrecent joint work with I. Rodnianski and G. Fournodavlos\
, we have given a rigorous proof of the heuristics. More precisely\, our r
esults apply to Sobolev-class perturbations - without symmetry - of genera
lized Kasner solutions whose exponents satisfy the sub-criticality conditi
on. Our main\ntheorem shows that - like the generalized Kasner solutions -
the perturbed solutions develop Big Bang singularities. \n\nIn this talk\
, I will provide an overview of our result and explain how it is tied to s
ome of the main themes of investigation by the mathematical general relati
vity community\, including the remarkable work of Dafermos-Luk on the stab
ility of Kerr Cauchy horizons. I will also discuss the new gauge that we u
sed in our work\, as well as intriguing connections to other problems conc
erning stable singularity formation.\n
LOCATION:https://researchseminars.org/talk/UCLAAnalysisSeminar/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aleksandr Logunov (Princeton)
DTSTART;VALUE=DATE-TIME:20201215T190000Z
DTEND;VALUE=DATE-TIME:20201215T200000Z
DTSTAMP;VALUE=DATE-TIME:20240423T101436Z
UID:UCLAAnalysisSeminar/18
DESCRIPTION:Title: Zero sets of Laplace eigenfunctions\nby Aleksandr Logunov
(Princeton) as part of UCLA analysis and PDE seminar\n\n\nAbstract\nIn th
e beginning of 19th century Napoleon set a prize for the best mathematical
explanation of Chladni’s resonance experiments. Nodal geometry studies
the zeroes of solutions to elliptic differential equations such as the vis
ible curves that appear in these physical experiments. We will discuss geo
metrical and analytic properties of zero sets of harmonic functions and ei
genfunctions of the Laplace operator. For harmonic functions on the plane
there is an interesting relation between local length of the zero set and
the growth of harmonic functions. The larger the zero set is\, the faster
the growth of harmonic function should be and vice versa. Zero sets of Lap
lace eigenfunctions on surfaces are unions of smooth curves with equiangul
ar intersections. Topology of the zero set could be quite complicated\, bu
t Yau conjectured that the total length of the zero set is comparable to t
he square root of the eigenvalue for all eigenfunctions. We will start wit
h open questions about spherical harmonics and explain some methods to stu
dy nodal sets.\n
LOCATION:https://researchseminars.org/talk/UCLAAnalysisSeminar/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Cristian Gonzales-Riquelme (IMPA)
DTSTART;VALUE=DATE-TIME:20201117T230000Z
DTEND;VALUE=DATE-TIME:20201118T000000Z
DTSTAMP;VALUE=DATE-TIME:20240423T101436Z
UID:UCLAAnalysisSeminar/19
DESCRIPTION:Title: BV and Sobolev continuity for maximal operators\nby Crist
ian Gonzales-Riquelme (IMPA) as part of UCLA analysis and PDE seminar\n\n\
nAbstract\nThe regularity of maximal operators has been a topic of\nintere
st in harmonic analysis over the past decades. In this topic we are intere
sted in what can be said about the variation of a maximal function Mf give
n some information about the original function f. In this talk we present\
nsome recent results about the continuity of the map $f \\mapsto \\nabla M
f$ for the uncentered Hardy-Littlewood maximal operator in both the $BV({\
\mathbb R})$ and the $W^{1\,1}_{rad}({\\mathbb R}^d)$ settings.\n\nThis is
based on joint works with D. Kosz (BV case) and E. Carneiro and J. Madrid
(radial case).\n
LOCATION:https://researchseminars.org/talk/UCLAAnalysisSeminar/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Paata Ivanisvili (NC State)
DTSTART;VALUE=DATE-TIME:20201201T230000Z
DTEND;VALUE=DATE-TIME:20201202T000000Z
DTSTAMP;VALUE=DATE-TIME:20240423T101436Z
UID:UCLAAnalysisSeminar/20
DESCRIPTION:Title: Sharpening the triangle inequality in Lp spaces\nby Paata
Ivanisvili (NC State) as part of UCLA analysis and PDE seminar\n\n\nAbstr
act\nThe classical triangle inequality in Lp estimates the norm of the sum
of two functions in terms of the sums of the norms of these functions. Pe
rhaps one drawback of this estimate is that it does not see how "orthogona
l" these functions are. For example\, if f and g are not identically zero
and they have disjoint supports then the triangle inequality is pretty str
ict (say for p>1).\n\nMotivated by the L2 case\, where one has a trivial i
nequality ||f+g||^2 \\leq ||f||^2 + ||g||^2 + 2 |fg|_1\, one can think abo
ut the quantity |fg|_1 as measuring the "overlap" between f and g. What is
the correct analog of this estimate in Lp for p different than 2?\n\nMy t
alk will be based on a joint work with Carlen\, Frank and Lieb where we ob
tain one extension of this estimate in Lp\, thereby proving and improving
the suggested possible estimates by Carbery\, and another work with Mooney
where we further refine these estimates. The estimates will be provided f
or all real p's.\n
LOCATION:https://researchseminars.org/talk/UCLAAnalysisSeminar/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Emanuel Carneiro (ICTP)
DTSTART;VALUE=DATE-TIME:20201215T180000Z
DTEND;VALUE=DATE-TIME:20201215T190000Z
DTSTAMP;VALUE=DATE-TIME:20240423T101436Z
UID:UCLAAnalysisSeminar/21
DESCRIPTION:Title: Uncertain signs\nby Emanuel Carneiro (ICTP) as part of UC
LA analysis and PDE seminar\n\n\nAbstract\nWe consider a generalized versi
on of the sign uncertainty\nprinciple for the Fourier transform\, first pr
oposed by Bourgain\, Clozel and\nKahane in 2010 and revisited by Cohn and
Gonçalves in 2019\, in connection\nto the sphere packing problem. In our
setup\, the signs of a function and\nits Fourier transform resonate with a
generic given function P outside of\na ball. One essentially wants to kno
w if and how soon this resonance can\nhappen\, when facing a suitable comp
eting weighted integral condition. The\noriginal version of the problem co
rresponds to the case P=1.\nSurprisingly\, even in such a rough setup\, we
are able to identify sharp\nconstants in some cases. This is a joint work
with Oscar Quesada-Herrera\n(IMPA - Rio de Janeiro).\n
LOCATION:https://researchseminars.org/talk/UCLAAnalysisSeminar/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Damanik (Rice)
DTSTART;VALUE=DATE-TIME:20201202T000000Z
DTEND;VALUE=DATE-TIME:20201202T010000Z
DTSTAMP;VALUE=DATE-TIME:20240423T101436Z
UID:UCLAAnalysisSeminar/22
DESCRIPTION:Title: Proving Positive Lyapunov Exponents: Beyond Independence\
nby David Damanik (Rice) as part of UCLA analysis and PDE seminar\n\n\nAbs
tract\nWe discuss the problem of proving the positivity of the Lyapunov ex
ponent for Schr\\"odinger operators with potentials defined by a hyperboli
c base transformation and a H \\"older continuous sampling function. Promi
nent examples of such base transformations are given by the doubling map a
nd the Arnold cat map. The talk is based on joint work with Artur Avila an
d Zhenghe Zhang.\n
LOCATION:https://researchseminars.org/talk/UCLAAnalysisSeminar/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shukun Wu (UIUC)
DTSTART;VALUE=DATE-TIME:20201027T210000Z
DTEND;VALUE=DATE-TIME:20201027T220000Z
DTSTAMP;VALUE=DATE-TIME:20240423T101436Z
UID:UCLAAnalysisSeminar/23
DESCRIPTION:Title: On the Bochner-Riesz problem in dimension 3\nby Shukun Wu
(UIUC) as part of UCLA analysis and PDE seminar\n\n\nAbstract\nWe improve
the Bochner-Riesz conjecture in dimension 3 to p>3.25. The main method we
used is the iterated polynomial partitioning algorithm. We also observe s
ome relations between wave packets at different scales.\n
LOCATION:https://researchseminars.org/talk/UCLAAnalysisSeminar/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yilin Wang (MIT)
DTSTART;VALUE=DATE-TIME:20201208T220000Z
DTEND;VALUE=DATE-TIME:20201208T230000Z
DTSTAMP;VALUE=DATE-TIME:20240423T101436Z
UID:UCLAAnalysisSeminar/24
DESCRIPTION:Title: SLE\, energy duality\, and foliations by Weil-Petersson quasi
circles\nby Yilin Wang (MIT) as part of UCLA analysis and PDE seminar\
n\n\nAbstract\nThe Loewner energy for Jordan curves first arises from the
small-parameter large deviations of Schramm-Loewner evolution (SLE). It is
finite if and only if the curve is a Weil-Petersson quasicircle\, an inte
resting class of Jordan curves appearing in Teichmuller theory\, geometric
function theory\, and string theory with currently more than 20 equivalen
t definitions. In this talk\, I will show that the large-parameter large d
eviations of SLE gives rise to a new Loewner-Kufarev energy\, which is dua
l to the Loewner energy via foliations by Weil-Petersson quasicircles and
exhibits remarkable features and symmetries. Based on joint works with Mor
ris Ang and Minjae Park (MIT) and with Fredrik Viklund (KTH).\n
LOCATION:https://researchseminars.org/talk/UCLAAnalysisSeminar/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Thomas Beck (Fordham)
DTSTART;VALUE=DATE-TIME:20201103T190000Z
DTEND;VALUE=DATE-TIME:20201103T200000Z
DTSTAMP;VALUE=DATE-TIME:20240423T101436Z
UID:UCLAAnalysisSeminar/25
DESCRIPTION:Title: Two-phase free boundary problems and the Friedland-Hayman ine
quality\nby Thomas Beck (Fordham) as part of UCLA analysis and PDE sem
inar\n\n\nAbstract\nThe Friedland-Hayman inequality provides a lower bound
on the first Dirichlet eigenvalues of complementary subsets of the sphere
. In this talk\, we will describe a variant of this inequality to geodesic
ally convex subsets of the sphere with mixed Dirichlet-Neumann boundary co
nditions. Using this inequality\, we prove an almost-monotonicity formula
and Lipschitz continuity up to the boundary for the minimizer of a two-pha
se free boundary problem. This is joint work with David Jerison and Sarah
Raynor.\n
LOCATION:https://researchseminars.org/talk/UCLAAnalysisSeminar/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Adrian Nachman (U. Toronto)
DTSTART;VALUE=DATE-TIME:20201110T220000Z
DTEND;VALUE=DATE-TIME:20201110T230000Z
DTSTAMP;VALUE=DATE-TIME:20240423T101436Z
UID:UCLAAnalysisSeminar/26
DESCRIPTION:Title: A Nonlinear Plancherel Theorem with Applications to Global We
ll-posedness for the Defocusing Davey-Stewartson Equation and to the Inver
se Boundary Value Problem of Calderon\nby Adrian Nachman (U. Toronto)
as part of UCLA analysis and PDE seminar\n\n\nAbstract\nThis is joint work
with Idan Regev and Daniel Tataru.\n\nThe talk will aim to present our so
lutions to 2+\\epsilon open problems.\n
LOCATION:https://researchseminars.org/talk/UCLAAnalysisSeminar/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Justin Forlano (UCLA)
DTSTART;VALUE=DATE-TIME:20201124T220000Z
DTEND;VALUE=DATE-TIME:20201124T230000Z
DTSTAMP;VALUE=DATE-TIME:20240423T101436Z
UID:UCLAAnalysisSeminar/27
DESCRIPTION:Title: Normal form approach to the one-dimensional cubic nonlinear S
chr\\"{o}dinger equation in almost critical spaces\nby Justin Forlano
(UCLA) as part of UCLA analysis and PDE seminar\n\n\nAbstract\nIn recent y
ears\, the normal form approach has provided an alternative method to esta
blishing the well-posedness of solutions to nonlinear dispersive PDEs\, as
compared to using heavy machinery from harmonic analysis. In this talk\,
I will describe how to apply the normal form approach to study the one-dim
ensional cubic nonlinear Schr\\"{o}dinger equation (NLS) on the real-line
and prove local well-posedness in almost critical Fourier-amalgam spaces.
This involves using an infinite iteration of normal form reductions (namel
y\, integration by parts in time) to derive the normal form equation\, whi
ch behaves better than NLS for rough functions.\n\nThis is joint work with
Tadahiro Oh (U. Edinburgh).\n
LOCATION:https://researchseminars.org/talk/UCLAAnalysisSeminar/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Dobner (UCLA)
DTSTART;VALUE=DATE-TIME:20210106T000000Z
DTEND;VALUE=DATE-TIME:20210106T010000Z
DTSTAMP;VALUE=DATE-TIME:20240423T101436Z
UID:UCLAAnalysisSeminar/28
DESCRIPTION:Title: Extreme values of the argument of the zeta function\nby A
lexander Dobner (UCLA) as part of UCLA analysis and PDE seminar\n\n\nAbstr
act\nLet $S(t) = \\frac{1}{\\pi}\\Im \\log \\zeta(\\frac{1}{2}+it)$. The b
ehavior of this function is intimately connected to irregularities in the
locations of the zeros of the zeta function. In particular $S(t)$ measures
the difference between the "expected" number of zeta zeros up to height $
t$ and the actual number of such zeros. I will discuss what is known about
the distribution of $S(t)$ and prove a new unconditional lower bound on h
ow often $S(t)$ achieves large values.\n
LOCATION:https://researchseminars.org/talk/UCLAAnalysisSeminar/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eugenia Malinnikova (Stanford)
DTSTART;VALUE=DATE-TIME:20210126T220000Z
DTEND;VALUE=DATE-TIME:20210126T230000Z
DTSTAMP;VALUE=DATE-TIME:20240423T101436Z
UID:UCLAAnalysisSeminar/29
DESCRIPTION:Title: Landis’ conjecture on the decay of solutions to Schrödinge
r equations on the plane.\nby Eugenia Malinnikova (Stanford) as part o
f UCLA analysis and PDE seminar\n\n\nAbstract\nWe consider a real-valued f
unction on the plane for which the absolute value of the Laplacian is boun
ded by the absolute value of the function at each point. In other words\,
we look at solutions of the stationary Schrödinger equation with a bounde
d potential. The question discussed in the talk is how fast such function
may decay at infinity. We give the answer in dimension two\, in higher dim
ensions the corresponding problem is open.\n\n \n\nThe talk is based on th
e joint work with A. Logunov\, N. Nadirashvili\, and F. Nazarov.\n
LOCATION:https://researchseminars.org/talk/UCLAAnalysisSeminar/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yufei Zhao (MIT)
DTSTART;VALUE=DATE-TIME:20210120T000000Z
DTEND;VALUE=DATE-TIME:20210120T010000Z
DTSTAMP;VALUE=DATE-TIME:20240423T101436Z
UID:UCLAAnalysisSeminar/30
DESCRIPTION:Title: Joints of varieties\nby Yufei Zhao (MIT) as part of UCLA
analysis and PDE seminar\n\n\nAbstract\nWe generalize the Guth-Katz joints
theorem from lines to varieties. A special case of our result says that $
N$ planes (2-flats) in 6 dimensions (over any field) have $O(N^{3/2})$ joi
nts\, where a joint is a point contained in a triple of these planes not a
ll lying in some hyperplane. Our most general result gives upper bounds\,
tight up to constant factors\, for joints with multiplicities for several
sets of varieties of arbitrary dimensions (known as Carbery's conjecture).
Our main innovation is a new way to extend the polynomial method to highe
r dimensional objects.\n\nJoint work with Jonathan Tidor and Hung-Hsun Han
s Yu.\n
LOCATION:https://researchseminars.org/talk/UCLAAnalysisSeminar/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Georgis Moschidis (UC Berkeley)
DTSTART;VALUE=DATE-TIME:20210112T180000Z
DTEND;VALUE=DATE-TIME:20210112T190000Z
DTSTAMP;VALUE=DATE-TIME:20240423T101436Z
UID:UCLAAnalysisSeminar/31
DESCRIPTION:Title: The instability of Anti-de Sitter spacetime for the Einstein-
scalar field system\nby Georgis Moschidis (UC Berkeley) as part of UCL
A analysis and PDE seminar\n\n\nAbstract\nhe AdS instability conjecture pr
ovides an example of weak turbulence appearing in the dynamics of the Eins
tein equations in the presence of a negative cosmological constant. The co
njecture claims the existence of arbitrarily small perturbations to the in
itial data of Anti-de Sitter spacetime which\, under evolution by the vacu
um Einstein equations with reflecting boundary conditions at conformal in
finity\, lead to the formation of black holes after sufficiently long time
. \n In this talk\, I will present a rigorous proof of the AdS instabil
ity conjecture in the setting of the spherically symmetric Einstein-scala
r field system. The construction of the unstable initial data will require
carefully designing a family of initial configurations of localized matte
r beams and estimating the exchange of energy taking place between interac
ting beams over long periods of time\, as well as estimating the decoheren
ce rate of those beams. I will also discuss possible paths for extending t
hese ideas to the vacuum case.\n
LOCATION:https://researchseminars.org/talk/UCLAAnalysisSeminar/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Elena Giorgi (Princeton)
DTSTART;VALUE=DATE-TIME:20210116T000000Z
DTEND;VALUE=DATE-TIME:20210116T010000Z
DTSTAMP;VALUE=DATE-TIME:20240423T101436Z
UID:UCLAAnalysisSeminar/32
DESCRIPTION:Title: Electromagnetic-gravitational perturbations of Kerr-Newman sp
acetime\nby Elena Giorgi (Princeton) as part of UCLA analysis and PDE
seminar\n\n\nAbstract\nThe Kerr-Newman spacetime is the most general expli
cit black hole solution\, and represents a stationary rotating charged bla
ck hole. Its stability to gravitational and electromagnetic perturbations
has eluded a proof since the 80s in the black hole perturbation community\
, because of "the apparent indissolubility of the coupling between the spi
n-1 and spin-2 fields in the perturbed spacetime"\, as put by Chandrasekha
r. We will present a derivation of the Teukolsky and Regge-Wheeler equatio
ns in Kerr-Newman in physical space and use it to obtain a quantitative pr
oof of stability.\n
LOCATION:https://researchseminars.org/talk/UCLAAnalysisSeminar/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Betsy Stovall (UW-Madison)
DTSTART;VALUE=DATE-TIME:20210302T190000Z
DTEND;VALUE=DATE-TIME:20210302T200000Z
DTSTAMP;VALUE=DATE-TIME:20240423T101436Z
UID:UCLAAnalysisSeminar/33
DESCRIPTION:Title: Existence of extremizers for Fourier restriction operators\nby Betsy Stovall (UW-Madison) as part of UCLA analysis and PDE seminar\
n\n\nAbstract\nWe learn in first year graduate analysis that an operator f
rom one Banach space to another is continuous if and only if the image of
the unit ball is a bounded set. In this talk\, we will discuss the questio
n of whether this image has a point of maximal norm\, in the specific cont
ext of certain Fourier restriction operators.\n
LOCATION:https://researchseminars.org/talk/UCLAAnalysisSeminar/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marta Lewicka (U. Pittsburgh)
DTSTART;VALUE=DATE-TIME:20210109T000000Z
DTEND;VALUE=DATE-TIME:20210109T010000Z
DTSTAMP;VALUE=DATE-TIME:20240423T101436Z
UID:UCLAAnalysisSeminar/34
DESCRIPTION:Title: Expansions of averaging operators and applications\nby Ma
rta Lewicka (U. Pittsburgh) as part of UCLA analysis and PDE seminar\n\n\n
Abstract\nhe following approach of finding solutions to a partial differen
tial equation Lu=0\, proved to be quite versatile:\n\n(i) develop an asymp
totic expansion of a suitable family of averaging operators (to be applied
on u)\; the operators are parametrized by the radius \\epsilon of averagi
ng\, and the coefficient in the expansion that multiplies the appropriate
power of \\epsilon should equal Lu\, the "appropriate power" refers to the
order of L\;\n\n(ii) study the related mean value equation by removing hi
gher order terms in the expansion\;\n\n(iii) interpret the mean value equa
tion as the dynamic programming principle of a two-player game incorporati
ng deterministic and stochastic components\;\n\n(iv) pass to the limit in
the radius of averaging \\epsilon\, in order to recover solutions to Lu=0
from the values of the game process.\n\nIn my talk\, I will explain this a
pproach in the contexts of p-Laplacian and the non-local geometric p-Lapla
cian. Other applications include: Robin boundary conditions and weighted L
aplace-Beltrami operator on a manifold. In each case\, finding the appropr
iate averaging principle is the key starting point in order to develop (i)
-(iv).\n
LOCATION:https://researchseminars.org/talk/UCLAAnalysisSeminar/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Philip T. Gressman (UPenn)
DTSTART;VALUE=DATE-TIME:20210105T230000Z
DTEND;VALUE=DATE-TIME:20210106T000000Z
DTSTAMP;VALUE=DATE-TIME:20240423T101436Z
UID:UCLAAnalysisSeminar/35
DESCRIPTION:Title: Radon-like Transforms\, Geometric Measures\, and Invariant Th
eory\nby Philip T. Gressman (UPenn) as part of UCLA analysis and PDE s
eminar\n\n\nAbstract\nFourier restriction\, Radon-like operators\, and dec
oupling theory are three active areas of harmonic analysis which involve s
ubmanifolds of Euclidean space in a fundamental way. In each case\, the ma
pping properties of the objects of study depend in a fundamental way on th
e "non-flatness" of the submanifold\, but with the exception of certain ex
treme cases (primarily curves and hypersurfaces)\, it is not clear exactly
how to quantify the geometry in an analytically meaningful way. In this t
alk\, I will discuss a series of recent results which shed light on this s
ituation using tools from an unusually broad range of mathematical sources
.\n
LOCATION:https://researchseminars.org/talk/UCLAAnalysisSeminar/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sigurd Angenent (UW-Madison)
DTSTART;VALUE=DATE-TIME:20210202T230000Z
DTEND;VALUE=DATE-TIME:20210203T000000Z
DTSTAMP;VALUE=DATE-TIME:20240423T101436Z
UID:UCLAAnalysisSeminar/36
DESCRIPTION:Title: Nonunique evolution through cones in Mean Curvature Flow and
Ricci Flow\nby Sigurd Angenent (UW-Madison) as part of UCLA analysis a
nd PDE seminar\n\n\nAbstract\nFor any integer $k>1$ there exist smooth sol
utions $M_t$ ($t<0$) of MCF that form a one-point singularity at time $t=0
$\, after which there exist at least $2k$ forward evolutions $M_t^1\, \\do
ts\, M_t^k\, N_t^1\, \\dots\, N_t^k$ ($t>0$) by the flow. The solutions $
M_t^j$ and $N_t^j$ are topologically distinct. The analogous statement f
or Ricci Flow also holds\, and I will explain both.\n\nBuilding on these s
elf similar solutions to MCF\, I will also describe non-self similar solut
ions that have a given cone as their initial data. One conclusion is that
for any $k>1$ there is a smooth self similar solution to MCF that forms a
one point singularity\, and for which the set of possible smooth forward
evolutions contains a k-dimensional continuum. Another conclusion is that
the set of smooth solutions to MCF whose initial condition is one of the
stationary cones in $\\mathbb{R}^n$ ($n\\in\\{4\, 5\, 6\, 7\\}$) is infini
te dimensional .\n
LOCATION:https://researchseminars.org/talk/UCLAAnalysisSeminar/36/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Cyrill Muratov (New Jersey Institute of Technology)
DTSTART;VALUE=DATE-TIME:20210302T180000Z
DTEND;VALUE=DATE-TIME:20210302T190000Z
DTSTAMP;VALUE=DATE-TIME:20240423T101436Z
UID:UCLAAnalysisSeminar/37
DESCRIPTION:Title: Magnetic skyrmions in the conformal limit\nby Cyrill Mura
tov (New Jersey Institute of Technology) as part of UCLA analysis and PDE
seminar\n\n\nAbstract\nWe characterize skyrmions in ultrathin ferromagneti
c films as local minimizers of a reduced micromagnetic energy appropriate
for quasi two-dimensional materials with perpendicular magnetic anisotropy
and interfacial Dzyaloshinskii-Moriya interaction. The minimization is ca
rried out in a suitable class of two-dimensional magnetization configurati
ons that prevents the energy from going to negative infinity\, while not i
mposing any restrictions on the spatial scale of the configuration. We fir
st demonstrate existence of minimizers for an explicit range of the model
parameters when the energy is dominated by the exchange energy. We then in
vestigate the conformal limit\, in which only the exchange energy survives
and identify the asymptotic profiles of the skyrmions as degree $1$ harmo
nic maps from the plane to the sphere\, together with their radii\, angles
and energies. A byproduct of our analysis is a quantitative rigidity resu
lt for degree $\\pm 1$ harmonic maps from the two-dimensional sphere to it
self.\n
LOCATION:https://researchseminars.org/talk/UCLAAnalysisSeminar/37/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hong Wang (IAS)
DTSTART;VALUE=DATE-TIME:20210115T230000Z
DTEND;VALUE=DATE-TIME:20210116T000000Z
DTSTAMP;VALUE=DATE-TIME:20240423T101436Z
UID:UCLAAnalysisSeminar/38
DESCRIPTION:Title: Restriction theory in Fourier analysis\nby Hong Wang (IAS
) as part of UCLA analysis and PDE seminar\n\n\nAbstract\nIf a function ha
s Fourier transform supported on a sphere\, what can we say about this fun
ction?\n\nGiven a collection of long thin tubes pointing in different dire
ctions\, how much do they overlap?\n\nThese two questions are closely rela
ted. In this talk\, we will discuss how understanding the second question
leads to progress on the first one. More precisely\, we will discuss Stein
's restriction conjecture and Sogge's local smoothing conjecture for the w
ave equation.\n
LOCATION:https://researchseminars.org/talk/UCLAAnalysisSeminar/38/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tsviqa Lakrec (U. Jerusalem)
DTSTART;VALUE=DATE-TIME:20210216T180000Z
DTEND;VALUE=DATE-TIME:20210216T190000Z
DTSTAMP;VALUE=DATE-TIME:20240423T101436Z
UID:UCLAAnalysisSeminar/39
DESCRIPTION:Title: Equidistribution of affine random walks on some nilmanifolds<
/a>\nby Tsviqa Lakrec (U. Jerusalem) as part of UCLA analysis and PDE semi
