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BEGIN:VEVENT
SUMMARY:Hong Wang (IAS)
DTSTART;VALUE=DATE-TIME:20200421T220000Z
DTEND;VALUE=DATE-TIME:20200421T230000Z
DTSTAMP;VALUE=DATE-TIME:20210120T055524Z
UID:UCLAAnalysisSeminar/1
DESCRIPTION:Title: Distinct distances for well-separated sets\nby Hong Wan
g (IAS) as part of UCLA analysis and PDE seminar\n\nLecture held in https:
//ucla.zoom.us/j/9264073849.\n\nAbstract\nGiven a set E of dimension s>1\,
Falconer conjectured that its distance set \\Delta(E)=\\{|x-y|: x\, y\\in
E\\} should have positive Lebesgue measure. Orponen\, Shmerkin and Keleti
-Shmerkin proved the conjecture for tightly spaced sets\, for example\, AD
-regular sets.\n\nIn this talk\, we are going to discuss the opposite type
: well-separated sets. This is joint work with Larry Guth and Noam Solomon
.\n
LOCATION:Lecture held in https://ucla.zoom.us/j/9264073849
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ioannis Angelopoulos (Caltech)
DTSTART;VALUE=DATE-TIME:20200421T230000Z
DTEND;VALUE=DATE-TIME:20200422T000000Z
DTSTAMP;VALUE=DATE-TIME:20210120T055524Z
UID:UCLAAnalysisSeminar/2
DESCRIPTION:Title: Semi-global constructions of vacuum spacetimes\nby Ioan
nis Angelopoulos (Caltech) as part of UCLA analysis and PDE seminar\n\nLec
ture held in https://ucla.zoom.us/j/9264073849.\n\nAbstract\nI will descri
be some techniques for constructing semi-global solutions to the character
istic initial value problem for the vacuum Einstein equations with differe
nt types of data\, and will also mention some applications as well as some
open problems in the area.\n
LOCATION:Lecture held in https://ucla.zoom.us/j/9264073849
END:VEVENT
BEGIN:VEVENT
SUMMARY:Joni Teravainen (Oxford)
DTSTART;VALUE=DATE-TIME:20200428T170000Z
DTEND;VALUE=DATE-TIME:20200428T180000Z
DTSTAMP;VALUE=DATE-TIME:20210120T055524Z
UID:UCLAAnalysisSeminar/3
DESCRIPTION:Title: Higher order uniformity of the Möbius function\nby Jon
i Teravainen (Oxford) as part of UCLA analysis and PDE seminar\n\nLecture
held in https://ucla.zoom.us/j/9264073849.\n\nAbstract\nRecently\, Matomä
ki\, Radziwiłł and Tao showed that the Möbius function is discorrelated
with linear exponential phases on almost all short intervals. I will disc
uss joint work where we generalize this result to a much wider class of ph
ase functions\, showing that the Möbius function does not correlate with
polynomial phases or more generally with nilsequences. I will also discuss
applications to superpolynomial word complexity for the Liouville sequenc
e and to counting polynomial patterns weighted by the Möbius function.\n
LOCATION:Lecture held in https://ucla.zoom.us/j/9264073849
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Beltran (U. Madison Wisconsin)
DTSTART;VALUE=DATE-TIME:20200505T220000Z
DTEND;VALUE=DATE-TIME:20200505T230000Z
DTSTAMP;VALUE=DATE-TIME:20210120T055524Z
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
seminar\n\nLecture held in https://caltech.zoom.us/j/747242458.\n\nAbstrac
t\nI will report some recent progress regarding the boundedness of the map
$f \\mapsto |\\nabla M_\\beta f|$ from the endpoint space $W^{1\,1}(\\mat
hbb{R}^d)$ to $L^{d/(d-\\beta)}(\\mathbb{R}^d)$\, where $M_\\beta$ denotes
the 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\, wh
ich allows to exploit the known techniques in the non-centered case.\n\nTh
is is joint work with José Madrid.\n
LOCATION:Lecture held in https://caltech.zoom.us/j/747242458
END:VEVENT
BEGIN:VEVENT
SUMMARY:Luca Spolaor (UCSD)
DTSTART;VALUE=DATE-TIME:20200505T230000Z
DTEND;VALUE=DATE-TIME:20200506T000000Z
DTSTAMP;VALUE=DATE-TIME:20210120T055524Z
UID:UCLAAnalysisSeminar/5
DESCRIPTION:Title: Regularity of the free boundary for the two-phase Berno
ulli problem\nby Luca Spolaor (UCSD) as part of UCLA analysis and PDE semi
nar\n\nLecture held in https://caltech.zoom.us/j/747242458.\n\nAbstract\nI
will describe a recent result obtained in collaboration with G. De Philip
pis and B. Velichkov concerning the regularity of the free boundaries in t
he two phase Bernoulli problems. The novelty of our work is the analysis o
f the free boundary at branch points\, where we show that it is given by t
he union of two C1 graphs. This completes the work started by Alt\, Caffar
elli\, and Friedman in the 80’s.\n
LOCATION:Lecture held in https://caltech.zoom.us/j/747242458
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dmitry Khavinson (U. South Florida)
DTSTART;VALUE=DATE-TIME:20200519T230000Z
DTEND;VALUE=DATE-TIME:20200520T000000Z
DTSTAMP;VALUE=DATE-TIME:20210120T055524Z
UID:UCLAAnalysisSeminar/6
DESCRIPTION:Title: Classical Potential Theory from the High Ground of Line
ar Holomorphic PDE\nby Dmitry Khavinson (U. South Florida) as part of UCLA
analysis and PDE seminar\n\nLecture held in https://ucla.zoom.us/j/926407
3849.\n\nAbstract\n"Between two truths of the real domain\, the easiest an
d shortest path quite often passes through the complex domain."\n\n
P. Painleve\, 1900.\n\n\nAbstract: \n\n
Newton noticed that the gravitational potential of a spherical mass with c
onstant density equals\, outside the ball\, the potential of the point-ma
ss at the center. Rephrasing\, the gravitational potential of the ball wi
th constant mass density continues as a harmonic function inside the ball
except for the center. Fairly recently\, it was noted that the latter stat
ement holds for any polynomial\, or even for entire densities.\n\nIf a har
monic in a spherical shell function vanishes on one piece of a line throug
h the 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 t
he Dirichlet problem in an ellipse with entire data\, the solution will al
ways be an entire harmonic function. Yet\, if we do that in a domain bound
ed by the curve x^4 + y^4 =1\, with the data as simple as x^2+y^2\, the so
lution will have infinitely many singularities outside the curve. \nWhere
and why do eigenfunctions of the Laplacian in domains bounded by algebraic
curves start having singularities?\n\nWe shall discuss these and some oth
er questions under the unified umbrella of analytic continuation of solut
ions to analytic pde in C^n.\n
LOCATION:Lecture held in https://ucla.zoom.us/j/9264073849
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kirsti Biggs (Chalmers U. Technology)
DTSTART;VALUE=DATE-TIME:20200526T170000Z
DTEND;VALUE=DATE-TIME:20200526T180000Z
DTSTAMP;VALUE=DATE-TIME:20210120T055524Z