nar\n\n\nAbstract\nWe consider the action of the group of affine transform
ations on a nilmanifold. \nGiven a probability measure on this group and a
starting point $x$\, a random walk on the nilmanifold is defined. \nWe st
udy quantitative equidistribution in law of such affine random walks on ni
lmanifolds. \nUnder certain assumptions\, we show that a failure to have f
ast equidistribution on a nilmanifold is due to a failure on some factor n
ilmanifold. \nCombined with equidistribution results on the torus\, this l
eads to an equidistribution statement on some nilmanifolds\, such as Heise
nberg nilmanifolds.\n\nThis talk is based on joint works with Weikun He an
d Elon Lindenstrauss.\n
LOCATION:https://researchseminars.org/talk/UCLAAnalysisSeminar/39/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Benjamin Seeger (College de France)
DTSTART;VALUE=DATE-TIME:20210111T230000Z
DTEND;VALUE=DATE-TIME:20210112T000000Z
DTSTAMP;VALUE=DATE-TIME:20240423T101436Z
UID:UCLAAnalysisSeminar/40
DESCRIPTION:Title: Interpolation results for pathwise Hamilton-Jacobi equations<
/a>\nby Benjamin Seeger (College de France) as part of UCLA analysis and P
DE seminar\n\n\nAbstract\nI will show how interpolation methods can be use
d to make sense of pathwise Hamilton-Jacobi equations for a wide range of
Hamiltonians and driving paths. The various function spaces describe regul
arity (including Sobolev\, Besov\, Holder\, and variation) as well as stru
cture. I will also discuss some criteria for a function to be representabl
e as a difference of convex functions\, a class which plays an important r
ole in the theory of pathwise Hamilton-Jacobi equations.\n
LOCATION:https://researchseminars.org/talk/UCLAAnalysisSeminar/40/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andreia Chapouto (U. Edinburgh)
DTSTART;VALUE=DATE-TIME:20210112T170000Z
DTEND;VALUE=DATE-TIME:20210112T180000Z
DTSTAMP;VALUE=DATE-TIME:20240423T101436Z
UID:UCLAAnalysisSeminar/41
DESCRIPTION:Title: Invariance of the Gibbs measures for the periodic generalized
KdV equations\nby Andreia Chapouto (U. Edinburgh) as part of UCLA ana
lysis and PDE seminar\n\n\nAbstract\nIn this talk\, we consider the period
ic generalized Korteweg-de Vries equations (gKdV). In particular\, we stud
y gKdV with the Gibbs measure initial data. The main difficulty lies in co
nstructing local-in-time dynamics in the support of the measure. Since gKd
V is analytically ill-posed in the $L^2$-based Sobolev support\, we instea
d prove deterministic local well-posedness in some Fourier-Lebesgue spaces
containing the support of the Gibbs measures. New key ingredients are bil
inear and trilinear Strichartz estimates adapted to the Fourier-Lebesgue s
etting. Once we construct local-in-time dynamics\, we apply Bourgain's inv
ariant measure argument to prove almost sure global well-posedness of the
defocusing gKdV with respect to the Gibbs measure and invariance of the Gi
bbs measure under the gauged gKdV dynamics.\n\nThis talk is based on joint
work with Nobu Kishimoto (RIMS\, University of Kyoto).\n
LOCATION:https://researchseminars.org/talk/UCLAAnalysisSeminar/41/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kihyun Kim (KAIST)
DTSTART;VALUE=DATE-TIME:20210129T230000Z
DTEND;VALUE=DATE-TIME:20210130T000000Z
DTSTAMP;VALUE=DATE-TIME:20240423T101436Z
UID:UCLAAnalysisSeminar/42
DESCRIPTION:Title: Blow-up dynamics for the self-dual Chern-Simons-Schrödinger
equation\nby Kihyun Kim (KAIST) as part of UCLA analysis and PDE semin
ar\n\n\nAbstract\nWe consider the blow-up dynamics of the self-dual Chern-
Simons-Schrödinger equation (CSS) under equivariance symmetry. (CSS) is $
L^2$-critical\, has the pseudoconformal symmetry\, and admits a soliton $Q
$ for each equivariance index $m \\geq 0$. An application of the pseudocon
formal transformation to $Q$ yields an explicit finite-time blow-up soluti
on $S(t)$ which contracts at the pseudoconformal rate $|t|$. In the high e
quivariance case $m \\geq 1$\, the pseudoconformal blow-up for smooth fini
te energy solutions in fact occurs in a codimension one sense\; it is stab
le under a codimension one perturbation\, but also exhibits an instability
mechanism. In the radial case $m=0$\, however\, $S(t)$ is no longer a fin
ite energy blow-up solution. Interestingly enough\, there are smooth finit
e energy blow-up solutions whose blow-up rates differ from the pseudoconfo
rmal rate by a power of logarithm. We will explore these interesting blow-
up dynamics (with more focus on the latter) via modulation analysis. This
talk is based on my joint works with Soonsik Kwon and Sung-Jin Oh.\n
LOCATION:https://researchseminars.org/talk/UCLAAnalysisSeminar/42/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Adi Glucksam (U. Toronto)
DTSTART;VALUE=DATE-TIME:20210119T230000Z
DTEND;VALUE=DATE-TIME:20210120T000000Z
DTSTAMP;VALUE=DATE-TIME:20240423T101436Z
UID:UCLAAnalysisSeminar/43
DESCRIPTION:Title: Stationary random entire functions and related questions\
nby Adi Glucksam (U. Toronto) as part of UCLA analysis and PDE seminar\n\n
\nAbstract\nThe complex plane acts on the space of entire function by tran
slations\, taking f(z) to f(z+w). B.Weiss showed in `97 that there exists
a probability measure defined on the space of entire functions\, which is
invariant under this action. In this talk I will present optimal bounds on
the minimal possible growth of functions in the support of such measures
and discuss other growth-related problems inspired by this work. In partic
ular\, I will focus on the question of minimal possible growth-rate of fre
quently oscillating subharmonic functions.\nThe talk is partly based on a
joint work with L. Buhovsky\, A. Logunov\, and M. Sodin.\n
LOCATION:https://researchseminars.org/talk/UCLAAnalysisSeminar/43/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Polona Durcik (Chapman University)
DTSTART;VALUE=DATE-TIME:20210203T000000Z
DTEND;VALUE=DATE-TIME:20210203T010000Z
DTSTAMP;VALUE=DATE-TIME:20240423T101436Z
UID:UCLAAnalysisSeminar/44
DESCRIPTION:Title: Multilinear singular and oscillatory integrals and applicatio
ns\nby Polona Durcik (Chapman University) as part of UCLA analysis and
PDE seminar\n\n\nAbstract\nWe give an overview of some recent results in
the area of multilinear singular and oscillatory integrals. We discuss the
ir connection with certain questions about point configurations in subsets
of the Euclidean space and convergence of some ergodic averages. Based on
joint works with Michael Christ\, Vjekoslav Kovac\, and Joris Roos.\n
LOCATION:https://researchseminars.org/talk/UCLAAnalysisSeminar/44/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Felipe Goncalves (Bonn)
DTSTART;VALUE=DATE-TIME:20210216T190000Z
DTEND;VALUE=DATE-TIME:20210216T200000Z
DTSTAMP;VALUE=DATE-TIME:20240423T101436Z
UID:UCLAAnalysisSeminar/45
DESCRIPTION:Title: Sign Uncertainty\nby Felipe Goncalves (Bonn) as part of U
CLA analysis and PDE seminar\n\n\nAbstract\nI will talk about some of the
recent developments of the sign\nuncertainty principle and its relation wi
th sphere packings and modular\nforms\n
LOCATION:https://researchseminars.org/talk/UCLAAnalysisSeminar/45/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lillian Pierce (Duke)
DTSTART;VALUE=DATE-TIME:20210319T220000Z
DTEND;VALUE=DATE-TIME:20210319T230000Z
DTSTAMP;VALUE=DATE-TIME:20240423T101436Z
UID:UCLAAnalysisSeminar/46
DESCRIPTION:Title: Counterexamples for high-degree analogues of the Schrödinger
maximal operator\nby Lillian Pierce (Duke) as part of UCLA analysis a
nd PDE seminar\n\n\nAbstract\nIn 1980 Carleson posed a question on the min
imal regularity of an initial data function that implies pointwise converg
ence for the solution of the linear Schrodinger equation. After progress b
y many authors\, this was recently resolved (up to the endpoint) by Bourga
in\, whose counterexample construction for the Schrodinger maximal operato
r proved a necessary condition on the regularity\, and Du and Zhang\, who
proved a sufficient condition. In this talk we describe how Bourgain's cou
nterexamples can be constructed from first principles. Then we describe a
new flexible number-theoretic method for constructing counterexamples\, wh
ich proves a necessary condition for high-degree analogues of the Schrodin
ger maximal operator to be bounded from H^s to\nlocal L^1.\n
LOCATION:https://researchseminars.org/talk/UCLAAnalysisSeminar/46/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Darren King (U. Texas)
DTSTART;VALUE=DATE-TIME:20210316T210000Z
DTEND;VALUE=DATE-TIME:20210316T220000Z
DTSTAMP;VALUE=DATE-TIME:20240423T101436Z
UID:UCLAAnalysisSeminar/47
DESCRIPTION:Title: A capillarity model for soap films\nby Darren King (U. Te
xas) as part of UCLA analysis and PDE seminar\n\n\nAbstract\nWe study a va
riational model for soap films based on capillarity theory and its relatio
n to minimal surfaces. Here\, soap films are modelled\, not as surfaces\,
but as regions of small volume satisfying a homotopic spanning condition.\
n
LOCATION:https://researchseminars.org/talk/UCLAAnalysisSeminar/47/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kasso Okoudjou (Tufts)
DTSTART;VALUE=DATE-TIME:20210309T220000Z
DTEND;VALUE=DATE-TIME:20210309T230000Z
DTSTAMP;VALUE=DATE-TIME:20240423T101436Z
UID:UCLAAnalysisSeminar/48
DESCRIPTION:Title: The HRT Conjecture\nby Kasso Okoudjou (Tufts) as part of
UCLA analysis and PDE seminar\n\n\nAbstract\nIn 1996\, C.~Heil\, J.~Ramana
tha\, and P.~Topiwala conjectured that the (finite) set $\\mathcal{G}(g\,
\\Lambda)=\\{e^{2\\pi i b_k \\cdot}g(\\cdot - a_k)\\}_{k=1}^N$ is linearly
independent for any non-zero square integrable function $g$ and subset
$\\Lambda=\\{(a_k\, b_k)\\}_{k=1}^N \\subset \\mathbb{R}^2.$ This problem
is now known as the HRT Conjecture\, and is still largely unresolved. \n
\n\nIn the first part of the talk\, I will give an overview of the state o
f the conjecture. I will then introduce an inductive approach to investiga
te the conjecture\, by attempting to answer the following question. Suppos
e the HRT conjecture is true for a function $g$ and a fixed set of $N$ poi
nts $\\Lambda=\\{(a_k\, b_k)\\}_{k=1}^N \\subset \\mathbb{R}^2.$ For what
other point $(a\, b)\\in \\mathbb{R}^2\\setminus \\Lambda$ will the HRT re
main true for the same function $g$ and the new set of $N+1$ points $\\Lam
bda'=\\Lambda \\cup \\{(a\, b)\\}$? I will illustrate this inductive argum
ent on special classes of sets $\\Lambda$ when $N\\leq 4$.\n
LOCATION:https://researchseminars.org/talk/UCLAAnalysisSeminar/48/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tuomas Hytonen (U. Helsinki)
DTSTART;VALUE=DATE-TIME:20210209T180000Z
DTEND;VALUE=DATE-TIME:20210209T190000Z
DTSTAMP;VALUE=DATE-TIME:20240423T101436Z
UID:UCLAAnalysisSeminar/49
DESCRIPTION:Title: Extrapolation of compactness on weighted spaces\nby Tuoma
s Hytonen (U. Helsinki) as part of UCLA analysis and PDE seminar\n\n\nAbst
ract\nThe extrapolation theorem of Rubio de Francia is one of the most pow
erful tools in the theory of weighted norm inequalities: it allows one to
deduce an inequality (often but not necessarily: the bounded of an operato
r) on all weighted L^p spaces with a range of p\, by checking it just for
one exponent p (but all relevant weights). My topic is an analogous method
for extrapolation of compactness. In a relatively soft way\, it recovers
several recent results about compactness of operators on weighted spaces a
nd also gives some new ones. I expect there to be many more applications t
o discover.\n
LOCATION:https://researchseminars.org/talk/UCLAAnalysisSeminar/49/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kyeongsik Nam (UCLA)
DTSTART;VALUE=DATE-TIME:20210223T220000Z
DTEND;VALUE=DATE-TIME:20210223T230000Z
DTSTAMP;VALUE=DATE-TIME:20240423T101436Z
UID:UCLAAnalysisSeminar/50
DESCRIPTION:Title: Spectral large deviations for sparse random matrices\nby
Kyeongsik Nam (UCLA) as part of UCLA analysis and PDE seminar\n\n\nAbstrac
t\nThe large deviation problem for the spectrum of random matrices has att
racted immense interest. It was first studied for GUE and GOE\, which are
exactly solvable\, and subsequently studied for Wigner matrices with gener
al distributions. Once the sparsity is induced (i.e. each entry is multipl
ied by the independent Bernoulli distribution\, Ber(p))\, eigenvalues can
exhibit a drastically different behavior. For a large class of Wigner matr
ices\, including Gaussian ensembles and the adjacency matrix of Erdos-Reny
i graphs\, dense behavior ceases to hold near the constant average degree
of sparsity\, p~1/n (up to a poly-logarithmic factor). In this talk\, I wi
ll talk about the spectral large deviation for Gaussian ensembles with a s
parsity p=1/n. Joint work with Shirshendu Ganguly.\n
LOCATION:https://researchseminars.org/talk/UCLAAnalysisSeminar/50/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nathan Keller (Bar Ilan University)
DTSTART;VALUE=DATE-TIME:20210420T170000Z
DTEND;VALUE=DATE-TIME:20210420T180000Z
DTSTAMP;VALUE=DATE-TIME:20240423T101436Z
UID:UCLAAnalysisSeminar/51
DESCRIPTION:Title: The mysteries of low-degree Boolean functions\nby Nathan
Keller (Bar Ilan University) as part of UCLA analysis and PDE seminar\n\n\
nAbstract\nAnalysis of Boolean functions studies functions on the discrete
cube {-1\,1}^n\, aiming at understanding what the structure of the (discr
ete) Fourier transform tells us about the function. In this talk we focus
on the structure of low-degree functions on the discrete cube\, namely\, o
n functions whose Fourier coefficients are concentrated on low degrees. Wh
ile such functions look very simple\, we are surprisingly far from underst
anding them well\, even in the most basic first-degree case. \nWe shall pr
esent several results on first-degree Boolean functions\, including the re
cent proof of Tomaszewski's conjecture (1986) which asserts that any first
-degree function (viewed as a random variable) lies within one standard de
viation from its expectation with probability at least 1/2. Then we shall
discuss several core open questions\, which boil down to understanding\, w
hat does the knowledge that a low-degree function is bounded\, or is two-v
alued\, tell us about its structure.\n\nBased on joint work with Ohad Klei
n\n
LOCATION:https://researchseminars.org/talk/UCLAAnalysisSeminar/51/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ramon van Handel (Princeton)
DTSTART;VALUE=DATE-TIME:20210406T220000Z
DTEND;VALUE=DATE-TIME:20210406T230000Z
DTSTAMP;VALUE=DATE-TIME:20240423T101436Z
UID:UCLAAnalysisSeminar/52
DESCRIPTION:Title: The extremals of the Alexandrov-Fenchel inequality\nby Ra
mon van Handel (Princeton) as part of UCLA analysis and PDE seminar\n\n\nA
bstract\nIt is a basic fact of convexity that the volume of convex bodies
is a polynomial\, whose coefficients (mixed volumes) define a large family
of natural geometric parameters. A fundamental result of convex geometry\
, the Alexandrov-Fenchel inequality\, states that these coefficients are l
og-concave. This result proves to have striking connections with other are
as of mathematics\, such as combinatorics and algebraic geometry.\n\nThere
is a long-standing problem surrounding the Alexandrov-Fenchel inequality
that has remained open since the original works of Minkowski (1903) and Al
exandrov (1937): in what cases is equality attained? This question corresp
onds to the solution of certain unusual isoperimetric problems\, whose ext
remal bodies turn out to be numerous and strikingly bizarre. With Y. Shenf
eld\, we recently succeeded to settle this problem completely in the setti
ng of convex polytopes\, as well as to develop new tools for the study of
general convex bodies. In this talk\, I aim to sketch what the extremals l
ook like and to indicate some combinatorial\, analytic\, and geometric iss
ues that arise in their characterization.\n
LOCATION:https://researchseminars.org/talk/UCLAAnalysisSeminar/52/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Oleksiy Klurman (Bristol)
DTSTART;VALUE=DATE-TIME:20210420T180000Z
DTEND;VALUE=DATE-TIME:20210420T190000Z
DTSTAMP;VALUE=DATE-TIME:20240423T101436Z
UID:UCLAAnalysisSeminar/53
DESCRIPTION:Title: On the zeros of Fekete polynomials\nby Oleksiy Klurman (B
ristol) as part of UCLA analysis and PDE seminar\n\n\nAbstract\nSince its
discovery by Dirichlet in the nineteenth century\, Fekete polynomials (wit
h coefficients being Legendre symbols) and their zeros attracted considera
ble attention\, in particular\, due to their intimate connection with puta
tive Siegel zero and small class number problem.\n\nThe goal of this talk
is to discuss what we knew\, know and would like to know about zeros of su
ch (and\, time permitting\, related) polynomials.\n
LOCATION:https://researchseminars.org/talk/UCLAAnalysisSeminar/53/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pavel Zorin-Kranich (Bonn)
DTSTART;VALUE=DATE-TIME:20210427T170000Z
DTEND;VALUE=DATE-TIME:20210427T180000Z
DTSTAMP;VALUE=DATE-TIME:20240423T101436Z
UID:UCLAAnalysisSeminar/54
DESCRIPTION:Title: Decoupling for quadratic forms\nby Pavel Zorin-Kranich (B
onn) as part of UCLA analysis and PDE seminar\n\n\nAbstract\nI will talk a
bout how decoupling inequalities benefit from\nscale-dependent Brascamp-Li
eb inequalities. The main result describes\nthe sharp decoupling exponents
for all manifolds that can be represented\nas graphs of tuples of quadrat
ic forms. Joint work with Shaoming Guo\,\nChangkeun Oh\, and Ruixiang Zhan
g.\n
LOCATION:https://researchseminars.org/talk/UCLAAnalysisSeminar/54/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dorin Bucur (Université de Savoie)
DTSTART;VALUE=DATE-TIME:20210504T170000Z
DTEND;VALUE=DATE-TIME:20210504T180000Z
DTSTAMP;VALUE=DATE-TIME:20240423T101436Z
UID:UCLAAnalysisSeminar/55
DESCRIPTION:Title: Rigidity results for measurable sets\nby Dorin Bucur (Uni
versité de Savoie) as part of UCLA analysis and PDE seminar\n\n\nAbstract
\nLet $\\Omega \\subset \\R^d$ be a set with finite Lebesgue measure such
that\, for a fixed radius $r>0$\, the Lebesgue measure of $\\Omega \\cap
B _ r (x)$ is equal to a positive constant when $x$ varies in the essenti
al boundary of $\\Omega$. We prove that $\\Omega$ is a ball (or a finite
union of equal balls) provided it satisfies a nondegeneracy condition\,
which holds in particular for any set of diameter larger than $r$ which is
either open and connected\, or of finite perimeter and indecomposable. Th
is is a joint work with Ilaria Fragala.\n
LOCATION:https://researchseminars.org/talk/UCLAAnalysisSeminar/55/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Stefanie Petermichl (University of Toulouse)
DTSTART;VALUE=DATE-TIME:20210504T180000Z
DTEND;VALUE=DATE-TIME:20210504T190000Z
DTSTAMP;VALUE=DATE-TIME:20240423T101436Z
UID:UCLAAnalysisSeminar/56
DESCRIPTION:Title: The matrix-weighted Hardy-Littlewood maximal function is unbo
unded\nby Stefanie Petermichl (University of Toulouse) as part of UCLA
analysis and PDE seminar\n\n\nAbstract\nIn a joint work with Nazarov\, Sk
reb and Treil\, we highlight a marked\ndifference in the presence of a mat
rix weight between the Doob type\nmaximal operator in the dyadic setting (
with absolute values outside)\nand the dyadic Hardy-Littlewood type maxima
l operator (with absolute\nvalues inside). The former is $L^2$ bounded whi
le the latter is not.\nFirst\, it will be discussed how to interpret these
operators in a\nspace with matrix weight. For this\, we will use convex b
odies to\nreplace absolute values. (equivalent to the more familiar\nChris
t-Goldberg type definition). We will also discuss the Carleson\nEmbedding
Theorems that are the natural partners of these maximal\noperators and obs
erve a different behaviour as well.\n
LOCATION:https://researchseminars.org/talk/UCLAAnalysisSeminar/56/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Izabella Laba (University of British Columbia)
DTSTART;VALUE=DATE-TIME:20210518T220000Z
DTEND;VALUE=DATE-TIME:20210518T230000Z
DTSTAMP;VALUE=DATE-TIME:20240423T101436Z
UID:UCLAAnalysisSeminar/57
DESCRIPTION:Title: Tiling the integers with translates of one tile: the Coven-Me
yerowitz tiling conditions for three prime factors\nby Izabella Laba (
University of British Columbia) as part of UCLA analysis and PDE seminar\n
\n\nAbstract\nIt is well known that if a finite set of integers A tiles th
e integers by translations\, then the translation set must be periodic\, s
o that the tiling is equivalent to a factorization A+B=Z_M of a finite cyc
lic group. Coven and Meyerowitz (1998) proved that when the tiling period
M has at most two distinct prime factors\, each of the sets A and B can be
replaced by a highly ordered "standard" tiling complement. It is not know
n whether this behaviour persists for all tilings with no restrictions on
the number of prime factors of M.\n\nIn joint work with Itay Londner\, we
proved that this is true when M=(pqr)^2 is odd. (We are currently finalizi
ng the even case.) In my talk I will discuss this problem and introduce th
e main ingredients in the proof.\n
LOCATION:https://researchseminars.org/talk/UCLAAnalysisSeminar/57/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Soeren Fournais (Aarhus University)
DTSTART;VALUE=DATE-TIME:20210518T230000Z
DTEND;VALUE=DATE-TIME:20210519T000000Z
DTSTAMP;VALUE=DATE-TIME:20240423T101436Z
UID:UCLAAnalysisSeminar/58
DESCRIPTION:Title: Energy of the Dilute Bose Gas in 3D\nby Soeren Fournais (
Aarhus University) as part of UCLA analysis and PDE seminar\n\n\nAbstract\
nIn this talk\, we will review recent progress on the energy of the 3 dime
nsional dilute Bose gas. It has recently become possible to verify the old
prediction by Bogoliubov and Lee-Huang-Yang of the first correction term
to the ground state energy of the interacting gas in the thermodynamic lim
it. \nIf time permits\, I will also discuss the relation of these energy r
esults to proofs of "Bose-Einstein condensation” on density dependent le
ngth scales.\n\nThis is joint work with Jan Philip Solovej.\n
LOCATION:https://researchseminars.org/talk/UCLAAnalysisSeminar/58/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pablo Shmerkin (University of British Columbia)
DTSTART;VALUE=DATE-TIME:20210406T230000Z
DTEND;VALUE=DATE-TIME:20210407T000000Z
DTSTAMP;VALUE=DATE-TIME:20240423T101436Z
UID:UCLAAnalysisSeminar/59
DESCRIPTION:Title: Explicit and nonlinear variants of Bourgain's projection theo
rem\nby Pablo Shmerkin (University of British Columbia) as part of UCL
A analysis and PDE seminar\n\n\nAbstract\nBourgain's projection theorem is
a significant extension of his celebrated discretized sum-product theorem
. After reviewing the original formulation of the projection theorem\, I w
ill present an explicit version\, an extension to parametrized families of
smooth maps\, and applications to the Falconer distance set problem. Part
ly based on joint work in progress with Hong Wang.\n
LOCATION:https://researchseminars.org/talk/UCLAAnalysisSeminar/59/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Guofang Wei (UCSB)
DTSTART;VALUE=DATE-TIME:20210608T170000Z
DTEND;VALUE=DATE-TIME:20210608T180000Z
DTSTAMP;VALUE=DATE-TIME:20240423T101436Z
UID:UCLAAnalysisSeminar/61
DESCRIPTION:Title: Fundamental Gap Estimate for Convex Domains\nby Guofang W
ei (UCSB) as part of UCLA analysis and PDE seminar\n\n\nAbstract\nIn their
celebrated work\, B. Andrews and J. Clutterbuck proved the fundamental ga
p conjecture that difference of first two eigenvalues of the Laplacian wi
th Dirichlet boundary condition on convex domain with diameter D in the Eu
clidean space is greater than or equal to $3\\pi^2/D^2$. In several join
t works with X. Dai\, Z. He\, S. Seto\, L. Wang (in various subsets) th
e estimate is generalized\, showing the same lower bound holds for convex
domains in the unit sphere. In sharp contrast\, in recent joint work wit
h T. Bourni\, J. Clutterbuck\, X. Nguyen\, A. Stancu and V. Wheeler\, we
prove that the product of the fundamental gap with the square of the diame
ter can be arbitrarily small for convex domains of any diameter in hyper
bolic space. Very recently\, jointed with X. Nguyen\, A. Stancu\, we sho
w that even for horoconvex domains in the hyperbolic space\, the product
of their fundamental gap with the square of their diameter has no positive
lower bound.\n
LOCATION:https://researchseminars.org/talk/UCLAAnalysisSeminar/61/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tamar Ziegler (HUJI)
DTSTART;VALUE=DATE-TIME:20210608T180000Z
DTEND;VALUE=DATE-TIME:20210608T190000Z
DTSTAMP;VALUE=DATE-TIME:20240423T101436Z
UID:UCLAAnalysisSeminar/62
DESCRIPTION:Title: Some applications of analysis over finite fields\nby Tama
r Ziegler (HUJI) as part of UCLA analysis and PDE seminar\n\nLecture held
in https://caltech.zoom.us/j/99420414248.\n\nAbstract\nWe describe how one
can use equidistribution properties of families of polynomials defined ov
er finite fields to derive some interesting effective results in algebra.
For example : given an ideal J generated by m complex homogeneous polynomi
als of degree < d\, we show that J is contained in an ideal J’ generated
by C(m) homogeneous polynomials of degree < d that form a regular sequenc
e\, where C(m) is polynomial in m. All terms will be defined and explain
ed in the talk.\n
LOCATION:https://researchseminars.org/talk/UCLAAnalysisSeminar/62/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Julian Weigt (Aalto University)
DTSTART;VALUE=DATE-TIME:20210312T180000Z
DTEND;VALUE=DATE-TIME:20210312T190000Z
DTSTAMP;VALUE=DATE-TIME:20240423T101436Z
UID:UCLAAnalysisSeminar/63
DESCRIPTION:Title: Endpoint regularity of the dyadic and the fractional maximal
function\nby Julian Weigt (Aalto University) as part of UCLA analysis
and PDE seminar\n\n\nAbstract\nThe well-known open $W^{1\,1}$-problem for
maximal operators asks if the\nbound\n$\n\\|\\nabla Mf\\|_{L^1(\\mathbb R^
d)}\n\\leq C_d\n\\|\\nabla f\\|_{L^1(\\mathbb R^d)}\n$\nholds for the unce
ntered and the centered Hardy-Littlewood maximal\noperator.\nWe prove the
variants\n$\n\\mathop{\\mathrm{var}}(M^{\\mathrm d}f)\n\\leq C_d\n\\mathop
{\\mathrm{var}}(f)\n$\nfor the dyadic maximal operator $M^{\\mathrm d}$ an
d\n$\n\\|\\nabla M_\\alpha f\\|_{L^{d/(d-\\alpha)}(\\mathbb R^d)}\n\\leq C
_{d\,\\alpha}\n\\|\\nabla f\\|_{L^1(\\mathbb R^d)}\n$\nfor the uncentered
and the centered fractional Hardy-Littlewood maximal\noperator $M_\\alpha$
if $0<\\alpha \\lt d$.\n\nThe latter bound has thus far been known to hol
d only for\n$1\\leq\\alpha \\lt d$.\n\nThe techniques are rather elementar
y.\nThe proof for the the fractional Hardy-Littlewood maximal operator use
s\n$\\alpha>0$ to organize the optimal balls in a dyadic manner\nand then
reduce to the setting of dyadic cubes and apply the proof from\n$M^{\\math
rm d}$.\n
LOCATION:https://researchseminars.org/talk/UCLAAnalysisSeminar/63/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jeffrey Galkowski (University College London)
DTSTART;VALUE=DATE-TIME:20210511T170000Z
DTEND;VALUE=DATE-TIME:20210511T180000Z
DTSTAMP;VALUE=DATE-TIME:20240423T101436Z
UID:UCLAAnalysisSeminar/64
DESCRIPTION:Title: Geodesic beams and Weyl remainders\nby Jeffrey Galkowski
(University College London) as part of UCLA analysis and PDE seminar\n\n\n
Abstract\nIn this talk we discuss quantitative improvements for Weyl remai
nders\nunder dynamical assumptions on the geodesic flow. We consider a var
iety\nof Weyl type remainders including asymptotics for the eigenvalue\nco
unting function as well as for the on and off diagonal spectral\nprojector
. These improvements are obtained by combining the geodesic\nbeam approach
to understanding eigenfunction concentration together\nwith an appropriat
e decomposition of the spectral projector into\nquasimodes for the Laplaci
an. One striking consequence of these\nestimates is a quantitatively impro
ved Weyl remainder on all product\nmanifolds. This is joint work with Y.Ca
nzani\n
LOCATION:https://researchseminars.org/talk/UCLAAnalysisSeminar/64/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Benjamin Harrop-Griffiths (UCLA)
DTSTART;VALUE=DATE-TIME:20210601T220000Z
DTEND;VALUE=DATE-TIME:20210601T230000Z
DTSTAMP;VALUE=DATE-TIME:20240423T101436Z
UID:UCLAAnalysisSeminar/65
DESCRIPTION:Title: Some recent progress on integrable PDEs\nby Benjamin Harr
op-Griffiths (UCLA) as part of UCLA analysis and PDE seminar\n\nLecture he
ld in https://ucla.zoom.us/j/9264073849.\n\nAbstract\nIn this talk we pres
ent some recent progress on integrable PDEs. We first consider the well-po
sedness of the cubic NLS and mKdV on the line. We then discuss results for
some related ODE and PDE models. This is joint work with Rowan Killip and
Monica Visan.\n
LOCATION:https://researchseminars.org/talk/UCLAAnalysisSeminar/65/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Terence Tao (UCLA)
DTSTART;VALUE=DATE-TIME:20210409T230000Z
DTEND;VALUE=DATE-TIME:20210410T000000Z
DTSTAMP;VALUE=DATE-TIME:20240423T101436Z
UID:UCLAAnalysisSeminar/66
DESCRIPTION:Title: Sendov's conjecture for sufficiently high degree polynomials<
/a>\nby Terence Tao (UCLA) as part of UCLA analysis and PDE seminar\n\n\nA
bstract\nIn 1958\, Blagovest Sendov made the following conjecture: if a po
lynomial $f$ of degree $n \\geq 2$ has all of its zeroes in the unit disk\
, and $a$ is one of these zeroes\, then at least one of the critical point
s of $f$ lies within a unit distance of $a$. Despite a large amount of ef
fort by many mathematicians and several partial results (such as the verif
ication of the conjecture for degrees $n \\leq 8$)\, the full conjecture r
emains unresolved. In this talk we present a new result that establishes
the conjecture whenever the degree $n$ is larger than some sufficiently la
rge absolute constant $n_0$. A result of this form was previously establi
shed in 2014 by Degot assuming that the distinguished zero $a$ stayed away
from the origin and the unit circle. To handle these latter cases we stu
dy the asymptotic limit as $n \\to \\infty$ using techniques from potentia
l theory (and in particular the theory of balayage)\, which has connection
s to probability theory (and Brownian motion in particular). Applying uni
que continuation theorems in the asymptotic limit\, one can control the as
ymptotic behavior of both the zeroes and the critical points\, which allow
s us to resolve the case when $a$ is near the origin via the argument prin
ciple\, and when $a$ is near the unit circle by careful use of Taylor expa
nsions to gain fine asymptotic control on the polynomial $f$.\n
LOCATION:https://researchseminars.org/talk/UCLAAnalysisSeminar/66/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shiri Artstein (Tel-Aviv University)
DTSTART;VALUE=DATE-TIME:20210525T170000Z
DTEND;VALUE=DATE-TIME:20210525T180000Z
DTSTAMP;VALUE=DATE-TIME:20240423T101436Z
UID:UCLAAnalysisSeminar/67
DESCRIPTION:Title: Transportation of measure with respect to non-traditional cos
t functions\nby Shiri Artstein (Tel-Aviv University) as part of UCLA a
nalysis and PDE seminar\n\nLecture held in https://ucla.zoom.us/j/92640738
49.\n\nAbstract\nWe will discuss some old and new transportation of measur
e results\, concentrating on the differences between the classical (quadra
tic\, and more generally – finite-valued) cost functions and the case of
so-called "non-traditional" costs\, when the cost considered is allowed t
o assume infinite values (that is\, some moves are prohibited).\n
LOCATION:https://researchseminars.org/talk/UCLAAnalysisSeminar/67/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shiri Artstein (Tel-Aviv University)
DTSTART;VALUE=DATE-TIME:20210520T180000Z
DTEND;VALUE=DATE-TIME:20210520T190000Z
DTSTAMP;VALUE=DATE-TIME:20240423T101436Z
UID:UCLAAnalysisSeminar/68
DESCRIPTION:Title: Polarity\, non-traditional measure transport\, and a new Rock
afellar-type theorem\nby Shiri Artstein (Tel-Aviv University) as part
of UCLA analysis and PDE seminar\n\nLecture held in Meeting ID: 973 5874 4
971\, Passcode: 015836.\n\nAbstract\nTransportation of measure is a classi
cal technique for proving many geometric and analytic results. The case wh
ere the cost considered is allowed to assume infinite values (that is\, so
me moves are prohibited) is less well studied. However\, the so-called “
polar-cost”\, which induces the polarity transform on geometric convex f
unction (a less-known-cousin of the Legendre transform) is such a cost. In
this talk we will discuss function classes and transforms induced by cost
s\, their associated cost-subgradients and optimal transportation. We will
discuss a new result\, characterizing plans which admit a “potential”
\, applicable to such “non-traditional” cost functions. If time permit
s\, we will also discuss an analogue of the Brenier/McCann theorem\, which
holds whenever two measures are strongly-compatible. All definitions and
notions will be explained throughout the talk\, as well as examples and in
tuition\, and no prior specialized knowledge in the theory of measure tran
sport is assumed.\n\nUCLA Distinguished Women in Math Lecture Series\n\nMe
eting ID: 973 5874 4971\, Passcode: 015836\n
LOCATION:https://researchseminars.org/talk/UCLAAnalysisSeminar/68/
END:VEVENT
BEGIN:VEVENT
SUMMARY:John Garnett (UCLA)
DTSTART;VALUE=DATE-TIME:20211116T220000Z
DTEND;VALUE=DATE-TIME:20211116T230000Z
DTSTAMP;VALUE=DATE-TIME:20240423T101436Z
UID:UCLAAnalysisSeminar/69
DESCRIPTION:Title: Carleson measure estimates for bounded harmonic functions\,
without Ahlfors regularity assumptions.\nby John Garnett (UCLA) as pa
rt of UCLA analysis and PDE seminar\n\n\nAbstract\nLet $\\Omega$ be a doma
in in $R^{d+1}$ where $d \\geq 1$. It is known that (using definitions g
iven at the start of the talk) if $\\Omega$ satisfies a corkscrew conditi
on and $\\partial \\Omega$ is $d$-Ahlfors\, then the following are equiva
lent:\n\n(a) a square function Carleson measure estimate holds for all b
ounded harmonic functions on $\\Omega\;$\n\n(b) an $\\varepsilon$-approxim
ation property holds for all such functions and all $0 < \\varepsilon < 1\
;$\n\n(c) $\\partial \\Omega$ is uniformly rectifiable.\n\n Here we explor
e (a) and (b) when $\\partial \\Omega$ is not required to be Ahlfors regu
lar.\n
LOCATION:https://researchseminars.org/talk/UCLAAnalysisSeminar/69/
END:VEVENT
BEGIN:VEVENT
SUMMARY:William Feldman (University of Utah)
DTSTART;VALUE=DATE-TIME:20211012T210000Z
DTEND;VALUE=DATE-TIME:20211012T220000Z
DTSTAMP;VALUE=DATE-TIME:20240423T101436Z
UID:UCLAAnalysisSeminar/70
DESCRIPTION:Title: Limit shapes of Bernoulli-type free boundaries in periodic me
dia\nby William Feldman (University of Utah) as part of UCLA analysis
and PDE seminar\n\n\nAbstract\nI will discuss some simplified models for t
he shape of liquid droplets on rough solid surfaces\, especially Bernoulli
-type free boundary problems. In these models small scale roughness leads
to large scale non-uniqueness\, hysteresis\, and anisotropies. In techni
cal terms we need to understand laminating/foliating families of plane-lik
e solutions\, this is related to ideas of Aubry-Mather theory\, but\, unli
ke most results in that area\, we need to consider local (but not global)
energy minimizers.\n
LOCATION:https://researchseminars.org/talk/UCLAAnalysisSeminar/70/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ayla Gafni (University of Mississippi)
DTSTART;VALUE=DATE-TIME:20211019T210000Z
DTEND;VALUE=DATE-TIME:20211019T220000Z
DTSTAMP;VALUE=DATE-TIME:20240423T101436Z
UID:UCLAAnalysisSeminar/71
DESCRIPTION:Title: Uniform Distribution and Incidence Theory\nby Ayla Gafni
(University of Mississippi) as part of UCLA analysis and PDE seminar\n\n\n
Abstract\nThe Szemeredi-Trotter Incidence Theorem\, a central result in ge
ometric combinatorics\, bounds the number of incidences between n points a
nd m lines in the Euclidean plane. Replacing lines with circles leads to
the unit distance problem\, which asks how many pairs of points in a plana
r set of n points can be at a unit distance. The unit distance problem br
eaks down in dimensions 4 and higher due to degenerate configurations that
attain the trivial bound. However\, nontrivial results are possible unde
r certain structural assumptions about the point set. In this talk\, we w
ill introduce a quantitative version of uniform distribution and use that
property to obtain nontrivial bounds on unit distances and point-hyperplan
e incidences in higher-dimensional Euclidean space. This is based on join
t work with Alex Iosevich and Emmett Wyman.\n
LOCATION:https://researchseminars.org/talk/UCLAAnalysisSeminar/71/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Monica Visan (UCLA)
DTSTART;VALUE=DATE-TIME:20211026T210000Z
DTEND;VALUE=DATE-TIME:20211026T220000Z
DTSTAMP;VALUE=DATE-TIME:20240423T101436Z
UID:UCLAAnalysisSeminar/72
DESCRIPTION:Title: Orbital stability of KdV multisolitons in $H^{-1}$\nby Mo
nica Visan (UCLA) as part of UCLA analysis and PDE seminar\n\n\nAbstract\n
We introduce a variational characterization of multisoliton\nsolutions to
the Korteweg-de Vries equation that is meaningful in\n$H^{-1}$\, which is
the space of optimal well-posedness for this\nequation. As a consequence\
, we obtain orbital stability of\nmultisoliton solutions in $H^{-1}$. Thi
s is based on joint work with\nRowan Killip.\n
LOCATION:https://researchseminars.org/talk/UCLAAnalysisSeminar/72/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jarkko Kari (University of Turku)
DTSTART;VALUE=DATE-TIME:20211005T180000Z
DTEND;VALUE=DATE-TIME:20211005T190000Z
DTSTAMP;VALUE=DATE-TIME:20240423T101436Z
UID:UCLAAnalysisSeminar/73
DESCRIPTION:Title: Low complexity tilings of the plane\nby Jarkko Kari (Univ
ersity of Turku) as part of UCLA analysis and PDE seminar\n\n\nAbstract\nA
two-dimensional configuration is a coloring of the infinite grid Z^2 usin
g a finite number of colors. For a finite subset D of Z^2\, the D-patterns
of a configuration are the patterns of shape D that appear in the configu
ration. The number of distinct D-patterns of a configuration is a natural
measure of its complexity. We consider low-complexity configurations where
the number of distinct D-patterns is at most |D|\, the size of the shape.
We use algebraic tools to study periodicity of such configurations [1]. I
n the case D is a rectangle - or in fact any convex shape - we establish t
hat a uniformly recurrent configuration that has low-complexity with respe
ct to shape D must be periodic [2]. This implies an algorithm to determine
if a given collection of mn rectangular patterns of size mxn admit a conf
iguration containing only these patterns. Without the complexity bound the
question is the well-known undecidable domino problem. We also show\, for
an arbitrary shape D\, that a low-complexity configuration must be period
ic if it comes from the well-known Ledrappier subshift\, or from a wide fa
mily of other similar algebraic subshifts [3].\n\nReferences\n[1] J. Kari\
, M. Szabados. An Algebraic Geometric Approach to Nivat’s Conjecture. In
formation and Computation 271\, pp. 104481 (2020).\n[2] J. Kari\, E. Mouto
t. Decidability and Periodicity of Low Complexity Tilings. Theory of Compu
ting Systems (in Press).\n[3] J. Kari\, E. Moutot. Nivat’s conjecture an
d pattern complexity in algebraic subshifts. Theoretical Computer Science
777\, pp. 379–386 (2019).\n
LOCATION:https://researchseminars.org/talk/UCLAAnalysisSeminar/73/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jared Speck (Vanderbilt Univeristy)
DTSTART;VALUE=DATE-TIME:20211130T180000Z
DTEND;VALUE=DATE-TIME:20211130T190000Z
DTSTAMP;VALUE=DATE-TIME:20240423T101436Z
UID:UCLAAnalysisSeminar/74
DESCRIPTION:Title: Advances in the mathematical theory of shock waves\nby Ja
red Speck (Vanderbilt Univeristy) as part of UCLA analysis and PDE seminar
\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/UCLAAnalysisSeminar/74/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yuming Paul Zhang (UCSD)
DTSTART;VALUE=DATE-TIME:20211102T220000Z
DTEND;VALUE=DATE-TIME:20211102T230000Z
DTSTAMP;VALUE=DATE-TIME:20240423T101436Z
UID:UCLAAnalysisSeminar/75
DESCRIPTION:Title: Optimal Estimates on the Propagation of Reactions with Fracti
onal Diffusion\nby Yuming Paul Zhang (UCSD) as part of UCLA analysis a
nd PDE seminar\n\n\nAbstract\nWe study the reaction-fractional-diffusion e
quation $u_t+(-\\Delta)^s u=f(u)$ with ignition and monostable reactions $
f$\, and $s\\in (0\,1)$. We obtain the first optimal bounds on the propaga
tion of front-like solutions in the cases where no traveling fronts exist.
Our results cover most of these cases\, and also apply to propagation fro
m localized initial data. This is a joint work with A. Zlatos.\n
LOCATION:https://researchseminars.org/talk/UCLAAnalysisSeminar/75/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Changkeun Oh (University of Wisconsin-Madison)
DTSTART;VALUE=DATE-TIME:20211123T220000Z
DTEND;VALUE=DATE-TIME:20211123T230000Z
DTSTAMP;VALUE=DATE-TIME:20240423T101436Z
UID:UCLAAnalysisSeminar/76
DESCRIPTION:Title: Decoupling inequalities for quadratic forms and beyond\nb
y Changkeun Oh (University of Wisconsin-Madison) as part of UCLA analysis
and PDE seminar\n\n\nAbstract\nIn this talk\, I will present some recent p
rogress on decoupling inequalities for some translation- and dilation-inva
riant systems (TDI systems in short). In particular\, I will emphasize dec
oupling inequalities for quadratic forms. If time permits\, I will also di
scuss some interesting phenomenon related to Brascamp-Lieb inequalities th
at appears in the study of a cubic TDI system. Joint work with Shaoming Gu
o\, Pavel Zorin-Kranich\, and Ruixiang Zhang.\n
LOCATION:https://researchseminars.org/talk/UCLAAnalysisSeminar/76/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ruoci Sun (Karlsruhe Institute of Technology)
DTSTART;VALUE=DATE-TIME:20211005T170000Z
DTEND;VALUE=DATE-TIME:20211005T180000Z
DTSTAMP;VALUE=DATE-TIME:20240423T101436Z
UID:UCLAAnalysisSeminar/77
DESCRIPTION:Title: Complete integrability of the Benjamin–Ono equation on the
multi-soliton manifolds\nby Ruoci Sun (Karlsruhe Institute of Technolo
gy) as part of UCLA analysis and PDE seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/UCLAAnalysisSeminar/77/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Luis Silvestre (University of Chicago)
DTSTART;VALUE=DATE-TIME:20211102T210000Z
DTEND;VALUE=DATE-TIME:20211102T220000Z
DTSTAMP;VALUE=DATE-TIME:20240423T101436Z
UID:UCLAAnalysisSeminar/78
DESCRIPTION:Title: Regularity estimates for the Boltzmann equation without cutof
f\nby Luis Silvestre (University of Chicago) as part of UCLA analysis
and PDE seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/UCLAAnalysisSeminar/78/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Or Shalom (HUJI)
DTSTART;VALUE=DATE-TIME:20211130T190000Z
DTEND;VALUE=DATE-TIME:20211130T200000Z
DTSTAMP;VALUE=DATE-TIME:20240423T101436Z
UID:UCLAAnalysisSeminar/79
DESCRIPTION:Title: A structure theorem for Gowers-Host-Kra seminorms for non-fin
itely generated countable abelian groups of unbounded torsion\nby Or S
halom (HUJI) as part of UCLA analysis and PDE seminar\n\n\nAbstract\nFurst
enberg's famous proof of Szemeredi's theorem leads to a natural question a
bout the convergence and limit of some multiple ergodic averages. In the c
ase of $\\mathbb{Z}$-actions these averages were studied by Host-Kra and Z
iegler. They show that the limiting behavior of such multiple ergodic aver
age is determined on a certain factor that can be given the structure of a
n inverse limit of nilsystems (i.e. rotations on a nilmanifold). This stru
cture result can be generalized to $\\mathbb{Z}^d$ actions (where the aver
age is taken over a Folner sequence)\, but the non-finitely generated case
is still open. The only progress prior to our work is due to Bergelson Ta
o and Ziegler\, who studied actions of the infinite direct sum $\\mathbb{Z
}/p\\mathbb{Z}$. In our work we generalize this further to the case where
the sum is taken over different primes (the most interesting case is when
the multiset of primes is unbounded). We will explain how this case is sig
nificantly different from the work of Bergelson Tao and Ziegler by describ
ing a new phenomenon that only happens in these settings. Moreover\, we wi
ll discuss a generalized version of nilsystems that plays a role in our wo
rk and some corollaries. If time allows we will also discuss the group act
ions of other abelian groups.\n
LOCATION:https://researchseminars.org/talk/UCLAAnalysisSeminar/79/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tongou Yang (UBC)
DTSTART;VALUE=DATE-TIME:20211207T220000Z
DTEND;VALUE=DATE-TIME:20211207T230000Z
DTSTAMP;VALUE=DATE-TIME:20240423T101436Z
UID:UCLAAnalysisSeminar/80
DESCRIPTION:Title: Decoupling for smooth surfaces in $\\mathbb R^3$\nby Tong
ou Yang (UBC) as part of UCLA analysis and PDE seminar\n\n\nAbstract\nFor
each $d\\geq 0$\, we prove decoupling inequalities in $\\mathbb R\n^3$ for
the graphs of all bivariate polynomials of degree at most $d$ with\nbound
ed coefficients\, with the decoupling constant depending uniformly in d\nb
ut not the coefficients of each individual polynomial. As a consequence\,\
nwe prove a decoupling inequality for (a compact piece of) every smooth\ns
urface in $\\mathbb R^3$\, which in particular solves a conjecture of\nBou
rgain\, Demeter and Kemp.\n
LOCATION:https://researchseminars.org/talk/UCLAAnalysisSeminar/80/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Steve Shkoller (UC Davis)
DTSTART;VALUE=DATE-TIME:20211109T230000Z
DTEND;VALUE=DATE-TIME:20211110T000000Z
DTSTAMP;VALUE=DATE-TIME:20240423T101436Z
UID:UCLAAnalysisSeminar/81
DESCRIPTION:Title: Simultaneous development of shocks and cusps for 2D compressi
ble Euler from smooth initial data\nby Steve Shkoller (UC Davis) as pa
rt of UCLA analysis and PDE seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/UCLAAnalysisSeminar/81/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hyunju Kwon (IAS)
DTSTART;VALUE=DATE-TIME:20211019T220000Z
DTEND;VALUE=DATE-TIME:20211019T230000Z
DTSTAMP;VALUE=DATE-TIME:20240423T101436Z
UID:UCLAAnalysisSeminar/82
DESCRIPTION:Title: Euler flows with local energy dissipation\nby Hyunju Kwon
(IAS) as part of UCLA analysis and PDE seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/UCLAAnalysisSeminar/82/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alan Chang (Princeton)
DTSTART;VALUE=DATE-TIME:20211022T220000Z
DTEND;VALUE=DATE-TIME:20211022T230000Z
DTSTAMP;VALUE=DATE-TIME:20240423T101436Z
UID:UCLAAnalysisSeminar/83
DESCRIPTION:Title: The Kakeya needle problem for rectifiable sets\nby Alan C
hang (Princeton) as part of UCLA analysis and PDE seminar\n\n\nAbstract\nW
e show that the classical results about rotating a line segment in arbitra
rily small area\, and the existence of a Besicovitch and a Nikodym set hol
d if we replace the line segment by an arbitrary rectifiable set. This is
joint work with Marianna Csörnyei.\n
LOCATION:https://researchseminars.org/talk/UCLAAnalysisSeminar/83/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Laura Cladek (UCLA)
DTSTART;VALUE=DATE-TIME:20211109T220000Z
DTEND;VALUE=DATE-TIME:20211109T230000Z
DTSTAMP;VALUE=DATE-TIME:20240423T101436Z
UID:UCLAAnalysisSeminar/84
DESCRIPTION:Title: Additive energy of regular measures in one and higher dimensi
ons\, and the fractal uncertainty principle\nby Laura Cladek (UCLA) as
part of UCLA analysis and PDE seminar\n\n\nAbstract\nWe obtain new bounds
on the additive energy of (Ahlfors-David type) regular measures in both o
ne and higher dimensions\, which implies expansion results for sums and pr
oducts of the associated regular sets\, as well as more general nonlinear
functions of these sets. As a corollary of the higher-dimensional results
we obtain some new cases of the fractal uncertainty principle in odd dimen
sions. This is joint work with Terence Tao.\n
LOCATION:https://researchseminars.org/talk/UCLAAnalysisSeminar/84/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Annina Iseli
DTSTART;VALUE=DATE-TIME:20220104T220000Z
DTEND;VALUE=DATE-TIME:20220104T230000Z
DTSTAMP;VALUE=DATE-TIME:20240423T101436Z
UID:UCLAAnalysisSeminar/85
DESCRIPTION:Title: Projection theorems for linear-fractional families of project
ions\nby Annina Iseli as part of UCLA analysis and PDE seminar\n\n\nAb
stract\nMarstrand’s theorem (1954) states that given a Borel set A in th
e\nEuclidean plane\, the Hausdorff dimension of the image of A under the\n
orthogonal projection onto a line L equals the smaller of 1 and dimA\,\nfo
r almost every line L that contains the origin. This theorem has since\nbe
en generalized to higher dimensions as well as to various different\nspace
s that carry natural families of projection mappings.\nIn the first part o
f this talk\, I will recall some of these\ngeneralizations and the differe
nt methods used to proving them. In the\nsecond part\, I am going to prese
nt some recent (joint with A.\nLukyanenko) about projection theorems for f
amilies of projections that\nare induced by either Möbius transformations
or real linear fractional\ntransformations.\n
LOCATION:https://researchseminars.org/talk/UCLAAnalysisSeminar/85/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sarah Peluse (Princeton)
DTSTART;VALUE=DATE-TIME:20220111T230000Z
DTEND;VALUE=DATE-TIME:20220112T000000Z
DTSTAMP;VALUE=DATE-TIME:20240423T101436Z
UID:UCLAAnalysisSeminar/86
DESCRIPTION:Title: Polynomial and multidimensional configurations in dense sets<
/a>\nby Sarah Peluse (Princeton) as part of UCLA analysis and PDE seminar\
n\n\nAbstract\nSeveral of the most important problems in combinatorial num
ber theory ask for the size of the largest subset of an abelian group or i
nterval of integers lacking points in some 'arithmetic' configuration. One
example of such a question is\, "What is the largest subset of {1\,...\,N
} with no nontrivial k-term arithmetic progressions x\,x+y\,...\,x+(k-1)y?
". Gowers initiated the study of higher order Fourier analysis while seeki
ng to answer this question and used it to give the first reasonable quanti
tative bounds. In this talk\, I'll discuss what higher order Fourier analy
sis is and why it is relevant to the study of arithmetic progressions and
other configurations\, including 'polynomial' and 'multidimensional' confi
gurations\, and survey recent progress on problems related to the polynomi
al and multidimensional generalizations of Szemer\\'edi's theorem.\n
LOCATION:https://researchseminars.org/talk/UCLAAnalysisSeminar/86/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marina Iliopoulou (University of Kent)
DTSTART;VALUE=DATE-TIME:20220111T220000Z
DTEND;VALUE=DATE-TIME:20220111T230000Z
DTSTAMP;VALUE=DATE-TIME:20240423T101436Z
UID:UCLAAnalysisSeminar/87
DESCRIPTION:Title: Sharp L^p estimates for oscillatory integral operators of arb
itrary signature\nby Marina Iliopoulou (University of Kent) as part of
UCLA analysis and PDE seminar\n\n\nAbstract\nThe restriction problem in h
armonic analysis asks for L^p bounds on the Fourier transform of functions
defined on curved surfaces. In this talk\, we will present restriction es
timates for hyperbolic paraboloids\, that depend on the signature of the p
araboloids. These estimates still hold\, and are sharp\, in the variable c
oefficient regime. This is joint work with Jonathan Hickman.\n
LOCATION:https://researchseminars.org/talk/UCLAAnalysisSeminar/87/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Malabika Pramanik (UBC)
DTSTART;VALUE=DATE-TIME:20220208T230000Z
DTEND;VALUE=DATE-TIME:20220209T000000Z
DTSTAMP;VALUE=DATE-TIME:20240423T101436Z
UID:UCLAAnalysisSeminar/88
DESCRIPTION:Title: On projections and circles\nby Malabika Pramanik (UBC) as
part of UCLA analysis and PDE seminar\n\n\nAbstract\nThis will be a surve
y of two classes of problems in analysis:\nmeasuring the size of projectio
ns of sets\, and counting incidences of\ncircles in the plane. I will ment
ion a few landmark results in each area\nand discuss recently discovered c
onnections between the two.\n
LOCATION:https://researchseminars.org/talk/UCLAAnalysisSeminar/88/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Joshua Zahl (UBC)
DTSTART;VALUE=DATE-TIME:20220301T220000Z
DTEND;VALUE=DATE-TIME:20220301T230000Z
DTSTAMP;VALUE=DATE-TIME:20240423T101436Z
UID:UCLAAnalysisSeminar/89
DESCRIPTION:Title: A Kaufman-type restricted projection theorem in R^3\nby J
oshua Zahl (UBC) as part of UCLA analysis and PDE seminar\n\n\nAbstract\nI
n this talk\, I will discuss the proof of a conjecture in projection theor
y posed by Fässler and Orponen. If K is a set in R^3 of Hausdorff dimensi
on at most one and if \\gamma is a space curve that obeys a natural non-de
generacy condition\, then Fässler and Orponen conjectured that for a typi
cal v \\in \\gamma\, the dimension of the projection K.v must be dim(K). W
e resolve this conjecture by proving a Kaufman-type bound on the dimension
of the set of exceptional projections.\n\nWhile Fässler and Orponen's co
njecture is a question in geometric measure theory\, the solution uses ide
as from harmonic analysis. In particular\, we resolve the conjecture by pr
oving L^p bounds on the Wolff circular maximal function for families of ro
ugh curves. This is joint work with Orit Raz\, Malabika Pramanik\, and Ton
gou Yang\n
LOCATION:https://researchseminars.org/talk/UCLAAnalysisSeminar/89/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Stan Palasek (UCLA)
DTSTART;VALUE=DATE-TIME:20220222T220000Z
DTEND;VALUE=DATE-TIME:20220222T230000Z
DTSTAMP;VALUE=DATE-TIME:20240423T101436Z
UID:UCLAAnalysisSeminar/90
DESCRIPTION:Title: Quantitative regularity theory for the Navier-Stokes equation
s in critical spaces\nby Stan Palasek (UCLA) as part of UCLA analysis
and PDE seminar\n\n\nAbstract\nAn important question in the theory of the
incompressible Navier-Stokes equations is whether boundedness of the veloc
ity in various norms implies regularity of the solution. Critical norms ar
e conjectured to be (roughly) the threshold between positive and negative
answers to this question. Of particular interest are 3D solutions in the c
ritical endpoint space $L_t^\\infty L_x^3$ for which Escauriaza-Seregin-Sv
erak famously proved global regularity. Recently Tao improved upon this re
sult by proving quantitative bounds on the solution and conditions on a hy
pothetical blowup. In this talk we discuss the quantitative approach to re
gularity including some sharper results in the axisymmetric case\, as well
as extensions to other critical spaces and to higher dimensions.\n
LOCATION:https://researchseminars.org/talk/UCLAAnalysisSeminar/90/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Cristina Pereyra (UNM)
DTSTART;VALUE=DATE-TIME:20220308T220000Z
DTEND;VALUE=DATE-TIME:20220308T230000Z
DTSTAMP;VALUE=DATE-TIME:20240423T101436Z
UID:UCLAAnalysisSeminar/91
DESCRIPTION:Title: Haar Multipliers Revisited\nby Cristina Pereyra (UNM) as
part of UCLA analysis and PDE seminar\n\n\nAbstract\nHaar multipliers are
akin to pseudo-differential operators where the trigonometric functions ar
e replaced by Haar functions. We are interested in their boundedness prope
rties. We will focus on some particular examples\, the t-Haar multipliers\
, for which the theory is well understood on Lebesgue spaces and will disc
uss recent progress regarding weighted inequalities. This is work in progr
ess joint with Daewon Chung\, Claire Huang\, Jean Moraes and Brett Wick.\n
LOCATION:https://researchseminars.org/talk/UCLAAnalysisSeminar/91/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Friedrich Klaus (KIT)
DTSTART;VALUE=DATE-TIME:20220125T180000Z
DTEND;VALUE=DATE-TIME:20220125T190000Z
DTSTAMP;VALUE=DATE-TIME:20240423T101436Z
UID:UCLAAnalysisSeminar/92
DESCRIPTION:Title: Well-posedness for the KdV hierarchy\nby Friedrich Klaus
(KIT) as part of UCLA analysis and PDE seminar\n\n\nAbstract\nWe show well
-posedness for the KdV hierarchy at H^{-1} regularity and for the Gardner
hierarchy at L^2 regularity\n
LOCATION:https://researchseminars.org/talk/UCLAAnalysisSeminar/92/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Young-heon Kim (UBC)
DTSTART;VALUE=DATE-TIME:20220315T210000Z
DTEND;VALUE=DATE-TIME:20220315T220000Z
DTSTAMP;VALUE=DATE-TIME:20240423T101436Z
UID:UCLAAnalysisSeminar/93
DESCRIPTION:Title: The Stefan problem and optimal transport along the Brownian m
otion\nby Young-heon Kim (UBC) as part of UCLA analysis and PDE semina
r\n\n\nAbstract\nWe discuss an optimal Brownian stopping problem from a gi
ven initial distribution where the target distribution is free and is cond
itioned to satisfy a given density height constraint. This is a variant of
optimal transport problem where transport is constrained to occur followi
ng the Brownian motion\, and the transport plan is given by when each part
icle is prescribed to stop. The solutions to this optimization problem the
n generate solutions to the Stefan problem\, a free boundary problem of th
e heat equation that describes supercooled fluid freezing (St1) or ice mel
ting (St2)\, depending on the type of cost for optimality. The freezing (S
t1) case has not been well understood in the literature beyond one dimensi
on\, while our result gives a well-posedness of weak solution in general d
imensions\, with naturally chosen initial data. We also give a new connect
ion between the freezing and melting Stefan problems. This is joint work w
ith Inwon Kim (UCLA).\n
LOCATION:https://researchseminars.org/talk/UCLAAnalysisSeminar/93/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michael Hochman (HUJI)
DTSTART;VALUE=DATE-TIME:20220125T170000Z
DTEND;VALUE=DATE-TIME:20220125T180000Z
DTSTAMP;VALUE=DATE-TIME:20240423T101436Z
UID:UCLAAnalysisSeminar/94
DESCRIPTION:Title: Host-type equidistribution results\nby Michael Hochman (H
UJI) as part of UCLA analysis and PDE seminar\n\n\nAbstract\nGive two some
what hyperbolic maps f\,g of a manifold\, fix an invariant probability mea
sure mu for f\, and act on mu\, or on mu-typical points\, by g. Assuming
the maps f\,g are not too closely related\, one expects the orbit to equid
istribute for some natural measure. Examples of this kind begin with Casse
l's and Schmidts theorems on normality of numbers in the ternary Cantor se
t\, and more recently in Host's theorem about measures on tori invariant u
nder endomoirphisms. In the talk\, I will discuss some new results of this
type which extend Host's theorem to its natural generality. The main focu
s will be on the method of proof\, which relies on soft ideas from equidis
tribution theory\, fractal geometry and harmonic analysis\, and some basic
linear algebra.\n
LOCATION:https://researchseminars.org/talk/UCLAAnalysisSeminar/94/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dallas Albritton (IAS)
DTSTART;VALUE=DATE-TIME:20220222T230000Z
DTEND;VALUE=DATE-TIME:20220223T000000Z
DTSTAMP;VALUE=DATE-TIME:20240423T101436Z
UID:UCLAAnalysisSeminar/95
DESCRIPTION:Title: Non-uniqueness of Leray solutions of the forced Navier-Stokes
equations\nby Dallas Albritton (IAS) as part of UCLA analysis and PDE
seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/UCLAAnalysisSeminar/95/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maria Colombo (EPFL)
DTSTART;VALUE=DATE-TIME:20220118T190000Z
DTEND;VALUE=DATE-TIME:20220118T200000Z
DTSTAMP;VALUE=DATE-TIME:20240423T101436Z
UID:UCLAAnalysisSeminar/96
DESCRIPTION:Title: Nonuniqueness results from 2D Euler equations to 3D Navier-St
okes equations\nby Maria Colombo (EPFL) as part of UCLA analysis and P
DE seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/UCLAAnalysisSeminar/96/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yu Deng (USC)
DTSTART;VALUE=DATE-TIME:20220118T180000Z
DTEND;VALUE=DATE-TIME:20220118T190000Z
DTSTAMP;VALUE=DATE-TIME:20240423T101436Z
UID:UCLAAnalysisSeminar/97
DESCRIPTION:Title: Mathematical wave turbulence and propagation of chaos\nby
Yu Deng (USC) as part of UCLA analysis and PDE seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/UCLAAnalysisSeminar/97/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mihaela Ifrim (University of Wisconsin)
DTSTART;VALUE=DATE-TIME:20220208T220000Z
DTEND;VALUE=DATE-TIME:20220208T230000Z
DTSTAMP;VALUE=DATE-TIME:20240423T101436Z
UID:UCLAAnalysisSeminar/98
DESCRIPTION:Title: The time-like minimal surface equation in Minkowski space: lo
w regularity solutions\nby Mihaela Ifrim (University of Wisconsin) as
part of UCLA analysis and PDE seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/UCLAAnalysisSeminar/98/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Frederick Manners (UCSD)
DTSTART;VALUE=DATE-TIME:20220201T233000Z
DTEND;VALUE=DATE-TIME:20220202T003000Z
DTSTAMP;VALUE=DATE-TIME:20240423T101436Z
UID:UCLAAnalysisSeminar/99
DESCRIPTION:Title: Iterated Cauchy--Schwarz arguments and true complexity\nb
y Frederick Manners (UCSD) as part of UCLA analysis and PDE seminar\n\n\nA
bstract\nThis talk is about useful facts that can be proved by repeated ap
plication of the Cauchy--Schwarz inequality. For example\, it is standard
that expressions $\\sum_{x\,y} f(x\,y) a(x) b(y)$ are controlled by the m
atrix norm $\\sum_{x\,y\,x'\,y'} f(x\,y) f(x\,y') f(x'\,y) f(x'\,y')$\, an
d an elementary proof is by applying Cauchy--Schwarz twice. Similarly in
additive combinatorics\, counting three-term arithmetic progressions (x\,x
+y\,x+2y) (i.e.\, averages $\\sum_{x\,y} f_1(x) f_2(x+y) f_3(x+2y)$) is co
ntrolled by the Gowers $U^2$-norm $\\sum_{x\,y\,x'\,y'} f(x+y) f(x+y') f(x
'+y) f(x'+y')$: generalizations of this are the starting point of Gowers'
proof of Szemeredi's theorem.\n\nHowever\, seemingly simple generalization
s of this statement quickly become subtle. For example\, linear configura
tions $(x\, x+z\, x+y\, x+y+z\, x+2y+3z\, 2x+3y+6z)$ are controlled by the
$U^2$-norm (and so by Fourier analysis) but it is not at all straightforw
ard to prove this just with Cauchy--Schwarz\; whereas controlling $(x\, x+
z\, x+y\, x+y+z\, x+2y+3z\, 13x+12y+9z)$ requires the $U^3$-norm (i.e.\, q
uadratic Fourier analysis) and this can be proved just with Cauchy--Schwar
z. A conjecture of Gowers and Wolf (resolved by the joint efforts of vari
ous authors) gives a condition to determine when a configuration is contro
lled by the $U^k$-norm\, but the proofs require deep structure theorems an
d (unlike Cauchy--Schwarz arguments) give very weak bounds.\n\nIn this tal
k\, I will describe how it is (sometimes) possible to find the missing Cau
chy--Schwarz arguments by "mining proofs". The equality cases of these Ca
uchy--Schwarz inequalities correspond (it turns out) to facts about functi
onal equations. For example\, the 3-term progression case states the foll
owing: if $f_1\,f_2\,f_3$ are functions such that $f_1(x)+f_2(x+h)+f_3(x+2
h) = 0$ for all $x\,h$\, then each $f_i$ must be affine-linear. This stat
ement is not completely obvious but has a short elementary proof.\n\nGiven
such an elementary proof\, sometimes we can reverse the process to find a
n iterated Cauchy--Schwarz proof of the corresponding inequality -- albeit
a very long and complicated one that would be hard to discover by hand\,
and requiring a proof of a very specific type. This answers the Gowers--W
olf question with polynomial bounds\, and hopefully other questions where
the availability of complicated Cauchy--Schwarz arguments is a limiting fa
ctor.\n
LOCATION:https://researchseminars.org/talk/UCLAAnalysisSeminar/99/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zane Li (IU)
DTSTART;VALUE=DATE-TIME:20220215T220000Z
DTEND;VALUE=DATE-TIME:20220215T230000Z
DTSTAMP;VALUE=DATE-TIME:20240423T101436Z
UID:UCLAAnalysisSeminar/100
DESCRIPTION:Title: A decoupling interpretation of an old argument for Vinogrado
v's Mean Value Theorem\nby Zane Li (IU) as part of UCLA analysis and P
DE seminar\n\n\nAbstract\nThere are two proofs of Vinogradov's Mean Value
Theorem (VMVT)\, the harmonic analysis decoupling proof by Bourgain\, Deme
ter\, and Guth from 2015 and the number theoretic efficient congruencing p
roof by Wooley from 2017. While there has been recent work illustrating th
e relation between these two methods\, VMVT has been open since 1935. It i
s then natural to ask: What does old partial progress on VMVT look like in
harmonic analysis language? How similar or different does it look from cu
rrent decoupling proofs? We talk about an old argument that shows VMVT "as
ymptotically" due to Karatsuba and interpret this in decoupling language.
This is ongoing work in progress with Brian Cook\, Kevin Hughes\, Olivier
Robert\, Akshat Mudgal\, and Po-Lam Yung.\n
LOCATION:https://researchseminars.org/talk/UCLAAnalysisSeminar/100/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sung-Jin Oh (UC Berkeley)
DTSTART;VALUE=DATE-TIME:20220301T230000Z
DTEND;VALUE=DATE-TIME:20220302T000000Z
DTSTAMP;VALUE=DATE-TIME:20240423T101436Z
UID:UCLAAnalysisSeminar/101
DESCRIPTION:Title: A tale of two tails\nby Sung-Jin Oh (UC Berkeley) as par
t of UCLA analysis and PDE seminar\n\n\nAbstract\nIn this talk\, I will in
troduce a general method for understanding the late-time tail for solution
s to wave equations on asymptotically flat spacetimes with odd spatial dim
ensions. A particular consequence of the method is a re-proof of Price’s
law-type results\, which concern the sharp decay rate of the late-time ta
ils on stationary spacetimes. Moreover\, the method also applies to dynami
cal spacetimes. In this case\, I will explain how the late-time tails are
in general different(!) from the stationary case in the presence of dynami
cal and/or nonlinear perturbations of the problem. This is joint work with
Jonathan Luk (Stanford).\n
LOCATION:https://researchseminars.org/talk/UCLAAnalysisSeminar/101/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sohrab Shahshahani (UMass\, Amherst)
DTSTART;VALUE=DATE-TIME:20220201T223000Z
DTEND;VALUE=DATE-TIME:20220201T233000Z
DTSTAMP;VALUE=DATE-TIME:20240423T101436Z
UID:UCLAAnalysisSeminar/102
DESCRIPTION:Title: Tidal energy in Newtonian two-body motion\nby Sohrab Sha
hshahani (UMass\, Amherst) as part of UCLA analysis and PDE seminar\n\n\nA
bstract\nIn this talk we discuss the tidal energy for the motion of two\n
gravitating incompressible fluid balls with free boundaries\, obeying the\
n Euler-Poisson equations. When the fluids are replaced by point\n masses\
, the conic curve describing the trajectories of the bodies are\n known ac
cording to the classical analysis of Newton. We will consider the\n effect
of replacing point masses by fluid balls in this analysis. This is\n join
t work with Shuang Miao from Wuhan University.\n
LOCATION:https://researchseminars.org/talk/UCLAAnalysisSeminar/102/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ben Krause (King's College London)
DTSTART;VALUE=DATE-TIME:20220315T220000Z
DTEND;VALUE=DATE-TIME:20220315T230000Z
DTSTAMP;VALUE=DATE-TIME:20240423T101436Z
UID:UCLAAnalysisSeminar/103
DESCRIPTION:by Ben Krause (King's College London) as part of UCLA analysis
and PDE seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/UCLAAnalysisSeminar/103/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alex Iosevich (University of Rochester)
DTSTART;VALUE=DATE-TIME:20220412T210000Z
DTEND;VALUE=DATE-TIME:20220412T220000Z
DTSTAMP;VALUE=DATE-TIME:20240423T101436Z
UID:UCLAAnalysisSeminar/104
DESCRIPTION:Title: A general viewpoint on finite point configurations\nby A
lex Iosevich (University of Rochester) as part of UCLA analysis and PDE se
minar\n\n\nAbstract\nWe are to study the existence of finite point configu
rations inside compact sets of a given Hausdorff dimension. These problems
can be viewed as generalizations of the Falconer distance problem\, and a
lso thin-set versions of point configuration problems studied\, by Bourgai
n\, Furstenberg\, Katznelson\, Weiss\, Ziegler\, and others. We are going
to describe a rather general combinatorial paradigm that allows one to red
uce the existence of a variety of point configurations to certain Fourier
Integral Operator estimates.\n
LOCATION:https://researchseminars.org/talk/UCLAAnalysisSeminar/104/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dominique Maldague (MIT)
DTSTART;VALUE=DATE-TIME:20220524T210000Z
DTEND;VALUE=DATE-TIME:20220524T220000Z
DTSTAMP;VALUE=DATE-TIME:20240423T101436Z
UID:UCLAAnalysisSeminar/105
DESCRIPTION:Title: Small cap decoupling for the moment curve in R^3\nby Dom
inique Maldague (MIT) as part of UCLA analysis and PDE seminar\n\n\nAbstra
ct\nI will present the full solution to a small cap decoupling problem for
the moment curve in R^3 motivated by a question about exponential sums. I
n particular\, we prove Conjecture 2.5 in dimension 3 from the original sm
all cap decoupling paper (https://arxiv.org/pdf/1908.09166.pdf) of Demeter
\, Guth\, and Wang. Decoupling for the moment curve involves the following
set-up. Begin with a function $f$ with Fourier transform supported on a s
mall neighborhood of a curve. Break the curve up into pieces which are app
roximately linear blocks. Then we estimate the size of $f$ in terms of an
expression with the Fourier projections onto each of these blocks. This is
possible since the Fourier projections of $f$ onto different blocks canno
t both be large for a long time\, which we exploit using a high-low freque
ncy argument. This is based on in-progress work in collaboration with Larr
y Guth.\n
LOCATION:https://researchseminars.org/talk/UCLAAnalysisSeminar/105/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Noam Lifshitz (HUJI)
DTSTART;VALUE=DATE-TIME:20220405T170000Z
DTEND;VALUE=DATE-TIME:20220405T180000Z
DTSTAMP;VALUE=DATE-TIME:20240423T101436Z
UID:UCLAAnalysisSeminar/106
DESCRIPTION:Title: Product free sets in A_n\nby Noam Lifshitz (HUJI) as par
t of UCLA analysis and PDE seminar\n\n\nAbstract\nA subset of a group is s
aid to be product free if it does not contain the product of two elements
in it. We consider how large can a product free subset of $A_n$ be? This p
roblem was considered by Gowers and improved by Eberhard. It appears as nu
mber 4 in Green's list of his 100 favorite open problems. In the talk we w
ill completely solve the problem by determining the largest product free s
ubset of $A_n$. \n\nOur proof combines a representation theoretic argument
due to Gowers\, with an analytic tool called hypercontractivity for globa
l functions. We also make use of a dichotomy between structure and pseudor
andomness of functions over the symmetric group.\nBased on a joint work wi
th Peter Keevash and Dor Minzer\n
LOCATION:https://researchseminars.org/talk/UCLAAnalysisSeminar/106/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sean Eberhard (Cambridge)
DTSTART;VALUE=DATE-TIME:20220607T180000Z
DTEND;VALUE=DATE-TIME:20220607T190000Z
DTSTAMP;VALUE=DATE-TIME:20240423T101436Z
UID:UCLAAnalysisSeminar/107
DESCRIPTION:Title: Random polynomials and random matrices\nby Sean Eberhard
(Cambridge) as part of UCLA analysis and PDE seminar\n\n\nAbstract\nI wil
l talk about some recent results about random polynomials (irreducibility
and Galois groups) and random discrete matrices. I will outline a proof\,
conditional on the extended Riemann hypothesis\, that random matrices have
irreducible characteristic polynomial with high probability and Galois gr
oup >= A_n. The method uses (a) the prime ideal theorem to reduce the glob
al problem about the matrix over Z to a local problem about matrices mod p
\, and (b) recent results about random matrices over finite fields to conc
lude.\n
LOCATION:https://researchseminars.org/talk/UCLAAnalysisSeminar/107/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ram Band (Technion)
DTSTART;VALUE=DATE-TIME:20220426T180000Z
DTEND;VALUE=DATE-TIME:20220426T190000Z
DTSTAMP;VALUE=DATE-TIME:20240423T101436Z
UID:UCLAAnalysisSeminar/108
DESCRIPTION:Title: Neumann domains\nby Ram Band (Technion) as part of UCLA
analysis and PDE seminar\n\n\nAbstract\nThe nodal set of a Laplacian eigen
function forms a partition of the underlying manifold.\nAnother natural pa
rtition is based on the gradient vector field of the eigenfunction.\nExpli
citly\, we take all the gradient flow lines which are connected to saddle
points of the eigenfunction.\nThese lines partition the manifold to subman
ifolds which are called Neumann domains (you may try to guess the reason f
or this name\, or wait for the talk \;)\nWe present some results obtained
so far for Neumann domains - their count\, geometric properties and spectr
al position.\nWe also compare the Neumann domain results to the analogous
ones within the nodal domain study.\n\nThe talk is based on joint works wi
th Philippe Charron\, Graham Cox\, Sebastian Egger\, David Fajman and Alex
ander Taylor.\n
LOCATION:https://researchseminars.org/talk/UCLAAnalysisSeminar/108/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rajula Srivastava (UWM)
DTSTART;VALUE=DATE-TIME:20220517T210000Z
DTEND;VALUE=DATE-TIME:20220517T220000Z
DTSTAMP;VALUE=DATE-TIME:20240423T101436Z
UID:UCLAAnalysisSeminar/109
DESCRIPTION:Title: Two Analogues of the Euclidean Spherical Maximal Function on
Heisenberg Groups\nby Rajula Srivastava (UWM) as part of UCLA analysi
s and PDE seminar\n\n\nAbstract\nWe shall discuss sharp (up to end points)
$L^p\\to L^q$ estimates for local maximal operators associated with dilat
es of two different surfaces on Heisenberg groups. The first is the ``hori
zontal sphere" of codimension two. The second is the Kor\\'anyi sphere: a
surface of codimension one compatible with the non-isotropic dilation str
ucture on the group but with points of vanishing curvature. We shall exami
ne the geometry of these surfaces in light of two different notions of cur
vature and compare their effect on the estimates for the corresponding max
imal operators. The Heisenberg group structure will play a crucial role in
our arguments. However\, the theory of Oscillatory Integral Operators wil
l be central despite the non-Euclidean setting. We shall also discuss two
new counterexamples which imply the sharpness of our results (up to endpoi
nts). Partly based on joint work with Joris Roos and Andreas Seeger.\n
LOCATION:https://researchseminars.org/talk/UCLAAnalysisSeminar/109/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jongchon Kim (CityU)
DTSTART;VALUE=DATE-TIME:20220503T223000Z
DTEND;VALUE=DATE-TIME:20220503T233000Z
DTSTAMP;VALUE=DATE-TIME:20240423T101436Z
UID:UCLAAnalysisSeminar/110
DESCRIPTION:Title: Nikodym sets for spheres and related maximal functions\n
by Jongchon Kim (CityU) as part of UCLA analysis and PDE seminar\n\n\nAbst
ract\nAny set containing a sphere centered at every point cannot have 0 Le
besgue measure. This is a consequence of the L^p boundedness of the spheri
cal maximal function. On the other hand\, there exist sets of 0 Lebesgue m
easure which contain a large family of spheres\, which may be considered a
s Kakeya/Nikodym sets for spheres. This talk will be a survey of such sets
and their Hausdorff dimension\, and related maximal functions. It will be
based on an ongoing joint work with Alan Chang and Georgios Dosidis.\n
LOCATION:https://researchseminars.org/talk/UCLAAnalysisSeminar/110/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yotam Smilansky (Rutgers)
DTSTART;VALUE=DATE-TIME:20220517T220000Z
DTEND;VALUE=DATE-TIME:20220517T230000Z
DTSTAMP;VALUE=DATE-TIME:20240423T101436Z
UID:UCLAAnalysisSeminar/111
DESCRIPTION:Title: Order and disorder in multiscale substitution tilings\nb
y Yotam Smilansky (Rutgers) as part of UCLA analysis and PDE seminar\n\n\n
Abstract\nThe study of aperiodic order and mathematical models of quasicry
stals is concerned with ways in which disordered structures can neverthele
ss manifest aspects of order. In the talk I will describe examples such as
the aperiodic Penrose and pinwheel tilings\, together with several geomet
ric\, dynamical\, functional and spectral properties that enable us to mea
sure how far such constructions are from demonstrating lattice-like behavi
or. A particular focus will be given to new results on multiscale substitu
tion tilings\, a class of tilings that was recently introduced jointly wit
h Yaar Solomon.\n
LOCATION:https://researchseminars.org/talk/UCLAAnalysisSeminar/111/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zhiwu Lin (Georgia Tech)
DTSTART;VALUE=DATE-TIME:20220510T210000Z
DTEND;VALUE=DATE-TIME:20220510T220000Z
DTSTAMP;VALUE=DATE-TIME:20240423T101436Z
UID:UCLAAnalysisSeminar/112
DESCRIPTION:Title: The existence of Prandtl-Batchelor flows on disk and annulus
\nby Zhiwu Lin (Georgia Tech) as part of UCLA analysis and PDE seminar
\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/UCLAAnalysisSeminar/112/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ibrahim Ekren (Florida State University)
DTSTART;VALUE=DATE-TIME:20220510T220000Z
DTEND;VALUE=DATE-TIME:20220510T230000Z
DTSTAMP;VALUE=DATE-TIME:20240423T101436Z
UID:UCLAAnalysisSeminar/113
DESCRIPTION:Title: Prediction problems and second order equations\nby Ibrah
im Ekren (Florida State University) as part of UCLA analysis and PDE semin
ar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/UCLAAnalysisSeminar/113/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matthew Schrecker (UCL)
DTSTART;VALUE=DATE-TIME:20220329T170000Z
DTEND;VALUE=DATE-TIME:20220329T180000Z
DTSTAMP;VALUE=DATE-TIME:20240423T101436Z
UID:UCLAAnalysisSeminar/114
DESCRIPTION:Title: Self-similar gravitational collapse for the Euler-Poisson eq
uations\nby Matthew Schrecker (UCL) as part of UCLA analysis and PDE s
eminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/UCLAAnalysisSeminar/114/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ryan Hynd (UPenn)
DTSTART;VALUE=DATE-TIME:20220329T180000Z
DTEND;VALUE=DATE-TIME:20220329T190000Z
DTSTAMP;VALUE=DATE-TIME:20240423T101436Z
UID:UCLAAnalysisSeminar/115
DESCRIPTION:Title: Asymptotic flatness of Morrey extremals\nby Ryan Hynd (U
Penn) as part of UCLA analysis and PDE seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/UCLAAnalysisSeminar/115/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Stefano Decio (NTNU)
DTSTART;VALUE=DATE-TIME:20220503T213000Z
DTEND;VALUE=DATE-TIME:20220503T223000Z
DTSTAMP;VALUE=DATE-TIME:20240423T101436Z
UID:UCLAAnalysisSeminar/116
DESCRIPTION:Title: Zeros of Steklov eigenfunctions\nby Stefano Decio (NTNU)
as part of UCLA analysis and PDE seminar\n\n\nAbstract\nA Steklov eigenfu
nction in a bounded domain is a harmonic function whose normal derivative
at the boundary is proportional to the function itself\, or in other words
it is the harmonic extension of an eigenfunction of the Dirichlet-to-Neum
ann operator. The focus of the talk will be the study of the zero sets of
such objects. I will show that there are many zeros near the boundary and
I will discuss upper and lower bounds on the Hausdorff measure of the zero
set.\n
LOCATION:https://researchseminars.org/talk/UCLAAnalysisSeminar/116/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Xiumin Du (Northwestern)
DTSTART;VALUE=DATE-TIME:20220412T220000Z
DTEND;VALUE=DATE-TIME:20220412T230000Z
DTSTAMP;VALUE=DATE-TIME:20240423T101436Z
UID:UCLAAnalysisSeminar/117
DESCRIPTION:Title: Falconer's distance set problem\nby Xiumin Du (Northwest
ern) as part of UCLA analysis and PDE seminar\n\n\nAbstract\nA classical q
uestion in geometric measure theory\, introduced by Falconer in the 80s is
\, how large does the Hausdorff dimension of a compact subset in Euclidean
space need to be to ensure that the Lebesgue measure of its set of pairwi
se Euclidean distances is positive. In this talk\, I'll report some recent
progress on this problem\, which combines several ingredients including O
rponen's radial projection theorem\, Liu's L^2 identity obtained using a g
roup action argument\, and the refined decoupling theory. This is based on
joint work with Alex Iosevich\, Yumeng Ou\, Hong Wang\, and Ruixiang Zhan
g.\n
LOCATION:https://researchseminars.org/talk/UCLAAnalysisSeminar/117/
END:VEVENT
BEGIN:VEVENT
SUMMARY:John Anderson (Stanford)
DTSTART;VALUE=DATE-TIME:20220531T220000Z
DTEND;VALUE=DATE-TIME:20220531T230000Z
DTSTAMP;VALUE=DATE-TIME:20240423T101436Z
UID:UCLAAnalysisSeminar/118
DESCRIPTION:Title: Nonlinear interactions of waves from distant sources\nby
John Anderson (Stanford) as part of UCLA analysis and PDE seminar\n\n\nAb
stract\nPhysical systems are often idealized as being isolated because ver
y distant events ought not have a significant influence. Mathematically\,
this often translates to solving problems with localized data. In this tal
k\, I will discuss results which make this intuitive idealization rigorous
. Indeed\, we study the effects that distant perturbations have on solutio
ns to nonlinear wave equations. We prove a stability statement\, which req
uires analyzing the spacetime geometry of the interaction of waves origina
ting from distant sources. I also hope to describe some of the additional
difficulties involved in extending these results to the physically interes
ting case of the Einstein vacuum equations of general relativity. This is
joint work with Federico Pasqualotto (Duke University).\n
LOCATION:https://researchseminars.org/talk/UCLAAnalysisSeminar/118/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jacob Shapiro (Princeton)
DTSTART;VALUE=DATE-TIME:20220531T210000Z
DTEND;VALUE=DATE-TIME:20220531T220000Z
DTSTAMP;VALUE=DATE-TIME:20240423T101436Z
UID:UCLAAnalysisSeminar/119
DESCRIPTION:Title: Monotonicity theorems for integer-valued fields and delocali
zation in two-dimensions\nby Jacob Shapiro (Princeton) as part of UCLA
analysis and PDE seminar\n\n\nAbstract\nInteger-valued fields are restric
ted to take values in Z and usually their Gibbs factor depends only on the
gradient of the field. When the Gibbs factor is such that the typical val
ue of the gradients is much larger than 1 (the spacing of points in Z)\, t
he integer constraint becomes less relevant so the field behaves as if it
were real-valued and “delocalizes”. In 2D\, this delocalization is ass
ociated with the Berezinskii–Kosterlitz–Thouless phase of the dual O(2
) spin model. I will explain these notions for various models and present
recent monotonicity theorems for fluctuations which are important to estab
lish the delocalized phase.\n\nJoint with: Michael Aizenman\, Matan Harel
and Ron Peled.\n
LOCATION:https://researchseminars.org/talk/UCLAAnalysisSeminar/119/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hongki Jung (Indiana)
DTSTART;VALUE=DATE-TIME:20220419T213000Z
DTEND;VALUE=DATE-TIME:20220419T223000Z
DTSTAMP;VALUE=DATE-TIME:20240423T101436Z
UID:UCLAAnalysisSeminar/120
DESCRIPTION:Title: A small cap decoupling for the twisted cubic\nby Hongki
Jung (Indiana) as part of UCLA analysis and PDE seminar\n\n\nAbstract\nSma
ll cap decouplings deal with decoupling estimates for caps that are smalle
r than the canonical size. In 2019\, Demeter\, Guth and Wang studied small
cap decoupling for exponential sums with frequency points supported on th
e cubic moment curve. In this talk\, I will discuss the proof of $L^{10}$
small cap decoupling for general functions\, which involves incidence esti
mates for tubes and planks in $\\mathbb{R}^3$.\n
LOCATION:https://researchseminars.org/talk/UCLAAnalysisSeminar/120/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jiajie Chen (Caltech)
DTSTART;VALUE=DATE-TIME:20220419T223000Z
DTEND;VALUE=DATE-TIME:20220419T233000Z
DTSTAMP;VALUE=DATE-TIME:20240423T101436Z
UID:UCLAAnalysisSeminar/121
DESCRIPTION:Title: On the competition between advection and vortex stretching\nby Jiajie Chen (Caltech) as part of UCLA analysis and PDE seminar\n\n\
nAbstract\nWhether the 3D incompressible Euler equations can develop a fin
ite-time singularity from smooth initial data is an outstanding open probl
em. The presence of vortex stretching is the primary source of a potential
finite-time singularity. However\, to construct a singularity\, the effec
t of the advection is one of the obstacles. In this talk\, we will first s
how some examples in incompressible fluids about the competition between a
dvection and vortex stretching. Then we will discuss the De Gregorio (DG)
model\, which adds an advection term to the Constantin-Lax-Majda model to
model this competition. In an effort to establish singularity formation in
incompressible fluids\, we develop a novel approach based on dynamic resc
aling formulation. Using this approach\, we construct finite time singular
ities of the DG model on the real line from smooth initial data and on a c
ircle from C^{\\alpha} initial data with any $0<\\alpha < 1$. On the other
hand\, for $C^1$ initial data with the same sign and symmetry properties
as those of the blowup solution\, we prove that the solution of the DG mod
el on a circle exists globally.\n
LOCATION:https://researchseminars.org/talk/UCLAAnalysisSeminar/121/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tamara Grava (Bristol)
DTSTART;VALUE=DATE-TIME:20220607T170000Z
DTEND;VALUE=DATE-TIME:20220607T180000Z
DTSTAMP;VALUE=DATE-TIME:20240423T101436Z
UID:UCLAAnalysisSeminar/122
DESCRIPTION:Title: Gibbs ensemble for Integrable Systems\, a case study: the A
blowitz Laddik lattice\nby Tamara Grava (Bristol) as part of UCLA anal
ysis and PDE seminar\n\n\nAbstract\nWe consider discrete integrable syst
ems with random initial data and connect them with the theory of random ma
trices.\nIn particular we consider the defocusing nonlinear Schrodinger
equation in its integrable version\, that is called Ablowitz Ladik lattic
e. In the random initial data setting the Lax matrix of the Ablowitz
Ladik lattice turns into a random matrix that is related to the circular
beta-ensemble at high temperature. We obtain the density of states of
the random Lax matrix\, when the size of the matrix goes to infinity\, by
establishing a mapping to the one-dimensional log-gas. The density of
states is obtained via a particular solution of the double-confluent Heu
n equation.\nJoint work with Guido Mazzuca https://arxiv.org/pdf/2107.0230
3.pdf\n
LOCATION:https://researchseminars.org/talk/UCLAAnalysisSeminar/122/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ben Krause (King's College London)
DTSTART;VALUE=DATE-TIME:20220524T220000Z
DTEND;VALUE=DATE-TIME:20220524T230000Z
DTSTAMP;VALUE=DATE-TIME:20240423T101436Z
UID:UCLAAnalysisSeminar/123
DESCRIPTION:Title: Discrete Analogues in Harmonic Analysis: Equidistribution of
Exponential Sums and a Theorem of Stein-Wainger\nby Ben Krause (King'
s College London) as part of UCLA analysis and PDE seminar\n\n\nAbstract\n
In this talk I will review the theory of maximally modulated oscillatory s
ingular integrals after Stein-Wainger\, and then will use equidistribution
-type results for exponential sums to adapt the Stein-Wainger theory to th
e discrete setting.\n
LOCATION:https://researchseminars.org/talk/UCLAAnalysisSeminar/123/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yifeng Yu (UC Irvine)
DTSTART;VALUE=DATE-TIME:20221018T210000Z
DTEND;VALUE=DATE-TIME:20221018T220000Z
DTSTAMP;VALUE=DATE-TIME:20240423T101436Z
UID:UCLAAnalysisSeminar/124
DESCRIPTION:Title: Existence of effective burning velocity in cellular flow for
curvature G-equation\nby Yifeng Yu (UC Irvine) as part of UCLA analys
is and PDE seminar\n\n\nAbstract\nG-equation is a popular level set model
in turbulent combustion\, and\nbecomes an advective mean curvature type ev
olution equation when the curvature effect is considered:\n$$\nG_t + \\lef
t(1-d\\\, \\Div{\\frac{DG}{|DG|}}\\right)_+|DG|+V(x)\\cdot DG=0.\n$$\nIn t
his talk\, I will show the existence of effective burning velocity under t
he above curvature G-equation model when $V$ is a two dimensional cellula
r flow. Our proof combines PDE methods with a dynamical analysis of the K
ohn-Serfaty deterministic game characterization of the curvature G-equatio
n based on the special structure of the cellular flow. This is a joint wit
h Hongwei Gao\, Ziang Long and Jack Xin.\n
LOCATION:https://researchseminars.org/talk/UCLAAnalysisSeminar/124/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Minh-Binh Tran (Texas A&M)
DTSTART;VALUE=DATE-TIME:20221025T210000Z
DTEND;VALUE=DATE-TIME:20221025T220000Z
DTSTAMP;VALUE=DATE-TIME:20240423T101436Z
UID:UCLAAnalysisSeminar/125
DESCRIPTION:Title: Some Recent Results On Wave Turbulence\nby Minh-Binh Tra
n (Texas A&M) as part of UCLA analysis and PDE seminar\n\n\nAbstract\nWave
turbulence describes the dynamics of both classical and non-classical non
linear waves out of thermal equilibrium. Recent mathematical interests o
n wave turbulence theory have the roots from the works of Bourgain\, Staff
ilani and Colliander-Keel-Staffilani-Takaoka-Tao. In this talk\, I will pr
esent some of our recent results on wave turbulence theory. The talk is ba
sed on my joint work with Bensoussan (UTD)\, Staffilani (MIT)\, Soffer (Ru
tgers)\, Pomeau (ENS Paris).\n
LOCATION:https://researchseminars.org/talk/UCLAAnalysisSeminar/125/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Agnieszka Zelerowicz (UC Riverside)
DTSTART;VALUE=DATE-TIME:20221129T233000Z
DTEND;VALUE=DATE-TIME:20221130T000000Z
DTSTAMP;VALUE=DATE-TIME:20240423T101436Z
UID:UCLAAnalysisSeminar/126
DESCRIPTION:Title: Lorentz gases on quasicrystals\nby Agnieszka Zelerowicz
(UC Riverside) as part of UCLA analysis and PDE seminar\n\nLecture held in
Caltech Linde 310.\n\nAbstract\nThe Lorentz gas was originally introduced
as a model for the movement of electrons in metals.\n\n It consists of a
massless point particle (electron) moving through Euclidean space bouncing
off a given set of scatterers $\\mathcal{S}$ (atoms of the metal) with el
astic collisions at the boundaries $\\partial \\mathcal{S}$. If the set of
scatterers is periodic in space\, then the quotient system\, which is com
pact\, is known as the Sinai billiard. There is a great body of work devot
ed to Sinai billiards and in many ways their dynamics is well understood.\
n\n In contrast\, very little is known about the behavior of the Lorentz g
ases with aperiodic configurations of scatterers which model quasicrystals
and other low-complexity aperiodic sets. This case is the focus of our jo
int work with Rodrigo Trevi\\~no. \n\nWe establish some dynamical properti
es which are common for the periodic and quasiperiodic billiards. We also
point out some significant differences between the two. The novelty of our
approach is the use of tiling spaces to obtain a compact model of the ape
riodic Lorentz gas on the plane.\n
LOCATION:https://researchseminars.org/talk/UCLAAnalysisSeminar/126/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jeremy Wu (UCLA)
DTSTART;VALUE=DATE-TIME:20220927T210000Z
DTEND;VALUE=DATE-TIME:20220927T220000Z
DTSTAMP;VALUE=DATE-TIME:20240423T101436Z
UID:UCLAAnalysisSeminar/127
DESCRIPTION:Title: The gradient flow structure of the Landau equation\nby J
eremy Wu (UCLA) as part of UCLA analysis and PDE seminar\n\nLecture held i
n UCLA Math 6221.\n\nAbstract\nThe Landau equation is one of the cornersto
nes of kinetic theory. It describes the evolution of a gas of plasma parti
cles. Complementing its physical relevance\, the mathematical theory of th
e Landau equation is very deep\, yet incomplete owing to the competing eff
ects of quasilinear diffusion and quadratic growth. Global regularity has
eluded researchers because of this competition and a related open question
is global uniqueness of weak solutions. This talk introduces the gradient
flow structure of the Landau equation to set the foundation for an approa
ch to answering this problem. The construction of the metric which induces
the gradient flow structure builds upon the dynamic formulation of classi
cal Wasserstein metrics. This is based on joint work with José A. Carrill
o\, Matias G. Delgadino\, and Laurent Desvillettes.\n
LOCATION:https://researchseminars.org/talk/UCLAAnalysisSeminar/127/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrew Lawrie (MIT)
DTSTART;VALUE=DATE-TIME:20221108T220000Z
DTEND;VALUE=DATE-TIME:20221108T230000Z
DTSTAMP;VALUE=DATE-TIME:20240423T101436Z
UID:UCLAAnalysisSeminar/128
DESCRIPTION:Title: The soliton resolution conjecture for equivariant wave maps<
/a>\nby Andrew Lawrie (MIT) as part of UCLA analysis and PDE seminar\n\n\n
Abstract\nI will present a joint work with Jacek Jendrej (CRNS\, Sorbonne
Paris Nord) on equivariant wave maps with values in the two-sphere. We pro
ve that every finite energy solution resolves\, as time passes\, into a su
perposition of harmonic maps (solitons) and radiation\, settling the solit
on resolution problem for this equation. It was proved in works of Côte\
, and Jia-Kenig\, that such a decomposition holds along a sequence of time
s. We show the resolution holds continuously-in-time via a “no-return”
lemma based on the virial identity. The proof combines a modulation analy
sis of solutions near a multi-soliton configuration with concentration com
pactness techniques. As a byproduct of our analysis we prove that there ar
e no pure multi-solitons in equivariance class k=1 and no elastic collisio
ns between pure multi-solitons in the higher equivariance classes.\n
LOCATION:https://researchseminars.org/talk/UCLAAnalysisSeminar/128/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Juhi Jang (USC)
DTSTART;VALUE=DATE-TIME:20220927T220000Z
DTEND;VALUE=DATE-TIME:20220927T230000Z
DTSTAMP;VALUE=DATE-TIME:20240423T101436Z
UID:UCLAAnalysisSeminar/129
DESCRIPTION:Title: On slowly rotating star solutions\nby Juhi Jang (USC) as
part of UCLA analysis and PDE seminar\n\nLecture held in UCLA Math 6221.\
n\nAbstract\nIn this talk we will review recent progress on the local and
global dynamics of Newtonian stars governed by the compressible Euler-Pois
son system and discuss mathematical constructions of slowly rotating star
solutions bifurcating from the non-rotating ones. In the case of non-isent
ropic stars\, we introduce a new ad hoc perturbative strategy to overcome
the loss of regularity and variational structure caused by the variable en
tropy. If time permits\, we will also discuss recent uniqueness and orbita
l stability of McCann’s uniformly rotating binary star solutions and its
application to binary galaxies. The talk is based on joint works with T.
Makino\, W. Strauss\, Y. Wu and J. Seok.\n
LOCATION:https://researchseminars.org/talk/UCLAAnalysisSeminar/129/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nets Katz (Caltech)
DTSTART;VALUE=DATE-TIME:20221011T210000Z
DTEND;VALUE=DATE-TIME:20221011T220000Z
DTSTAMP;VALUE=DATE-TIME:20240423T101436Z
UID:UCLAAnalysisSeminar/130
DESCRIPTION:Title: A proto-inverse Szemer\\'edi Trotter theorem\nby Nets Ka
tz (Caltech) as part of UCLA analysis and PDE seminar\n\nLecture held in C
altech Linde 310.\n\nAbstract\nThe symmetric case of the Szemer\\'edi-Trot
ter theorem says that any configuration of N lines and N points in the pla
ne has at most O(N^{4/3}) incidences. We describe a recipe involving just
O(N^{1/3}) parameters which sometimes (that is\, for some choices of the p
arameters) produces a configuration of N point and N lines. (Otherwise\, w
e say the recipe fails.) We show that any near-extremal example for Szemer
\\'edi Trotter is densely related to a successful instance of the recipe.
We discuss the relation of this statement to the inverse Szemer\\'edi Trot
ter problem. (joint work in progress with Olivine Silier.)\n
LOCATION:https://researchseminars.org/talk/UCLAAnalysisSeminar/130/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michael Perlmutter (UCLA)
DTSTART;VALUE=DATE-TIME:20221011T220000Z
DTEND;VALUE=DATE-TIME:20221011T230000Z
DTSTAMP;VALUE=DATE-TIME:20240423T101436Z
UID:UCLAAnalysisSeminar/131
DESCRIPTION:Title: The scattering transform\, a harmonic analysis perspective o
n neural networks\nby Michael Perlmutter (UCLA) as part of UCLA analys
is and PDE seminar\n\nLecture held in Caltech Linde 310.\n\nAbstract\nThe
scattering transform is a mathematical model of convolutional neural netwo
rks (CNNs) initially introduced (for Euclidean data) by Mallat in 2012. Th
is work models the filter convolutions of a CNN as a wavelet transform and
uses methods from harmonic analysis to analyze the stability and invarian
ce of CNNs to certain group actions. I will introduce Mallat’s construct
ion and explain how it has improved our understanding of CNNs. Then\, in t
he second half of my talk\, I will discuss recent generalizations of the s
cattering transform to graphs\, manifolds\, and other measure spaces. Thes
e generalized scattering transforms utilize wavelets constructed from the
spectral decomposition of a suitable Laplacian. I will also discuss a diff
usion maps-based method\, with a provable convergence rate\, for implement
ing the manifold scattering transform from finitely samples of an unknown
manifold.\n
LOCATION:https://researchseminars.org/talk/UCLAAnalysisSeminar/131/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shengwen Gan (MIT)
DTSTART;VALUE=DATE-TIME:20221129T223000Z
DTEND;VALUE=DATE-TIME:20221129T230000Z
DTSTAMP;VALUE=DATE-TIME:20240423T101436Z
UID:UCLAAnalysisSeminar/132
DESCRIPTION:Title: The restricted projection to planes in R^3.\nby Shengwen
Gan (MIT) as part of UCLA analysis and PDE seminar\n\nLecture held in Cal
tech Linde 310.\n\nAbstract\nIn this talk\, I will discuss a conjecture ma
de by Fässler and Orponen on the restricted\nprojection to planes in R^3.
I will first talk about the Falconer-type exceptional set estimate in R^2
\, and then I will talk about the proof of the conjecture.\n
LOCATION:https://researchseminars.org/talk/UCLAAnalysisSeminar/132/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Brian Hall (Notre Dame)
DTSTART;VALUE=DATE-TIME:20221004T210000Z
DTEND;VALUE=DATE-TIME:20221004T220000Z
DTSTAMP;VALUE=DATE-TIME:20240423T101436Z
UID:UCLAAnalysisSeminar/133
DESCRIPTION:Title: Random matrices and heat flow on polynomials\nby Brian H
all (Notre Dame) as part of UCLA analysis and PDE seminar\n\n\nAbstract\nS
everal recent results have demonstrated a “model deformation phenomenon
” in random matrix theory\, in which the limiting eigenvalue distributio
ns of two different random matrix models are\, in certain cases\, related
by push-forward under an explicit\, canonical map of the plane to itself.
The prototype example is the case of the circular and semicircular laws\,
which are related by push-forward under the map z —> 2Re(z). There are b
y now several broad families of examples extending this simple case. \n\nI
will discuss a conjecture\, developed with Ching Wei Ho\, that provides a
finite-N version of the model deformation phenomenon\, at the level of ch
aracteristic polynomials. Specifically\, the conjecture says that applying
the heat operator to the characteristic polynomial of one random matrix g
ives a polynomial whose bulk distribution of zeros resembles that of a dif
ferent random matrix. As an example\, consider applying the heat operator
for time 1/N to the characteristic polynomial of an NxN GUE matrix. We bel
ieve that the zeros of the resulting polynomial will be almost surely asym
ptotically uniform over the unit disk. Thus\, the heat operator can turn t
he semicircular law into the circular law. I will explain the conjecture a
nd describe some rigorous results in this direction.\n
LOCATION:https://researchseminars.org/talk/UCLAAnalysisSeminar/133/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Wojciech Ozanski (Florida State University)
DTSTART;VALUE=DATE-TIME:20221018T220000Z
DTEND;VALUE=DATE-TIME:20221018T230000Z
DTSTAMP;VALUE=DATE-TIME:20240423T101436Z
UID:UCLAAnalysisSeminar/134
DESCRIPTION:Title: Well-posedness of logarithmic spiral vortex sheets\nby W
ojciech Ozanski (Florida State University) as part of UCLA analysis and PD
E seminar\n\n\nAbstract\nWe will discuss a family of 2D logarithmic spiral
vortex sheets which include the celebrated spirals introduced by Prandtl
(Vortr¨age aus dem Gebiete der Hydro- und Aerodynamik\, 1922) and by Alex
ander (Phys. Fluids\, 1971). We will discuss a recent result regarding a c
omplete characterization of such spirals in terms of weak solutions of the
2D incompressible Euler equations. Namely\, we will explain that a spiral
gives rise to such solution if and only if two conditions hold across eve
ry spirals: a velocity matching condition and a pressure matching conditio
n\, which provides the first rigorous mathematical framework for the spira
ls since their introduction by Prandtl in 1922\, despite significant progr
ess of the theory of vortex sheets and the Birkhoff-Rott equations. We wil
l also discuss well-posedness of the symmetric Alexander spiral with two b
ranches\, despite recent evidence for the contrary\, as well as an existen
ce result of nonsymmetric spirals.\n
LOCATION:https://researchseminars.org/talk/UCLAAnalysisSeminar/134/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Thierry Laurens (UCLA)
DTSTART;VALUE=DATE-TIME:20221115T220000Z
DTEND;VALUE=DATE-TIME:20221115T230000Z
DTSTAMP;VALUE=DATE-TIME:20240423T101436Z
UID:UCLAAnalysisSeminar/135
DESCRIPTION:Title: Sharp well-posedness for the Benjamin--Ono equation\nby
Thierry Laurens (UCLA) as part of UCLA analysis and PDE seminar\n\n\nAbstr
act\nWe will discuss a proof of sharp well-posedness for the Benjamin--Ono
equation in the class of H^s spaces\, on both the line and the circle. T
his result was previously unknown on the line\, while on the circle it was
obtained recently by Gérard\, Kappeler\, and Topalov. This is joint wor
k with Rowan Killip and Monica Visan.\n
LOCATION:https://researchseminars.org/talk/UCLAAnalysisSeminar/135/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Timothy Buttsworth (U. Penn)
DTSTART;VALUE=DATE-TIME:20221122T220000Z
DTEND;VALUE=DATE-TIME:20221122T230000Z
DTSTAMP;VALUE=DATE-TIME:20240423T101436Z
UID:UCLAAnalysisSeminar/136
DESCRIPTION:Title: The prescribed cross curvature equation on the three-sphere<
/a>\nby Timothy Buttsworth (U. Penn) as part of UCLA analysis and PDE semi
nar\n\n\nAbstract\nFor a given Riemannian manifold\, the cross curvature t
ensor is a symmetric (0\,2)-tensor field which describes how close the und
erlying geometry is to being hyperbolic. The cross curvature was introduce
d by Chow and Hamilton in 2004\; they hoped that the corresponding cross c
urvature flow could be used to continuously deform an arbitrary Riemannian
metric of negative sectional curvature into one of constant negative sect
ional curvature. In this talk\, I will discuss the 'prescribed cross curva
ture equation'\, which is the underlying inhomogeneous steady-state versio
n of the cross curvature flow. About this problem\, Hamilton conjectured t
hat any positive symmetric tensor on the three-sphere was the cross curvat
ure of exactly one Riemannian metric. I will discuss some recent results w
hich support the existence component of this conjecture\, and refute the u
niqueness component. Joint work with Artem Pulemotov.\n
LOCATION:https://researchseminars.org/talk/UCLAAnalysisSeminar/136/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yannick Sire (Johns Hopkins University)
DTSTART;VALUE=DATE-TIME:20230110T220000Z
DTEND;VALUE=DATE-TIME:20230110T230000Z
DTSTAMP;VALUE=DATE-TIME:20240423T101436Z
UID:UCLAAnalysisSeminar/137
DESCRIPTION:Title: Nematic Liquid crystal flows with free boundary\nby Yann
ick Sire (Johns Hopkins University) as part of UCLA analysis and PDE semin
ar\n\n\nAbstract\nI will introduce a new parabolic system for the flow of
nematic liquid crystals\, enjoying a free boundary condition. After recent
works related to the construction of blow-up solutions for several critic
al parabolic problems (such as the Fujita equation\, the heat flow of harm
onic maps\, liquid crystals without free boundary\, etc...)\, I will const
ruct a physically relevant weak solution blowing-up in finite time. We mak
e use of the so-called inner/outer parabolic gluing. Along the way\, I wil
l present a set of optimal estimates for the Stokes operator with Navier s
lip boundary conditions. I will state several open problems related to the
partial regularity of the system under consideration. This is joint work
with F.-H. Lin (NYU)\, Y. Zhou (JHU) and J. Wei (UBC).\n
LOCATION:https://researchseminars.org/talk/UCLAAnalysisSeminar/137/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexandros Eskenazis (Sorbonne)
DTSTART;VALUE=DATE-TIME:20221108T230000Z
DTEND;VALUE=DATE-TIME:20221109T000000Z
DTSTAMP;VALUE=DATE-TIME:20240423T101436Z
UID:UCLAAnalysisSeminar/138
DESCRIPTION:Title: Regularity for weighted convex isoperimetric problems\nb
y Alexandros Eskenazis (Sorbonne) as part of UCLA analysis and PDE seminar
\n\n\nAbstract\nWe shall discuss results and open questions pertaining to
the regularity (and irregularity) of solutions of weighted isoperimetric-t
ype problems over the class of symmetric convex sets. Based on joint work
with G. Moschidis (EPFL).\n
LOCATION:https://researchseminars.org/talk/UCLAAnalysisSeminar/138/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ewelina Zatorska (ICL)
DTSTART;VALUE=DATE-TIME:20221025T193000Z
DTEND;VALUE=DATE-TIME:20221025T203000Z
DTSTAMP;VALUE=DATE-TIME:20240423T101436Z
UID:UCLAAnalysisSeminar/139
DESCRIPTION:Title: The dissipative Aw-Rascle system: existence theory and hard-
congestion limit\nby Ewelina Zatorska (ICL) as part of UCLA analysis a
nd PDE seminar\n\n\nAbstract\nIn this talk I am going to analyze the compr
essible dissipative hydrodynamic model of crowd motion or of granular flow
. The model resembles the famous Aw-Rascle model of traffic\, except that
the difference between the actual and the desired velocities (the offset f
unction) is a gradient of the density function\, and not a scalar. This mo
dification gives rise to a dissipation term in the momentum equation that
vanishes when the density is equal to zero.\nI will compare the dissipativ
e Aw-Rascle system with the compressible Euler and compressible Navier-Sto
kes equations\, and back it up with two existence and ill-posedness result
s. In the last part of my talk I will explain the proof of conjecture made
by Lefebvre-Lepot and Maury\, that the hard congestion limit of this syst
em (with singular offset function) leads to congested compressible/incompr
essible Euler equations.\n
LOCATION:https://researchseminars.org/talk/UCLAAnalysisSeminar/139/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hong Wang (UCLA)
DTSTART;VALUE=DATE-TIME:20221101T210000Z
DTEND;VALUE=DATE-TIME:20221101T220000Z
DTSTAMP;VALUE=DATE-TIME:20240423T101436Z
UID:UCLAAnalysisSeminar/140
DESCRIPTION:Title: Sticky Kakeya sets in R^3\nby Hong Wang (UCLA) as part o
f UCLA analysis and PDE seminar\n\n\nAbstract\nA Kakeya set is a set of po
ints in R^n which contains a unit line segment in every direction. The Kak
eya conjecture states that the Hausdorff dimension of any Kakeya set is n.
We study a special collection of the Kakeya sets\, namely the sticky Kak
eya sets\, where the line segments in nearby directions stay close. Joint
with Josh Zahl\, we show that the sticky Kakeya sets in R^3 has Hausdorff
dimension 3.\n
LOCATION:https://researchseminars.org/talk/UCLAAnalysisSeminar/140/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Deniz Bilman (University of Cincinnati)
DTSTART;VALUE=DATE-TIME:20230131T210000Z
DTEND;VALUE=DATE-TIME:20230131T220000Z
DTSTAMP;VALUE=DATE-TIME:20240423T101436Z
UID:UCLAAnalysisSeminar/141
DESCRIPTION:Title: Wave patterns generated by large-amplitude rogue waves and t
heir universal character\nby Deniz Bilman (University of Cincinnati) a
s part of UCLA analysis and PDE seminar\n\n\nAbstract\nIt is known from ou
r recent work that both fundamental rogue wave solutions (with Peter Mille
r and Liming Ling) and multi-pole soliton solutions (with Robert Buckingha
m) of the nonlinear Schrödinger (NLS) equation exhibit the same universal
asymptotic behavior in the limit of large order in a shrinking region nea
r their peak amplitude point\, despite the quite different boundary condit
ions these solutions satisfy at infinity. This behavior is described by a
special solution of again the NLS equation that also satisfies ordinary di
fferential equations from the Painlev\\’e-III hierarchy. We review these
results and show that this profile also arises universally from arbitrary
background fields. We then show how rogue waves and solitons of arbitrary
orders can be placed within a common analytical framework in which the "o
rder" becomes a continuous parameter\, allowing one to tune continuously b
etween types of solutions satisfying different boundary conditions. In thi
s framework\, solitons and rogue waves of increasing integer orders altern
ate as the continuous order parameter increases. We show that in a bounded
region of the space-time of size proportional to the order\, these soluti
ons all appear to be the same when the order is large. However\, in the u
nbounded complementary region one sees qualitatively different asymptotic
behavior along different sequences. This is joint work with Peter Miller (
U. Michigan).\n
LOCATION:https://researchseminars.org/talk/UCLAAnalysisSeminar/141/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Robert Buckingham (University of Cincinnati)
DTSTART;VALUE=DATE-TIME:20230228T210000Z
DTEND;VALUE=DATE-TIME:20230228T220000Z
DTSTAMP;VALUE=DATE-TIME:20240423T101436Z
UID:UCLAAnalysisSeminar/142
DESCRIPTION:Title: Universality of High-Order Rogue Waves\nby Robert Buckin
gham (University of Cincinnati) as part of UCLA analysis and PDE seminar\n
\n\nAbstract\nWe will discuss a series of recent results indicating that h
igh-order rogue-wave behavior is universally described for a variety of di
fferent equations and initial conditions by a family of functions connecte
d to the Painleve-III hierarchy and first encountered by Suleimanov in 201
7. This is joint work with Deniz Bilman\, Bob Jenkins\, and Peter Miller.
\n
LOCATION:https://researchseminars.org/talk/UCLAAnalysisSeminar/142/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Katy Craig (UC Santa Barbara)
DTSTART;VALUE=DATE-TIME:20230221T220000Z
DTEND;VALUE=DATE-TIME:20230221T230000Z
DTSTAMP;VALUE=DATE-TIME:20240423T101436Z
UID:UCLAAnalysisSeminar/144
DESCRIPTION:Title: Nonlocal particle approximations of the porous medium equati
on and applications to sampling and two-layer neural networks\nby Katy
Craig (UC Santa Barbara) as part of UCLA analysis and PDE seminar\n\n\nAb
stract\nGiven a desired target distribution and an initial guess of its sa
mples\, what is the best way to evolve the locations of the samples so tha
t they accurately represent the desired distribution? A classical solution
to this problem is to evolve the samples according to Langevin dynamics\,
a stochastic particle method for the Fokker-Planck equation. In today’s
talk\, I will contrast this with a nonlocal\, deterministic particle meth
od inspired by the porous medium equation. Using the Wasserstein gradient
flow structure of the equations and Serfaty’s scheme of Gamma-convergenc
e of gradient flows\, I will show that\, as the number of samples increase
s and the interaction scale goes to zero\, the interacting particle system
indeed converges to a solution of the porous medium equation. I will clos
e by discussing practical implications of this result to both sampling and
the training dynamics two-layer neural networks. This is based on joint w
ork with Karthik Elamvazhuthi\, Matt Haberland\, and Olga Turanova.\n
LOCATION:https://researchseminars.org/talk/UCLAAnalysisSeminar/144/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Amir Mohammadi (UC San Diego)
DTSTART;VALUE=DATE-TIME:20230221T230000Z
DTEND;VALUE=DATE-TIME:20230222T000000Z
DTSTAMP;VALUE=DATE-TIME:20240423T101436Z
UID:UCLAAnalysisSeminar/145
DESCRIPTION:Title: Dynamics on homogeneous spaces: a quantitative account\n
by Amir Mohammadi (UC San Diego) as part of UCLA analysis and PDE seminar\
n\n\nAbstract\nRigidity phenomena in homogeneous spaces have been extensiv
ely studied over the past few decades with several striking results and ap
plications. We will give an overview of activities pertaining to the quant
itative aspect of the analysis in this context with an emphasis on recent
developments and applications. This is based on joint works with Elon Lind
enstrauss and Zhiren Wang.\n
LOCATION:https://researchseminars.org/talk/UCLAAnalysisSeminar/145/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Davit Harutyunyan (UC Santa Barbara)
DTSTART;VALUE=DATE-TIME:20230214T220000Z
DTEND;VALUE=DATE-TIME:20230214T230000Z
DTSTAMP;VALUE=DATE-TIME:20240423T101436Z
UID:UCLAAnalysisSeminar/147
DESCRIPTION:Title: On Geometric rigidity of thin domains\nby Davit Harutyun
yan (UC Santa Barbara) as part of UCLA analysis and PDE seminar\n\n\nAbstr
act\nA famous theorem of Reshetnyak states that if the gradient of a Sobol
ev field belongs to the group of proper rotations SO(n)\, then \nthe field
has to be affine. Friesecke\, James and Mueller proved a quantitative ver
sion of this statement in a celebrated work in 2002\,\nwhich is the so-cal
led Geometric Rigidity Estimate (GRE). A linearization is the Korn inequal
ity in linear Elasticity. It turned out that \nthe "best" constant in the
estimate is tied with the actual physical rigidity of the domain. In this
presentation\, we will discuss the GRE and Korn inequality \n(the lineariz
ation of GRE) for thin domains\, where the question is to find the asympto
tics of the "best" constant in terms of the domain \nthickness.\n
LOCATION:https://researchseminars.org/talk/UCLAAnalysisSeminar/147/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Antoine Song (Caltech)
DTSTART;VALUE=DATE-TIME:20230110T230000Z
DTEND;VALUE=DATE-TIME:20230111T000000Z
DTSTAMP;VALUE=DATE-TIME:20240423T101436Z
UID:UCLAAnalysisSeminar/148
DESCRIPTION:Title: Entropy\, first eigenvalue and stability of the hyperbolic p
lane\nby Antoine Song (Caltech) as part of UCLA analysis and PDE semin
ar\n\n\nAbstract\nConsider a closed surface of genus at least 2 endowed wi
th a Riemannian metric g\, and let (S\,g) be its universal cover. There ar
e two important invariants for (S\,g): the first eigenvalue \\lambda of th
e Laplacian and the volume entropy h\, which measures the exponential grow
th rate of the volume of geodesic balls. We can normalize g so that h=1. T
hen a classical inequality states that \\lambda is at most 1/4. When g is
a hyperbolic metric\, equality holds. We will discuss a stability property
for the hyperbolic plane: if \\lambda is close to the upper bound 1/4\, t
hen (S\,g) is close to the hyperbolic plane in a Benjamini-Schramm topolog
y.\n
LOCATION:https://researchseminars.org/talk/UCLAAnalysisSeminar/148/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jan Peszek (University of Warsaw)
DTSTART;VALUE=DATE-TIME:20230124T190000Z
DTEND;VALUE=DATE-TIME:20230124T200000Z
DTSTAMP;VALUE=DATE-TIME:20240423T101436Z
UID:UCLAAnalysisSeminar/149
DESCRIPTION:Title: Heterogeneous gradient flows with applications to collective
dynamics\nby Jan Peszek (University of Warsaw) as part of UCLA analys
is and PDE seminar\n\n\nAbstract\nIn 2001 F. Otto discovered a (nowadays w
ell-known) relationship between the continuity equation and gradient flows
with respect to the 2-Wasserstein metric. This connection provides a conv
enient description of many new and classical models and PDEs including Kel
ler-Segel and Fokker-Planck as well as models of first-order collective dy
namics. \nI am going to present a recent work (joint with David Poyato)\,
wherein we introduce the so-called fibered 2-Wasserstein metric (which adm
its only transportation along fibers controlled by a prescribed probabilis
tic distribution) and explore its applicability in gradient flows. Based o
n such a metric\, we develop the notion of heterogeneous gradient flows\,
and prove that they are equivalent to solutions of parameterized continuit
y equations. Lastly\, I will present a collection of applications ranging
from mixtures of fluids\, to multispecies models of collective dynamics\,
and to (the essential) applications in alignment models.\n
LOCATION:https://researchseminars.org/talk/UCLAAnalysisSeminar/149/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Xiaoyutao Luo (Duke)
DTSTART;VALUE=DATE-TIME:20230124T200000Z
DTEND;VALUE=DATE-TIME:20230124T210000Z
DTSTAMP;VALUE=DATE-TIME:20240423T101436Z
UID:UCLAAnalysisSeminar/150
DESCRIPTION:Title: Illposedness for vortex patches of the Euler and alpha-SQG e
quations\nby Xiaoyutao Luo (Duke) as part of UCLA analysis and PDE sem
inar\n\n\nAbstract\nI will talk about joint work with A. Kiselev (Duke) on
patch solutions of the Euler and alpha-SQG equations. It is well-known th
at the vortex patch of the 2D Euler equation is globally well-posed in non
-endpoint Holder spaces. We prove that the Euler vortex patch is ill-posed
at the C^2 endpoint by showing the existence of a patch with C^2 initial
data such that the curvature of the patch boundary becomes infinite instan
taneously. The alpha-SQG equations are a family of active scalar interpola
ting the 2D Euler and SQG equations. In contrast to the Euler case\, we sh
ow that the alpha-SQG patch\, in a suitable regime of regularity\, is ill-
posed in all non-L^2 Sobolev spaces and Holder spaces.\n
LOCATION:https://researchseminars.org/talk/UCLAAnalysisSeminar/150/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fazel Hadadifard (University of California\, Riverside)
DTSTART;VALUE=DATE-TIME:20230207T223000Z
DTEND;VALUE=DATE-TIME:20230207T233000Z
DTSTAMP;VALUE=DATE-TIME:20240423T101436Z
UID:UCLAAnalysisSeminar/151
DESCRIPTION:Title: Sharp time asymptotics for the quasi-geostrophic equation an
d near plane waves of reaction-diffusion models\nby Fazel Hadadifard (
University of California\, Riverside) as part of UCLA analysis and PDE sem
inar\n\nLecture held in Linde Hall 310\, Caltech.\n\nAbstract\nThe long-te
rm dynamics of the equations arising in fluid mechanics is a ubiquitous an
d well-studied subject\, and several methods have been developed. In this
talk\, we introduce the scaled variable method of Gallay-Wayne. We expand
the method to cover a wider range of equations/models. \n\nThe method is
then applied to the quasi-geostrophic equation and the Boussinesq system\,
both subject to fractional dissipation. We also present the stability of
the plane wave equations in higher dimensions. The method produces sharp t
ime rates\, the leading order terms as well as sharp asymptotics.\n \nOur
work\, joint with Prof. A. Stefanov\, generalizes the classical works on t
he Navier-Stokes system. Since the Green's functions in the fractional dis
sipation context are not sufficiently decaying at infinity\, the center-s
table manifold construction of Gallay-Wayne appears to be out of reach. In
stead\, we rely on appropriate a priori estimates for the solutions (both
in weighted and unweighted settings) to derive the asymptotic profiles.\n
LOCATION:https://researchseminars.org/talk/UCLAAnalysisSeminar/151/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hong Wang (University of California\, Los Angeles)
DTSTART;VALUE=DATE-TIME:20230207T233000Z
DTEND;VALUE=DATE-TIME:20230208T003000Z
DTSTAMP;VALUE=DATE-TIME:20240423T101436Z
UID:UCLAAnalysisSeminar/152
DESCRIPTION:Title: Radial projections in the plane\nby Hong Wang (Universit
y of California\, Los Angeles) as part of UCLA analysis and PDE seminar\n\
n\nAbstract\nLet $x$ be a point in the plane\, and the radial projection $
\\pi_x$ is defined by $\\pi_x(y)= \\frac{x-y}{|x-y|}$ for any $y\\neq x\\i
n \\mathbb{R}^2$. Suppose that $X$ is a Borel set in the plane and is not
contained in any line\, then we show that there exists a point $x\\in X$ s
uch that $\\pi_x (X)$ has dimension equal to $\\min \\{ \\dim_H X\, 1\\}$.
This is joint work with Tuomas Orponen and Pablo Shmerkin.\n
LOCATION:https://researchseminars.org/talk/UCLAAnalysisSeminar/152/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Seung-Yeon Ryoo (Princeton)
DTSTART;VALUE=DATE-TIME:20230411T200000Z
DTEND;VALUE=DATE-TIME:20230411T210000Z
DTSTAMP;VALUE=DATE-TIME:20240423T101436Z
UID:UCLAAnalysisSeminar/153
DESCRIPTION:Title: On embedding finitely generated groups of polynomial growth
into Euclidean spaces\nby Seung-Yeon Ryoo (Princeton) as part of UCLA
analysis and PDE seminar\n\n\nAbstract\nIt is well-known that a finitely
generated group of \npolynomial growth embeds bilipschitzly into\nEuclidea
n space (or Hilbert space) if and only if it is virtually \nabelian. Thus\
, in the not virtually abelian case\,\nthe Euclidean distortion of the bal
l of radius $n$ in the group grows \nto infinity as $n\\to\\infty$.\nWe ma
y therefore ask: what is the precise asymptotics of the Euclidean \ndistor
tion of $n$-balls?\nAnd what role does the dimension of the target Euclide
an space play in \nthe distortion?\nWe compute the (infinite-dimensional)
Euclidean distortion of \n$n$-balls to be a constant multiple of $\\sqrt{\
\log n}$\,\nby establishing for nilpotent Lie groups the classical Dorrons
oro \ntheorem\, which measures the $L^p$ norm of the fractional Laplacian\
nof a function in terms of a singular integral measuring the local \ndevia
tion of the function from suitable polynomials at all points\nand at all s
cales. We then show that\, in the special case of lattices \nof Carnot gro
ups\, the target dimension essentially does not affect\nthe distortion\, b
y constructing embeddings that simultaneously \noptimize the distortion an
d target dimension.\nThis construction involves a combination of the Lová
sz Local Lemma\, \nthe concentration of measure on the Euclidean sphere\,\
nand a version of the Nash-Moser iteration scheme pioneered by Tao (2018).
\n
LOCATION:https://researchseminars.org/talk/UCLAAnalysisSeminar/153/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jonas Luhrmann (Texas A&M)
DTSTART;VALUE=DATE-TIME:20230307T223000Z
DTEND;VALUE=DATE-TIME:20230307T233000Z
DTSTAMP;VALUE=DATE-TIME:20240423T101436Z
UID:UCLAAnalysisSeminar/154
DESCRIPTION:Title: On co-dimension one stability of the soliton for the 1D focu
sing cubic Klein-Gordon equation\nby Jonas Luhrmann (Texas A&M) as par
t of UCLA analysis and PDE seminar\n\nLecture held in Linde Hall 187\, Cal
tech.\n\nAbstract\nSolitons are particle-like solutions to dispersive evol
ution equations\nwhose shapes persist as time goes by. In some situations\
, these solitons\nappear due to the balance between nonlinear effects and
dispersion\, in\nother situations their existence is related to topologica
l properties of\nthe model. Broadly speaking\, they form the building bloc
ks for the\nlong-time dynamics of dispersive equations.\n\nIn this talk I
will present joint work with W. Schlag on long-time decay\nestimates for c
o-dimension one type perturbations of the soliton for the\n1D focusing cub
ic Klein-Gordon equation (up to exponential time scales)\,\nand I will dis
cuss our previous work on the asymptotic stability of the\nsine-Gordon kin
k under odd perturbations. While these two problems are\nquite similar at
first sight\, we will see that they differ by a subtle\ncancellation prope
rty\, which has significant consequences for the\nlong-time dynamics of th
e perturbations of the respective solitons.\n
LOCATION:https://researchseminars.org/talk/UCLAAnalysisSeminar/154/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andreia Chapouto (UCLA)
DTSTART;VALUE=DATE-TIME:20230307T233000Z
DTEND;VALUE=DATE-TIME:20230308T003000Z
DTSTAMP;VALUE=DATE-TIME:20240423T101436Z
UID:UCLAAnalysisSeminar/155
DESCRIPTION:Title: Disproving the Deift conjecture: the loss of almost periodic
ity\nby Andreia Chapouto (UCLA) as part of UCLA analysis and PDE semin
ar\n\nLecture held in Linde Hall 187\, Caltech.\n\nAbstract\nIn 2008\, Dei
ft conjectured that almost periodic initial data leads to almost periodic
solutions to the Korteweg-de Vries equation (KdV). In this talk\, we show
that this is not always the case. Namely\, we construct almost periodic in
itial data whose KdV evolution remains bounded but loses almost periodicit
y at a later time\, by building on the new observation that the conjecture
fails for the Airy equation.\nThis is joint work with Rowan Killip and Mo
nica Visan\n
LOCATION:https://researchseminars.org/talk/UCLAAnalysisSeminar/155/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rachel Greenfeld (IAS)
DTSTART;VALUE=DATE-TIME:20230509T200000Z
DTEND;VALUE=DATE-TIME:20230509T210000Z
DTSTAMP;VALUE=DATE-TIME:20240423T101436Z
UID:UCLAAnalysisSeminar/156
DESCRIPTION:Title: The structure of translational tilings\nby Rachel Greenf
eld (IAS) as part of UCLA analysis and PDE seminar\n\n\nAbstract\nTranslat
ional tiling is a covering of a space (e.g.\, Euclidean space) using trans
lated copies of a building block\, called a "tile''\, without any positive
measure overlaps. What are the possible ways that a space can be tiled? O
ne of the most well known conjectures in this area is the periodic tiling
conjecture. It asserts that any tile of Euclidean space can tile the space
periodically. In a joint work with Terence Tao\, we disprove the periodic
tiling conjecture in high dimensions. \nIn the talk\, I will survey the s
tudy of the periodic tiling conjecture\, motivate our recent result and di
scuss our counterexample as well as new developments.\n
LOCATION:https://researchseminars.org/talk/UCLAAnalysisSeminar/156/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Cheng Yu (University of Florida)
DTSTART;VALUE=DATE-TIME:20230404T190000Z
DTEND;VALUE=DATE-TIME:20230404T200000Z
DTSTAMP;VALUE=DATE-TIME:20240423T101436Z
UID:UCLAAnalysisSeminar/157
DESCRIPTION:Title: Infinitely many solutions to the isentropic system of gas dy
namics\nby Cheng Yu (University of Florida) as part of UCLA analysis a
nd PDE seminar\n\n\nAbstract\nIn this talk\, I will discuss the non-unique
ness of global weak solutions to the isentropic system of gas dynamics. In
particular\, I will show that for any initial data belonging to a dense s
ubset of the energy space\, there exists infinitely many global weak solut
ions to the isentropic Euler equations for any 1 < γ ≤ 1 + 2/n. The pro
of is based on a generalization of convex integration techniques and weak
vanishing viscosity limit of the Navier-Stokes equations. This talk is bas
ed on the joint work with M. Chen and A. Vasseur.\n
LOCATION:https://researchseminars.org/talk/UCLAAnalysisSeminar/157/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Petronela Radu (University of Nebraska)
DTSTART;VALUE=DATE-TIME:20230404T200000Z
DTEND;VALUE=DATE-TIME:20230404T210000Z
DTSTAMP;VALUE=DATE-TIME:20240423T101436Z
UID:UCLAAnalysisSeminar/158
DESCRIPTION:Title: Analytical\, geometrical\, and applied aspects in nonlocal f
rameworks\nby Petronela Radu (University of Nebraska) as part of UCLA
analysis and PDE seminar\n\n\nAbstract\nThe emergence of nonlocality as a
successful framework for capturing a variety of different physical phenome
na has catalyzed research in many directions at the applied\, computationa
l\, as well as at the theoretical levels. While models formulated with the
classical continuum mechanics theory have brought huge developments in te
chnology and science over the last century\, the new frontier requires tac
kling discontinuous\, singular\, or irregular behavior encountered in many
applications such as deformations and damage of solid bodies\, phase tran
sitions and image processing. To this end\, the study of systems that allo
w low-regularity (possibly discontinuous) solutions becomes the critical c
enter-piece. In this talk I will present basic nonlocal formulations for e
lasticity\, diffusion\, conservation laws\, as well as some geometric aspe
cts for studying curvature for boundaries that lack (classical) C^2 regula
rity. For the corresponding nonlocal systems of equations we will discuss
recent results (most of them belonging to the nonlinear realm) that we hav
e obtained with our students and collaborators\, as well as ongoing proble
ms and future directions.\n
LOCATION:https://researchseminars.org/talk/UCLAAnalysisSeminar/158/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jacob Bedrossian (UCLA)
DTSTART;VALUE=DATE-TIME:20230418T223000Z
DTEND;VALUE=DATE-TIME:20230418T233000Z
DTSTAMP;VALUE=DATE-TIME:20240423T101436Z
UID:UCLAAnalysisSeminar/159
DESCRIPTION:Title: Lower bounds on the top Lyapunov exponent of Galerkin-Navier
-Stokes and other stochastic differential equations\nby Jacob Bedrossi
an (UCLA) as part of UCLA analysis and PDE seminar\n\nLecture held in Calt
ech - Linde 255.\n\nAbstract\nWe review our recent joint work with Alex Bl
umenthal and Sam Punshon-Smith\, which introduced methods for obtaining st
rictly positive lower bounds on the top Lyapunov exponent of high-dimensio
nal\, stochastic differential equations such as the weakly damped Lorenz-9
6 (L96) model or Galerkin truncations of the 2d Navier-Stokes equations. T
his hallmark of chaos has long been observed in these models\, however\, n
o mathematical proof had previously been made for either deterministic or
stochastic forcing. The method is a combination of a new identity connecti
ng the Lyapunov exponents to a Fisher information of the stationary measur
e of the "projective process" with an L1-based uniform hypoelliptic regula
rity estimate. We will also discuss some related results\, such as dichoto
mies regarding Lyapunov exponents of general non-dissipative SDEs with app
lications to chaotic charged particle motion (joint with Chi-Hao Wu) and o
ther applications of uniform hypoelliptic estimates\, such as sharp estima
tes on the spectral gap of Markov semigroups (joint with Kyle Liss).\n
LOCATION:https://researchseminars.org/talk/UCLAAnalysisSeminar/159/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jun Kitagawa (Michigan State University)
DTSTART;VALUE=DATE-TIME:20230425T200000Z
DTEND;VALUE=DATE-TIME:20230425T210000Z
DTSTAMP;VALUE=DATE-TIME:20240423T101436Z
UID:UCLAAnalysisSeminar/160
DESCRIPTION:Title: Monge solutions of nontwisted optimal transport on nonstrict
ly convex boundaries\nby Jun Kitagawa (Michigan State University) as p
art of UCLA analysis and PDE seminar\n\n\nAbstract\nIn the optimal transpo
rt (Monge-Kantorovich) problem\, the existence of a single-valued optimal
map is guaranteed under certain conditions on the cost function and measur
es. However if the cost is ambient Euclidean distance squared restricted t
o the boundary of a convex body\, a result of Gangbo and McCann demonstrat
es there may be nice measures for which there is no singled-valued optimal
map. In this talk I discuss a recent result of ours showing that when the
transported measures have sufficiently small optimal transport cost\, the
re exists a single-valued optimal map\, when the body is $C^1$ and convex
(but not necessarily strictly convex). This result is sharp in the sense t
hat the claim can fail for a non-$C^1$ domain\, even if it is uniformly co
nvex. This talk is based on joint work with Seonghyeon Jeong.\n
LOCATION:https://researchseminars.org/talk/UCLAAnalysisSeminar/160/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sameer Iyer (UC Davis)
DTSTART;VALUE=DATE-TIME:20230530T200000Z
DTEND;VALUE=DATE-TIME:20230530T200000Z
DTSTAMP;VALUE=DATE-TIME:20240423T101436Z
UID:UCLAAnalysisSeminar/161
DESCRIPTION:Title: Reversal in the Stationary Prandtl Equations\nby Sameer
Iyer (UC Davis) as part of UCLA analysis and PDE seminar\n\n\nAbstract\nWe
investigate reversal and recirculation for the stationary Prandtl equatio
ns. Reversal describes the solution after the Goldstein singularity\, and
is characterized by spatio-temporal regions in which $u > 0$ and $u < 0$.
The classical point of view of regarding the Prandtl equations as an evolu
tion $x$ completely breaks down. Instead\, we view the problem as a quasil
inear\, mixed-type\, free-boundary problem. Joint work with Nader Masmoudi
.\n
LOCATION:https://researchseminars.org/talk/UCLAAnalysisSeminar/161/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Enno Lenzmann (U. Basel)
DTSTART;VALUE=DATE-TIME:20230523T200000Z
DTEND;VALUE=DATE-TIME:20230523T210000Z
DTSTAMP;VALUE=DATE-TIME:20240423T101436Z
UID:UCLAAnalysisSeminar/162
DESCRIPTION:Title: Turbulence in completely integrable PDEs: The Calogero-Moser
derivative NLS\nby Enno Lenzmann (U. Basel) as part of UCLA analysis
and PDE seminar\n\n\nAbstract\nI will discuss a new type of a derivative n
onlinear Schrödinger equation on the line\, which can be seen as a contin
uum version of completely integrable Calogero-Moser many-body systems in c
lassical mechanics. The resulting NLS exhibits many intriguing features su
ch as a Lax pair structure on Hardy spaces\, L^2-criticality\, and turbule
nt solutions. In my talk\, I will focus on the dynamics of multi-soliton s
olutions. We prove global-in-time existence (which is a large data result)
and\, more strikingly\, we show that these multi-solitons always exhibit
an unbounded growth of Sobolev norms (turbulence) as time tends to infinit
y. This talk is based on joint work with Patrick Gérard (Orsay).\n
LOCATION:https://researchseminars.org/talk/UCLAAnalysisSeminar/162/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Louise Gassot (ENS)
DTSTART;VALUE=DATE-TIME:20230523T190000Z
DTEND;VALUE=DATE-TIME:20230523T200000Z
DTSTAMP;VALUE=DATE-TIME:20240423T101436Z
UID:UCLAAnalysisSeminar/163
DESCRIPTION:Title: Zero-dispersion limit for the Benjamin-Ono equation on the t
orus\nby Louise Gassot (ENS) as part of UCLA analysis and PDE seminar\
n\n\nAbstract\nWe discuss the zero-dispersion limit for the Benjamin-Ono e
quation on the torus given a bell-shaped initial data. We prove that the s
olutions admit a weak limit as the dispersion parameter tends to zero\, wh
ich is explicit and constructed from the Burgers' equation. The approach r
elies on the complete integrability for the Benjamin-Ono equation from Gé
rard\, Kappeler and Topalov\, and also on the spectral study of the Lax op
erator associated to the initial data in the zero-dispersion limit.\n
LOCATION:https://researchseminars.org/talk/UCLAAnalysisSeminar/163/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Christoph Kehle (ETH)
DTSTART;VALUE=DATE-TIME:20230418T213000Z
DTEND;VALUE=DATE-TIME:20230418T223000Z
DTSTAMP;VALUE=DATE-TIME:20240423T101436Z
UID:UCLAAnalysisSeminar/164
DESCRIPTION:Title: Turbulence for quasilinear waves on Schwarzschild-AdS\nb
y Christoph Kehle (ETH) as part of UCLA analysis and PDE seminar\n\nLectur
e held in Caltech - Linde 255.\n\nAbstract\nIn this talk\, I will present
upcoming work proving a "weak turbulent" instability for quasilinear wave
equations on Schwarzschild-AdS black holes. The instability is governed b
y a stably trapped 3-mode interaction transferring energy from low-to high
-frequency modes. Our result is motivated by the question of the stability
of black holes in the presence of a negative cosmological constant. This
is joint work with Georgios Moschidis.\n
LOCATION:https://researchseminars.org/talk/UCLAAnalysisSeminar/164/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sung-Jin Oh (Berkeley)
DTSTART;VALUE=DATE-TIME:20230516T223000Z
DTEND;VALUE=DATE-TIME:20230516T233000Z
DTSTAMP;VALUE=DATE-TIME:20240423T101436Z
UID:UCLAAnalysisSeminar/165
DESCRIPTION:Title: Codimension one stability of the catenoid under the hyperbol
ic vanishing mean curvature flow\nby Sung-Jin Oh (Berkeley) as part of
UCLA analysis and PDE seminar\n\nLecture held in Caltech.\n\nAbstract\nTh
e catenoid is one of the simplest examples of a minimal hypersurface\, nex
t to the hyperplane. In this talk\, we will view the catenoid as a station
ary solution to the hyperbolic vanishing mean curvature flow\, which is th
e hyperbolic analog of the (elliptic) minimal hypersurface equation\, and
study its nonlinear stability under no symmetry assumptions. The main resu
lt\, which is a recent joint work with Jonas Luhrmann and Sohrab Shahshaha
ni\, is that with respect to a "codimension one" set of initial data pertu
rbations of the n-dimensional catenoid\, the corresponding flow asymptotes
to an adequate translation and Lorentz boost of the catenoid for n greate
r than or equal to 5. Note that the codimension one condition is necessary
and sharp in view of the fact that the catenoid is an index 1 minimal hyp
ersurface. \n\nAmong the key challenges of the present problem compared to
the more classical stability problems for nontrivial stationary solutions
are: (1) the quasilinearity of the equation\, (2) the slow (polynomial) d
ecay of the catenoid at infinity\, and (3) the lack of symmetry assumption
s. To address these challenges\, we introduce several new ideas\, such as
a geometric construction of modulated profiles\, smoothing of modulation p
arameters\, and a robust framework for proving decay for the radiation.\n
LOCATION:https://researchseminars.org/talk/UCLAAnalysisSeminar/165/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mohit Bansil (UCLA)
DTSTART;VALUE=DATE-TIME:20230502T200000Z
DTEND;VALUE=DATE-TIME:20230502T210000Z
DTSTAMP;VALUE=DATE-TIME:20240423T101436Z
UID:UCLAAnalysisSeminar/166
DESCRIPTION:Title: The Master Equation in Mean Field Games\nby Mohit Bansil
(UCLA) as part of UCLA analysis and PDE seminar\n\n\nAbstract\nA Mean Fie
ld Game is a differential game (in the sense of game theory) where instead
of a finite number of players we have a continuous distribution of (infin
itely) many players\, however we make the simplifying assumption that all
players are identical.\n\nIn this talk we consider the existence and uniqu
eness of Nash Equilibrium in Mean Field Games. We show why the study of Na
sh Equilibrium naturally leads to the study of a Hamilton-Jacobi equation
over the space of measures called the master equation\, whose solutions gi
ve rise to Nash Equilibrium for our game.\n\nFor mean field games there is
n't a general theory of viscosity solutions analogous to Hamilton-Jacobi e
quations in finite dimensions. Motivated by this we revisit the clas-\nsic
al solution theory (as opposed to viscosity solutions) of Hamilton Jacobi
equations and identify a symmetry that extends the well-posedness theory i
nto new regimes. This\nsymmetry also yields results for the master equatio
n in mean field games.\n\nWe will see that there are two natural types of
noise that one can impose in a Mean Field Game\, individual noise and comm
on noise\, which correspond to cases where the noise of each player is ind
ependent and identical respectively. Individual noise has a regularizing e
ffect that is utilized in most well-posedness results for the master equat
ion.\nWe explore well-posedness for the master equation in the case withou
t individual noise\, under a monotonicity condition.\n
LOCATION:https://researchseminars.org/talk/UCLAAnalysisSeminar/166/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marianna Russkikh (Caltech)
DTSTART;VALUE=DATE-TIME:20230502T210000Z
DTEND;VALUE=DATE-TIME:20230502T220000Z
DTSTAMP;VALUE=DATE-TIME:20240423T101436Z
UID:UCLAAnalysisSeminar/167
DESCRIPTION:Title: Dimers and embeddings\nby Marianna Russkikh (Caltech) as
part of UCLA analysis and PDE seminar\n\n\nAbstract\nWe introduce a conce
pt of ‘t-embeddings’ of weighted bipartite planar graphs. We believe t
hat these t-embeddings always exist and that they are good candidates to r
ecover the complex structure of big bipartite planar graphs carrying a dim
er model. We also developed a relevant theory of discrete holomorphic func
tions on t-embeddings\; this theory unifies Kenyon’s holomorphic functio
ns on T-graphs and s-holomorphic functions coming from the Ising model. We
provide a meta-theorem on convergence of the height fluctuations to the G
aussian Free Field.\n
LOCATION:https://researchseminars.org/talk/UCLAAnalysisSeminar/167/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lei Wu (Lehigh)
DTSTART;VALUE=DATE-TIME:20230516T210000Z
DTEND;VALUE=DATE-TIME:20230516T220000Z
DTSTAMP;VALUE=DATE-TIME:20240423T101436Z
UID:UCLAAnalysisSeminar/168
DESCRIPTION:Title: Ghost effect from Boltzmann theory\nby Lei Wu (Lehigh) a
s part of UCLA analysis and PDE seminar\n\nLecture held in Caltech.\n\nAbs
tract\nThe hydrodynamic limit aims to derive fluid equations (such\nas the
Euler and Navier-Stokes equations) from kinetic theory (such as the Boltz
mann and Landau equations) in a rigorous manner. This is a key ingredient
for addressing the Hilbert Sixth Problem. As the Knudsen number (which me
asures mean free path) approaches zero\, almost all standard fluid equatio
ns can be derived through proper scaling. Our work presents an unusual hyd
rodynamic limit that shows genuine kinetic effects\, known as the ghost ef
fect. The density and\ntemperature of order are coupled with the velocity
of order which acts like a "ghost" that can't be observed at the fluid l
evel. This suggests that standard fluid mechanics is incomplete in describ
ing many-particle systems even at the continuum regime. This is joint work
with Raffaele Esposito\, Yan Guo and Rossana Marra\, and is mainly based
on preprints https://arxiv.org/abs/2301.09427 and https://arxiv.org/abs/23
01.09560 .\n
LOCATION:https://researchseminars.org/talk/UCLAAnalysisSeminar/168/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Quentin Berger (Sorbonne)
DTSTART;VALUE=DATE-TIME:20230530T210000Z
DTEND;VALUE=DATE-TIME:20230530T220000Z
DTSTAMP;VALUE=DATE-TIME:20240423T101436Z
UID:UCLAAnalysisSeminar/169
DESCRIPTION:Title: The Stochastic Heat Equation with multiplicative Lévy noise
\nby Quentin Berger (Sorbonne) as part of UCLA analysis and PDE semina
r\n\n\nAbstract\nI will introduce the Stochastic Heat Equation with multip
licative noise and I will discuss its well-posedness and some of its prope
rties. This has been well studied when the noise is Gaussian but it is onl
y recently that the case of non-Gaussian (Lévy) noise has been considered
. \nThis is based on joint work with Carsten Chong (Columbia) and Hubert L
acoin (IMPA).\nDisclaimer: I come from a probability/statistical mechanics
background\, but I plan on introducing all objects that are not necessari
ly familiar to analysts.\n
LOCATION:https://researchseminars.org/talk/UCLAAnalysisSeminar/169/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hung Tran (U. Wisc. Madison)
DTSTART;VALUE=DATE-TIME:20240206T220000Z
DTEND;VALUE=DATE-TIME:20240206T230000Z
DTSTAMP;VALUE=DATE-TIME:20240423T101436Z
UID:UCLAAnalysisSeminar/170
DESCRIPTION:Title: Periodic homogenization of Hamilton-Jacobi equations: some r
ecent progress.\nby Hung Tran (U. Wisc. Madison) as part of UCLA analy
sis and PDE seminar\n\n\nAbstract\nI first give a quick introduction to fr
ont propagations\, Hamilton-Jacobi equations\, level-set forced mean curva
ture flows\, and homogenization theory. I will then show the optimal rates
of convergence for homogenization of both first-order and second-order Ha
milton-Jacobi equations. Based on joint works with J. Qian\, T. Sprekeler\
, and Y. Yu.\n
LOCATION:https://researchseminars.org/talk/UCLAAnalysisSeminar/170/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Changyou Wang (Purdue)
DTSTART;VALUE=DATE-TIME:20231010T210000Z
DTEND;VALUE=DATE-TIME:20231010T220000Z
DTSTAMP;VALUE=DATE-TIME:20240423T101436Z
UID:UCLAAnalysisSeminar/171
DESCRIPTION:Title: Analysis on Isotropic-Nematic Phase Transition and Liquid Cr
ystal Droplet\nby Changyou Wang (Purdue) as part of UCLA analysis and
PDE seminar\n\n\nAbstract\nIn this talk\, I will discuss the phase transit
ion phenomena between the isotropic and nematic states within the framewor
k of Ericksen theory of liquid crystals with variable degrees of orientati
ons. Treating it as the singular perturbation problems within the Gamma c
onvergence theory\, we will show that the sharp interface formed between i
sotropic and nematic states is an area minimizing surface. Under suitable
assumptions either on the strong anchoring boundary values on the boundary
of a bounded domain or the volume constraint of nematic regions in the en
tire space\, we also show that the limiting nematic liquid configuration i
n the nematic region is a minimizer of the corresponding Oseen-Frank energ
y with either homeotropic or planar anchoring on the free sharp interface
pending on the relative sizes of leading Frank elasticity coefficients. Th
is is a joint work with Fanghua Lin.\n
LOCATION:https://researchseminars.org/talk/UCLAAnalysisSeminar/171/
END:VEVENT
BEGIN:VEVENT
SUMMARY:James Leng (UCLA)
DTSTART;VALUE=DATE-TIME:20231017T210000Z
DTEND;VALUE=DATE-TIME:20231017T220000Z
DTSTAMP;VALUE=DATE-TIME:20240423T101436Z
UID:UCLAAnalysisSeminar/172
DESCRIPTION:Title: The equidistribution of nilsequences\nby James Leng (UCL
A) as part of UCLA analysis and PDE seminar\n\n\nAbstract\nConsider a Nilp
otent Lie group $G$ and a discrete subgroup $\\Gamma$ such that the topolo
gical quotient $G/\\Gamma$ is compact. Certain problems in arithmetic comb
inatorics are concerned with an equidistribution theory on $G/\\Gamma$. Th
is theory studies the behavior of orbits $g^n\\Gamma$ and classification o
f their limit sets in $G/\\Gamma$. \n\nIn 2012\, Green and Tao proved a qu
antitative equidistribution theory on $G/\\Gamma$\, achieving polynomial b
ounds on the rate of equidistribution and with exponent single exponential
in the dimension of $G$. In this talk\, we go over a recent result\, whic
h improves the bounds to have exponent polynomial in the dimension of $G$.
We also discuss implications of this result to arithmetic combinatorics.
A key obstruction that the proof of this result overcomes is "induction on
dimensions"\, which also seem to appear elsewhere in higher order Fourier
analysis over $\\mathbb{Z}/N\\mathbb{Z}$.\n
LOCATION:https://researchseminars.org/talk/UCLAAnalysisSeminar/172/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rowan Killip (UCLA)
DTSTART;VALUE=DATE-TIME:20231003T210000Z
DTEND;VALUE=DATE-TIME:20231003T220000Z
DTSTAMP;VALUE=DATE-TIME:20240423T101436Z
UID:UCLAAnalysisSeminar/173
DESCRIPTION:Title: The Benjamin--Ono equation\nby Rowan Killip (UCLA) as pa
rt of UCLA analysis and PDE seminar\n\n\nAbstract\nThe BO equation is an e
ffective model for interfacial waves in fluids of infinite depth. Like its
shallow-water cousin\, the Korteweg--de Vries equation\, BO is completely
integrable\; however\, the relevant spectral theory is far removed from t
he comfortable familiarity of Sturm--Liouville equations. After describing
this model and its integrable structures\, we will then present a sharp w
ell-posedness theory and a slew of new virial-type identities. This talk i
s based on joint work with Thierry Laurens and Monica Visan.\n
LOCATION:https://researchseminars.org/talk/UCLAAnalysisSeminar/173/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matthew Jacobs (U. Michigan)
DTSTART;VALUE=DATE-TIME:20231128T220000Z
DTEND;VALUE=DATE-TIME:20231128T230000Z
DTSTAMP;VALUE=DATE-TIME:20240423T101436Z
UID:UCLAAnalysisSeminar/174
DESCRIPTION:Title: Lagrangian solutions to the Porous Media Equation (and frien
ds)\nby Matthew Jacobs (U. Michigan) as part of UCLA analysis and PDE
seminar\n\n\nAbstract\nMany works have been devoted to understanding and p
redicting the time evolution of a growing population of cells (bacterial c
olonies\, tumors\, etc...). At the macroscopic scale\, cell growth is ty
pically modeled through Porous Media type equations that describe the chan
ge in cell density. While these cell growth PDEs have been studied since t
he 70s\, our understanding is far from complete\, particularly in the case
where there are several distinct cell populations.\n\nAn important open q
uestion is whether it is possible for two populations that were separated
at initial time to become mixed during the flow. For instance\, can tumor
cells get mixed into healthy cell regions? \n\nIn this talk\, I will show
that it is possible to construct non-mixing solutions to these equations.
The key is to construct the Lagrangian flow map along the pressure gradi
ent generated by the Porous Media Equation. The main obstruction is the f
act that the pressure gradient is not sufficiently regular to apply any ge
neric theory for Lagrangian flows. To overcome this difficulty\, we devel
op a new argument combining features of the Porous Media Equation with the
quantitative Lagrangian flow theory of Crippa and De Lellis.\n
LOCATION:https://researchseminars.org/talk/UCLAAnalysisSeminar/174/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrew Lawrie (MIT)
DTSTART;VALUE=DATE-TIME:20231107T210000Z
DTEND;VALUE=DATE-TIME:20231107T220000Z
DTSTAMP;VALUE=DATE-TIME:20240423T101436Z
UID:UCLAAnalysisSeminar/175
DESCRIPTION:Title: Dynamics of kink clusters for scalar fields in dimension 1+1
\nby Andrew Lawrie (MIT) as part of UCLA analysis and PDE seminar\n\n\
nAbstract\nI will present joint work with Jacek Jendrej. We consider class
ical scalar fields in dimension 1+1 with a symmetric double-well self-inte
raction potential\, covering\, for example\, the phi-4 model and the sine-
Gordon equation. Such equations admit non-trivial static solutions called
kinks and antikinks. We define a kink cluster to be a solution approaching
\, for large positive times\, a superposition of alternating kinks and ant
ikinks whose velocities converge to zero and mutual distances grow to infi
nity. Our main result is a determination of the leading order asymptotic b
ehavior of any kink cluster. Our results are partially inspired by the not
ion of "parabolic motions" in the Newtonian n-body problem. We explain thi
s analogy and its limitations. We also explain the role of kink clusters a
s universal profiles for the formation/annihilation of multi-kink configur
ations.\n
LOCATION:https://researchseminars.org/talk/UCLAAnalysisSeminar/175/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tongou Yang (UCLA)
DTSTART;VALUE=DATE-TIME:20231003T220000Z
DTEND;VALUE=DATE-TIME:20231003T230000Z
DTSTAMP;VALUE=DATE-TIME:20240423T101436Z
UID:UCLAAnalysisSeminar/176
DESCRIPTION:Title: Maximal planar Radon transform via local smoothing\, and an
elliptical maximal operator\nby Tongou Yang (UCLA) as part of UCLA ana
lysis and PDE seminar\n\n\nAbstract\nWe prove maximal operator bounds for
a multi-parameter family of nondegnerate planar curves via local smoothing
. Using a slight twist\, we are also able to obtain a sharp estimate on th
e unrotated elliptical maximal operator. This is joint work with Shaoming
Guo and Mingfeng Chen.\n
LOCATION:https://researchseminars.org/talk/UCLAAnalysisSeminar/176/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jake Fillman (Texas State)
DTSTART;VALUE=DATE-TIME:20231020T200000Z
DTEND;VALUE=DATE-TIME:20231020T210000Z
DTSTAMP;VALUE=DATE-TIME:20240423T101436Z
UID:UCLAAnalysisSeminar/177
DESCRIPTION:Title: The Spectrum of the Unitary Almost-Mathieu Operator\nby
Jake Fillman (Texas State) as part of UCLA analysis and PDE seminar\n\nLec
ture held in Math 6943.\n\nAbstract\nWe introduce the unitary almost-Mathi
eu operator\, which is a family of one-dimensional quasi-periodic quantum
walks obtained from an isotropic two-dimensional quantum walk in a uniform
magnetic field. This operator family exhibits several remarkable features
: its spectrum is a Cantor subset of the unit circle\, and it experiences
a metal-insulator transition as the strength of the hopping terms is varie
d. We will discuss background information\, the origins of the model\, its
interesting spectral features\, and some key ideas needed in proofs of th
e main results. [Joint work with Christopher Cedzich\, Darren C. Ong\, and
Zhenghe Zhang]\n\nNote: due to technical issues it may not be possible to
livestream this talk.\n
LOCATION:https://researchseminars.org/talk/UCLAAnalysisSeminar/177/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tristan Buckmaster (NYU)
DTSTART;VALUE=DATE-TIME:20231114T210000Z
DTEND;VALUE=DATE-TIME:20231114T220000Z
DTSTAMP;VALUE=DATE-TIME:20240423T101436Z
UID:UCLAAnalysisSeminar/178
DESCRIPTION:Title: Smooth Imploding Solutions for 3D Compressible Fluids\nb
y Tristan Buckmaster (NYU) as part of UCLA analysis and PDE seminar\n\n\nA
bstract\nIn recent work by Merle-Rodnianski-Szeftel\, the authors construc
ted smooth self-similar imploding solutions to the isentropic compressible
Euler equations for almost every adiabatic exponent. The result was also
used to construct asymptotically self-similar imploding solutions to the c
ompressible Navier-Stokes equations for the case of mildly decaying densit
y at infinity. The papers left open two natural questions: whether exact s
elf-similar imploding solutions exist for all adiabatic exponents and whet
her singularities can form for the compressible Navier-Stokes equations in
the case of density constant at infinity. During this talk I will present
joint work with Gonzalo Cao-Labora and Javier Gomez-Serrano that will res
olve both of these questions.\n
LOCATION:https://researchseminars.org/talk/UCLAAnalysisSeminar/178/
END:VEVENT
BEGIN:VEVENT
SUMMARY:John Garnett (UCLA)
DTSTART;VALUE=DATE-TIME:20231107T220000Z
DTEND;VALUE=DATE-TIME:20231107T230000Z
DTSTAMP;VALUE=DATE-TIME:20240423T101436Z
UID:UCLAAnalysisSeminar/179
DESCRIPTION:Title: H^1-BMO duality revisited\nby John Garnett (UCLA) as pa
rt of UCLA analysis and PDE seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/UCLAAnalysisSeminar/179/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Max Engelstein (U. Minnesota)
DTSTART;VALUE=DATE-TIME:20231205T210000Z
DTEND;VALUE=DATE-TIME:20231205T220000Z
DTSTAMP;VALUE=DATE-TIME:20240423T101436Z
UID:UCLAAnalysisSeminar/180
DESCRIPTION:Title: The Robin problem on rough domains\nby Max Engelstein (U
. Minnesota) as part of UCLA analysis and PDE seminar\n\n\nAbstract\nRobin
boundary conditions for elliptic operators model a diffusion contained by
a semipermeable membrane (think oxygen being absorbed into the lung). Des
pite huge advances in understanding both the Neumann and Dirichlet problem
s in rough domains\, the Robin problem is still mostly not understood. \n\
nWe construct a ``Robin harmonic measure" for any elliptic operator in a b
road class of domains and prove the surprising fact that this measure is m
utually absolutely continuous with respect to surface measure\, even when
the boundary of the domain is fractal. Along the way we will also address
some older conjectures about partially reflecting Brownian motion.\n\nThis
is joint work with Guy David (Paris Saclay)\, Stefano Decio (IAS)\, Svitl
ana Mayboroda (ETH/UMN) and Marco Michetti (Paris Saclay).\n
LOCATION:https://researchseminars.org/talk/UCLAAnalysisSeminar/180/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zaher Hani (U. Michigan)
DTSTART;VALUE=DATE-TIME:20240227T210000Z
DTEND;VALUE=DATE-TIME:20240227T220000Z
DTSTAMP;VALUE=DATE-TIME:20240423T101436Z
UID:UCLAAnalysisSeminar/181
DESCRIPTION:Title: Hilbert’s sixth problem for nonlinear waves\nby Zaher
Hani (U. Michigan) as part of UCLA analysis and PDE seminar\n\n\nAbstract\
nHilbert’s sixth problem asks for a mathematically rigorous justificatio
n of the macroscopic laws of statistical physics from the microscopic laws
of dynamics. The classical setting of this problem asks for the justifica
tion of Boltzmann’s kinetic equation from Newtonian particle dynamics. T
his justification has been proven for short times\, starting with the work
of Lanford in 1975\, but its long time justification remains one of the b
iggest open problems in kinetic theory.\n
LOCATION:https://researchseminars.org/talk/UCLAAnalysisSeminar/181/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Linfeng Li (UCLA)
DTSTART;VALUE=DATE-TIME:20231031T210000Z
DTEND;VALUE=DATE-TIME:20231031T220000Z
DTSTAMP;VALUE=DATE-TIME:20240423T101436Z
UID:UCLAAnalysisSeminar/182
DESCRIPTION:Title: A regularity result for the free boundary compressible Euler
equations of a liquid\nby Linfeng Li (UCLA) as part of UCLA analysis
and PDE seminar\n\n\nAbstract\nWe derive a priori estimates for the compre
ssible free boundary Euler equations in the case of a liquid without surfa
ce tension. We provide a new weighted functional framework which leads to
the improved regularity of the flow map by using the Hardy inequality. One
of main ideas is to decompose the initial density function. It is worth m
entioning that in our analysis we do not need the higher order wave equati
on for the density.\n
LOCATION:https://researchseminars.org/talk/UCLAAnalysisSeminar/182/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jesse Gell-Redman (U. Melbourne)
DTSTART;VALUE=DATE-TIME:20240109T220000Z
DTEND;VALUE=DATE-TIME:20240109T230000Z
DTSTAMP;VALUE=DATE-TIME:20240423T101436Z
UID:UCLAAnalysisSeminar/183
DESCRIPTION:Title: Microlocal methods in scattering for nonlinear evolution equ
ations\nby Jesse Gell-Redman (U. Melbourne) as part of UCLA analysis a
nd PDE seminar\n\nLecture held in MS 6627.\n\nAbstract\nI will discuss a n
ew methodology for proving small data scattering for the nonlinear Schröd
inger equation\, which avoids the use of Strichartz estimates\, and uses i
nstead methods from microlocal analysis. This methodology is flexible and
can in principle be applied to massive wave propagation as in the Klein-G
ordon or massive Dirac equations. This is joint work with Andrew Hassell
and Sean Gomes and with Dean Baskin and Moritz Doll\n
LOCATION:https://researchseminars.org/talk/UCLAAnalysisSeminar/183/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ruixiang Zhang (UC Berkeley)
DTSTART;VALUE=DATE-TIME:20240305T210000Z
DTEND;VALUE=DATE-TIME:20240305T220000Z
DTSTAMP;VALUE=DATE-TIME:20240423T101436Z
UID:UCLAAnalysisSeminar/184
DESCRIPTION:Title: A new conjecture to unify Fourier restriction and Bochner-Ri
esz\nby Ruixiang Zhang (UC Berkeley) as part of UCLA analysis and PDE
seminar\n\nLecture held in MS 6627.\n\nAbstract\nThe Fourier restriction c
onjecture and the Bochner-Riesz conjecture ask for Lebesgue space mapping
properties of certain oscillatory integral operators. They both are centra
l in harmonic analysis\, are open in dimensions $\\geq 3$\, and notably ha
ve the same conjectured exponents. In the 1970s\, H\\"{o}rmander asked if
a more general class of operators (known as H\\"{o}rmander type operators)
all satisfy the same $L^p$-boundedness as in the above two conjectures. A
positive answer to H\\"{o}rmander's question would resolve the above two
conjectures and have more applications such as in the manifold setting. Un
fortunately H\\"{o}rmander's question is known to fail in all dimensions $
\\geq 3$ by the work of Bourgain and many others. It continues to fail in
all dimensions $\\geq 3$ even if one adds a ``positive curvature'' assumpt
ion which one does have in restriction and Bochner-Riesz settings. Bourgai
n showed that in dimension $3$ one always has the failure unless a derivat
ive condition is satisfied everywhere. Joint with Shaoming Guo and Hong Wa
ng\, we generalize this condition to arbitrary dimension and call it ``Bou
rgain's condition''. We unify Fourier restriction and Bochner-Riesz by con
jecturing that any H\\"{o}rmander type operator satisfying Bourgain's cond
ition should have the same $L^p$-boundedness as in those two conjectures.
As evidence\, we prove that the failure of Bourgain's condition immediatel
y implies the failure of such an $L^p$-boundedness in every dimension. We
also prove that current techniques on the two conjectures apply equally we
ll in our conjecture and make some progress on our conjecture that consequ
ently improves the two conjectures in higher dimensions. I will talk about
some history and some interesting components in our proof.\n
LOCATION:https://researchseminars.org/talk/UCLAAnalysisSeminar/184/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Benjamin Royce Pineau (UC Berkeley)
DTSTART;VALUE=DATE-TIME:20231128T190000Z
DTEND;VALUE=DATE-TIME:20231128T200000Z
DTSTAMP;VALUE=DATE-TIME:20240423T101436Z
UID:UCLAAnalysisSeminar/185
DESCRIPTION:Title: Sharp Hadamard well-posedness for the incompressible free bo
undary Euler equations\nby Benjamin Royce Pineau (UC Berkeley) as part
of UCLA analysis and PDE seminar\n\nLecture held in MS 6627.\n\nAbstract\
nI will talk about a recent preprint in which we establish an optimal loca
l well-posedness theory in $H^s$ based Sobolev spaces for the free boundar
y incompressible Euler equations on a connected fluid domain. Some compone
nts of this result include: (i) Local well-posedness in the Hadamard sense
\, i.e.\, local existence\, uniqueness\, and the first proof of continuous
dependence on the data\, all in low regularity Sobolev spaces\; (ii) Enha
nced uniqueness: A uniqueness result which holds at the level of the Lipsc
hitz norm of the velocity and the $C^{1\,\\frac{1}{2}}$ regularity of the
free surface\; (iii) Stability bounds: We construct a nonlinear functiona
l which measures\, in a suitable sense\, the distance between two solution
s (even when defined on different domains) and we show that this distance
is propagated by the flow\; (iv) Energy estimates: We prove essentially sc
ale invariant energy estimates for solutions\, relying on a newly const
ructed family of refined elliptic estimates\; (v) Continuation criterion:
We give the first proof of a continuation criterion at the same scale as t
he classical Beale-Kato-Majda criterion for the Euler equation on the whol
e space. Roughly speaking\, we show that solutions can be continued as lon
g as the velocity is in $L_T^1W^{1\,\\infty}$ and the free surface is in $
L_T^1C^{1\,\\frac{1}{2}}$\; (vi) A novel proof of the construction of reg
ular solutions. \n \n Our entire approach is in the Eulerian framework and
can be adapted to work in relatively general fluid domains. This is based
on joint work with Mihaela Ifrim\, Daniel Tataru and Mitchell Taylor.\n
LOCATION:https://researchseminars.org/talk/UCLAAnalysisSeminar/185/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Katie Marsden (EPFL)
DTSTART;VALUE=DATE-TIME:20240109T210000Z
DTEND;VALUE=DATE-TIME:20240109T220000Z
DTSTAMP;VALUE=DATE-TIME:20240423T101436Z
UID:UCLAAnalysisSeminar/186
DESCRIPTION:Title: Global Solutions for the Half-Wave Maps Equation at Critical
Regularity\nby Katie Marsden (EPFL) as part of UCLA analysis and PDE
seminar\n\nLecture held in MS 6627.\n\nAbstract\nIn this talk I will discu
ss a small data-global wellposedness result for the three-dimensional Half
-Wave Maps equation in the critical Besov space. The Half-Wave Maps equati
on is a nonlocal equation into the sphere\, with a close link to the bette
r-known Wave Maps equation. The global wellposedness in dimensions greater
than or equal to 4 is already known\, however the 3 dimensional case pres
ents new difficulties due to the loss of a key Strichartz estimate. To ove
rcome this we use a simplified version of Tao’s gauge transformation for
the wave maps equation\, and a new argument involving commuting vector fi
elds and Sterbenz’s improved Strichartz estimates for functions with ang
ular regularity. Naturally the use of these estimates comes at a cost\, an
d we are forced to assume additional angular regularity on the initial dat
a.\n
LOCATION:https://researchseminars.org/talk/UCLAAnalysisSeminar/186/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rena Badreddine (U. Paris-Saclay)
DTSTART;VALUE=DATE-TIME:20240116T210000Z
DTEND;VALUE=DATE-TIME:20240116T220000Z
DTSTAMP;VALUE=DATE-TIME:20240423T101436Z
UID:UCLAAnalysisSeminar/187
DESCRIPTION:Title: The Calogero-Sutherland Derivative NLS Equation\nby Rena
Badreddine (U. Paris-Saclay) as part of UCLA analysis and PDE seminar\n\n
Lecture held in MS 6627.\n\nAbstract\nWe consider a type of nonlocal nonli
near derivative\nSchrödinger equation on the torus\, called the Calogero-
Sutherland DNLS\nequation. We derive an explicit formula to the solution o
f this\nnonlinear PDE. Moreover\, using the integrability tools\, we estab
lish\nthe global well-posedness of this equation in all the Hardy-Sobolev\
nspaces $H^s_+(\\mathbb{T})$\, $s\\geq 0$\, down to the critical regularit
y\nspace\, and under a mass assumption on the initial data for the\nfocusi
ng equation\, and for arbitrary initial data for the defocusing\nequation.
Finally\, a sketch of the proof for extending the flow to the\ncritical r
egularity $L^2_+(\\mathbb{T})$ will be presented.\n
LOCATION:https://researchseminars.org/talk/UCLAAnalysisSeminar/187/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dominique Maldague (MIT)
DTSTART;VALUE=DATE-TIME:20240109T190000Z
DTEND;VALUE=DATE-TIME:20240109T200000Z
DTSTAMP;VALUE=DATE-TIME:20240423T101436Z
UID:UCLAAnalysisSeminar/188
DESCRIPTION:Title: Wave envelope estimates in Fourier restriction theory\nb
y Dominique Maldague (MIT) as part of UCLA analysis and PDE seminar\n\nLec
ture held in MS 6627.\n\nAbstract\nWave packet decomposition allows us to
express functions with restricted frequency support as a superposition of
wave packets (simpler functions which are localized in both space and freq
uency)\, with one "active" wave packet per direction. I will explain the s
ignificance of a new type of inequality called a wave envelope estimate\,
which provides detailed information about the possible overlap patterns of
wave packets that maximize the L^p norm. Wave envelope estimates were fir
st introduced in the work of Guth-Wang-Zhang (GWZ) proving the sharp L^4 s
quare function estimate for the cone in R^3. Guth-Maldague subsequently in
troduced a stopping time algorithm based on the amplitude of the function
compared to its square function which yielded a refined version of the GWZ
wave envelope estimates. Our so-called amplitude-dependent wave envelope
estimate simultaneously implies both sharp decoupling and sharp square fun
ction estimates. Applications include sharp small cap decoupling estimates
for the cone\, new estimates for the size of exceptional sets in the 3D r
estricted projections problem\, and a sharp multiplier-type problem for th
e moment curve.\n
LOCATION:https://researchseminars.org/talk/UCLAAnalysisSeminar/188/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kyeongsik Nam (KAIST)
DTSTART;VALUE=DATE-TIME:20240206T210000Z
DTEND;VALUE=DATE-TIME:20240206T220000Z
DTSTAMP;VALUE=DATE-TIME:20240423T101436Z
UID:UCLAAnalysisSeminar/189
DESCRIPTION:Title: Universality of log-correlated fields\nby Kyeongsik Nam
(KAIST) as part of UCLA analysis and PDE seminar\n\nLecture held in MS 662
7.\n\nAbstract\nLog-correlation naturally appears in diverse objects such
as random matrices and random discrete geometries. In this talk\, I will g
ive an overview on the theory of log-correlated fields and talk about rece
nt progress on it. This is based on the joint work with Shirshendu Ganguly
.\n
LOCATION:https://researchseminars.org/talk/UCLAAnalysisSeminar/189/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lars Becker (Bonn)
DTSTART;VALUE=DATE-TIME:20240123T210000Z
DTEND;VALUE=DATE-TIME:20240123T220000Z
DTSTAMP;VALUE=DATE-TIME:20240423T101436Z
UID:UCLAAnalysisSeminar/190
DESCRIPTION:Title: A degree one Carleson operator along the paraboloid\nby
Lars Becker (Bonn) as part of UCLA analysis and PDE seminar\n\nLecture hel
d in MS 6627.\n\nAbstract\nCarleson proved in 1966 that the Fourier series
of any square integrable\nfunction converges pointwise to the function\,
by establishing boundedness\nof the maximally modulated Hilbert transform
from L^2 into weak L^2. This\ntalk is about a generalization of his result
\, where the Hilbert transform\nis replaced by a singular integral operato
r along a paraboloid.\nI will review the history of extensions of Carleson
's theorem\, and then\ndiscuss the two main ingredients needed to deduce o
ur result: sparse\nbounds for singular integrals along the paraboloid\, an
d a square function\nargument relying on the geometry of the paraboloid.\n
LOCATION:https://researchseminars.org/talk/UCLAAnalysisSeminar/190/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fei Xu (Jilin University)
DTSTART;VALUE=DATE-TIME:20240123T200000Z
DTEND;VALUE=DATE-TIME:20240123T210000Z
DTSTAMP;VALUE=DATE-TIME:20240423T101436Z
UID:UCLAAnalysisSeminar/191
DESCRIPTION:Title: On the Nonlinear Schr\\"odinger Equation with Quasi-periodic
Initial Data\nby Fei Xu (Jilin University) as part of UCLA analysis a
nd PDE seminar\n\nLecture held in MS 6627.\n\nAbstract\nThis talk discusse
s the (derivative) NLS with quasi-periodic initial data. It is dedicated t
o the memory of Thomas Kappeler\, who proposed this problem in 2021. We fi
rst discuss recent progress on the Deift conjecture and almost periodic fu
nctions. Then we consider the (derivative) nonlinear Schr\\"odinger equati
on with quasi-periodic initial data. Under (exponential) polynomial decay
assumption in the Fourier space for the initial Fourier data\, this Cauchy
problem has a unique local-in-time solution that retains the spatial quas
i-periodicity. To this end\, we use a new combinatorial analysis method an
d introduce the so-called Feynman diagram. Finally\, some remarks on the g
lobal problem are given.\n
LOCATION:https://researchseminars.org/talk/UCLAAnalysisSeminar/191/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Theo Sturm (Bonn)
DTSTART;VALUE=DATE-TIME:20240130T210000Z
DTEND;VALUE=DATE-TIME:20240130T220000Z
DTSTAMP;VALUE=DATE-TIME:20240423T101436Z
UID:UCLAAnalysisSeminar/192
DESCRIPTION:Title: Wasserstein Diffusion on Multidimensional Spaces\nby The
o Sturm (Bonn) as part of UCLA analysis and PDE seminar\n\nLecture held in
MS 6627.\n\nAbstract\nGiven any closed Riemannian manifold $M$\, we const
ruct a reversible diffusion process\non the space $P(M)$ of probability me
asures on $M$ that is\n• reversible w.r.t. the entropic measure $P^\\bet
a$ on $P(M)$\, heuristically given as\n$$ dP^\\beta(\\mu) = \\frac{1}{Z} e
^{-\\beta \\mathrm{Ent}(\\mu|m)}\\ dP^0(\\mu)\;$$\n• associated with a r
egular Dirichlet form with carre du champ derived from the Wasserstein\ngr
adient in the sense of Otto calculus\n$$ E_W (f) = \\lim \\inf_{\\tilde f
\\to f} \\frac{1}{2} \\int_{P(M)} \\| \\nabla_W \\tilde f\\|^2(\\mu)\\ dP^
\\beta(\\mu).$$\n• non-degenerate\, at least in the case of the n-sphere
and the n-torus.\n
LOCATION:https://researchseminars.org/talk/UCLAAnalysisSeminar/192/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Noemi David (Lyon)
DTSTART;VALUE=DATE-TIME:20240402T200000Z
DTEND;VALUE=DATE-TIME:20240402T210000Z
DTSTAMP;VALUE=DATE-TIME:20240423T101436Z
UID:UCLAAnalysisSeminar/193
DESCRIPTION:Title: Convergence rates for the incompressible limit of nonlinear
diffusion equations\nby Noemi David (Lyon) as part of UCLA analysis an
d PDE seminar\n\nLecture held in MS 6627.\n\nAbstract\nNowadays a vast lit
erature is available on the Hele-Shaw or incompressible limit for nonlinea
r degenerate diffusion equations. This problem has attracted a lot of atte
ntion due to its applications to tissue growth and crowd motion modelling
as it constitutes a way to link soft congestion (or compressible) models t
o hard congestion (or incompressible) descriptions. Nevertheless\, little
is known about the rate of convergence of this asymptotic. In this talk\,
I will address the question of estimating the rate in the presence of exte
rnal drifts. In a joint work with Tomasz Dębiec and Benoit Perthame\, we
computed the rate in a negative Sobolev norm for generic bounded potential
s\, while in a work in progress with Alpár Mészáros and Filippo Santamb
rogio\, we provide improved results in the 2-Wasserstein distance which ar
e global in time thanks to the contractivity property that holds for stric
tly convex potentials. I will present these two results\, which hold both
for the barotropic pressure law (hence the porous medium equation) and for
a singular pressure law with density constraints.\n
LOCATION:https://researchseminars.org/talk/UCLAAnalysisSeminar/193/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ovidiu-Neculai Avadanei (Berkeley)
DTSTART;VALUE=DATE-TIME:20240430T200000Z
DTEND;VALUE=DATE-TIME:20240430T210000Z
DTSTAMP;VALUE=DATE-TIME:20240423T101436Z
UID:UCLAAnalysisSeminar/194
DESCRIPTION:by Ovidiu-Neculai Avadanei (Berkeley) as part of UCLA analysis
and PDE seminar\n\nInteractive livestream: https://ucla.zoom.us/j/9264073
849\nLecture held in MS 6627.\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/UCLAAnalysisSeminar/194/
URL:https://ucla.zoom.us/j/9264073849
END:VEVENT
BEGIN:VEVENT
SUMMARY:Antoine Mellet (U. Maryland)
DTSTART;VALUE=DATE-TIME:20240319T200000Z
DTEND;VALUE=DATE-TIME:20240319T210000Z
DTSTAMP;VALUE=DATE-TIME:20240423T101436Z
UID:UCLAAnalysisSeminar/196
DESCRIPTION:Title: On the regularity of optimal transportation potentials with
discrete measures\nby Antoine Mellet (U. Maryland) as part of UCLA ana
lysis and PDE seminar\n\nLecture held in MS 6627.\n\nAbstract\nWe consider
a Kantorovich potential associated to an optimal transportation problem b
etween measures that are not necessarily absolutely continuous with respec
t to the Lebesgue measure\, but are comparable to the Lebesgue measure whe
n restricted to balls with radius greater than some $\\delta>0$. Such a fr
amework is very natural in the context of the numerical computations of op
timal maps\, which often involves approximating "nice" measures by sums of
Dirac masses.\n\nWe will present some recent results (collaboration with
P.E. Jabin and M. Molina) which extend the classical regularity theory of
optimal transportation to this framework. In particular\, we establish bot
h Hölder and Sobolev regularity results for Kantorovich potentials up to
some critical length scale depending on $\\delta$.\n
LOCATION:https://researchseminars.org/talk/UCLAAnalysisSeminar/196/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michael Hitrik (UCLA)
DTSTART;VALUE=DATE-TIME:20240409T200000Z
DTEND;VALUE=DATE-TIME:20240409T210000Z
DTSTAMP;VALUE=DATE-TIME:20240423T101436Z
UID:UCLAAnalysisSeminar/197
DESCRIPTION:Title: Magic angles and classically forbidden regions for twisted b
ilayer graphene\nby Michael Hitrik (UCLA) as part of UCLA analysis and
PDE seminar\n\nLecture held in MS 6627.\n\nAbstract\nMagic angles are a t
opic of current interest in condensed matter physics and refer to a remark
able theoretical (Bistritzer--MacDonald\, 2011) and experimental (Jarillo-
Herrero et al\, 2018) discovery: two sheets of graphene twisted by a certa
in (magic) angle display unusual electronic properties\, such as supercond
uctivity. In this talk\, we shall discuss a simple periodic Hamiltonian de
scribing the chiral limit of twisted bilayer graphene (Tarnopolsky-Kruchko
v-Vishwanath\, 2019)\, whose spectral properties are thought to determine
which angles are magical. We show that the corresponding eigenfunctions de
cay exponentially in suitable geometrically determined regions as the angl
e of twisting decreases\, which can be viewed as a form of semiclassical a
nalytic hypoellipticity. This is joint work with Maciej Zworski.\n
LOCATION:https://researchseminars.org/talk/UCLAAnalysisSeminar/197/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shi Zhuo Looi (Caltech)
DTSTART;VALUE=DATE-TIME:20240213T210000Z
DTEND;VALUE=DATE-TIME:20240213T220000Z
DTSTAMP;VALUE=DATE-TIME:20240423T101436Z
UID:UCLAAnalysisSeminar/198
DESCRIPTION:Title: Fourier-based and physical approaches to late-time asymptoti
cs of hyperbolic PDE\nby Shi Zhuo Looi (Caltech) as part of UCLA analy
sis and PDE seminar\n\nLecture held in MS 6627.\n\nAbstract\nWe present an
algorithm for deriving the precise and sharp asymptotics of linear and no
n-linear wave equations on asymptotically flat spacetimes\, including non-
stationary spacetimes without any spherical symmetry assumptions. Some fea
tures of our proofs include integrated local energy decay and a weighted v
ersion thereof\, spectral-theoretic methods involving resolvent expansions
near zero energy\, and a method called geometric singular analysis\, whic
h distinguishes between different scales of the spacetime.\n
LOCATION:https://researchseminars.org/talk/UCLAAnalysisSeminar/198/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jani Virtanen (U. Reading)
DTSTART;VALUE=DATE-TIME:20240312T200000Z
DTEND;VALUE=DATE-TIME:20240312T210000Z
DTSTAMP;VALUE=DATE-TIME:20240423T101436Z
UID:UCLAAnalysisSeminar/199
DESCRIPTION:Title: Asymptotics of block Toeplitz determinants with piecewise co
ntinuous symbols\nby Jani Virtanen (U. Reading) as part of UCLA analys
is and PDE seminar\n\nLecture held in MS 6627.\n\nAbstract\nA Toeplitz mat
rix can be easily defined as a matrix constant along the parallels to the
main diagonal given by the Fourier coefficients of an integrable function
(referred to as the symbol) on the unit circle. The study of the determina
nts of Toeplitz matrices dates back to Szegő\, who described their asympt
otic behavior for sufficiently smooth symbols in 1915 and 1952. The latter
result was generalized to the case of matrix-valued symbols by Widom in t
he 1970s using operator theoretic methods. In the scalar case\, the asympt
otic behavior of Toeplitz determinants with Fisher-Hartwig symbols\, which
allow for zeros\, (integrable) singularities\, discontinuities\, and nonz
ero winding numbers\, was described completely by Deift\, Its\, and Krasov
sky in 2011 using the Riemann-Hilbert approach. In this talk\, I discuss t
he case of matrix-valued symbols that have finitely many discontinuities a
nd some of their applications\, such as the study of entanglement entropy
in quantum spin chain models. The approach is largely based on operator th
eoretic methods\, and it requires a new localization theorem for Toeplitz
determinants and a new method of computing the Fredholm index of Toeplitz
operators with piecewise continuous matrix-valued symbols. Joint work with
Estelle Basor and Torsten Ehrhardt.\n
LOCATION:https://researchseminars.org/talk/UCLAAnalysisSeminar/199/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jiajie Chen (Courant)
DTSTART;VALUE=DATE-TIME:20240312T210000Z
DTEND;VALUE=DATE-TIME:20240312T220000Z
DTSTAMP;VALUE=DATE-TIME:20240423T101436Z
UID:UCLAAnalysisSeminar/200
DESCRIPTION:Title: Nearly self-similar blowup of the slightly perturbed homogen
eous Landau equation with very soft potentials\nby Jiajie Chen (Couran
t) as part of UCLA analysis and PDE seminar\n\nLecture held in MS 6627.\n\
nAbstract\nWhether the Landau equation can develop a finite time singulari
ty is an important open problem in kinetic equations. In this talk\, we wi
ll first discuss several similarities between the Landau equation and some
incompressible fluids equations. Then we will focus on the slightly pertu
rbed homogeneous Landau equation with very soft potentials\, where we incr
ease the nonlinearity from $ c(f) f$ in the Landau equation to $\\alpha c(
f) f$ with $\\alpha>1$. For $\\alpha > 1 $ and close to $1$\, we establish
finite time nearly self-similar blowup from some smooth non-negative init
ial data\, which can be radially symmetric or non-radially symmetric. The
blowup results are sharp as the homogeneous Landau equation $(\\alpha=1)$
is globally well-posed\, which was recently established by Guillen and Sil
vestre. The proof builds on our previous framework on sharp blowup results
of the De Gregorio model with nearly self-similar singularity to overcome
the diffusion. Our results shed light on potential singularity formation
in the inhomogeneous setting\n
LOCATION:https://researchseminars.org/talk/UCLAAnalysisSeminar/200/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexandria Rose (ANU)
DTSTART;VALUE=DATE-TIME:20240425T200000Z
DTEND;VALUE=DATE-TIME:20240425T210000Z
DTSTAMP;VALUE=DATE-TIME:20240423T101436Z
UID:UCLAAnalysisSeminar/201
DESCRIPTION:Title: Lattice Covering Densities and Additive Combinatorics\nb
y Alexandria Rose (ANU) as part of UCLA analysis and PDE seminar\n\nLectur
e held in MS 6627.\n\nAbstract\nThe well-known Lattice Covering Problem as
ks for the most optimal way to cover the space $\\mathbb{R}^n$\, $n \\geq
2$\, by using copies of an Euclidean ball centered at points of a given la
ttice. More precisely\, consider a closed Euclidean ball $B$ and a lattice
$L \\subset \\mathbb{R}^d$\, we say that $L$ is a covering lattice for $B
$ if\n$$ \\mathbb{R}^n = L + B \\tag{1}$$\nThe {\\emph{covering density} $
\\displaystyle \\Theta (L)$ of whole space $\\mathbb{R}^n$ is defined as t
he minimal volume of a closed Euclidean Ball $B$ for which (1) holds. Defi
ne\n$$\\Theta_n := \\inf \\left \\{ \\Theta (L): L \\text{ is a lattice
in $\\mathbb{R}^n$ of covolume one} \\right \\} $$\nto be the minimal den
sity of lattice coverings of $\\mathbb{R}^n$. Where the covolume of $L$ is
the volume of its fundamental parallepipeds (sometimes refer as the deter
minant of $L$). Thus the Lattice Covering Problem asks for the best upper
bound for $\\displaystyle \\Theta_n$.\nSo far\, this problem has only been
studied geometrically using Kakeya-type methods to obtain results for con
vex bodies in place of balls. In this talk\, we make a connection between
lattice covering densities and additive combinatorics\, and consider the m
ore general setting of approximate groups and sets with low doubling or hi
gh additive energy. This is joint work with Francisco Romero Acosta.\n
LOCATION:https://researchseminars.org/talk/UCLAAnalysisSeminar/201/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zane Li (NCSU)
DTSTART;VALUE=DATE-TIME:20240507T210000Z
DTEND;VALUE=DATE-TIME:20240507T220000Z
DTSTAMP;VALUE=DATE-TIME:20240423T101436Z
UID:UCLAAnalysisSeminar/202
DESCRIPTION:by Zane Li (NCSU) as part of UCLA analysis and PDE seminar\n\n
Interactive livestream: https://ucla.zoom.us/j/9264073849\nLecture held in
MS 6627.\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/UCLAAnalysisSeminar/202/
URL:https://ucla.zoom.us/j/9264073849
END:VEVENT
BEGIN:VEVENT
SUMMARY:Allen Wu (Oklahoma)
DTSTART;VALUE=DATE-TIME:20240416T200000Z
DTEND;VALUE=DATE-TIME:20240416T210000Z
DTSTAMP;VALUE=DATE-TIME:20240423T101436Z
UID:UCLAAnalysisSeminar/203
DESCRIPTION:Title: The Scattering Problem of the Intermediate Long Wave Equatio
n\nby Allen Wu (Oklahoma) as part of UCLA analysis and PDE seminar\n\n
Lecture held in MS 6627.\n\nAbstract\nThe Intermediate Long Wave equation
(ILW) describes long internal gravity waves in stratified fluids. Kodama\,
Ablowitz and Satsuma discovered the formal complete integrability of ILW
and formulated inverse scattering transform solutions. If made rigorous\,
the inverse scattering method will provide powerful tools for asymptotic a
nalysis of ILW. In this talk\, I will present some recent results on the I
LW direct scattering problem. In particular\, a Lax pair formulation is cl
arified\, and the spectral theory of the Lax operators can be studied. Exi
stence and uniqueness of scattering states are established for small inter
action potential. The scattering matrix can then be constructed from the s
cattering states. The solution is related to the theory of analytic functi
ons on a strip. This is joint work with Peter Perry.\n
LOCATION:https://researchseminars.org/talk/UCLAAnalysisSeminar/203/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Iván Moyano (Université Côte-d'Azur)
DTSTART;VALUE=DATE-TIME:20240507T210000Z
DTEND;VALUE=DATE-TIME:20240507T220000Z
DTSTAMP;VALUE=DATE-TIME:20240423T101436Z
UID:UCLAAnalysisSeminar/204
DESCRIPTION:by Iván Moyano (Université Côte-d'Azur) as part of UCLA ana
lysis and PDE seminar\n\nInteractive livestream: https://ucla.zoom.us/j/92
64073849\nLecture held in MS 6627.\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/UCLAAnalysisSeminar/204/
URL:https://ucla.zoom.us/j/9264073849
END:VEVENT
END:VCALENDAR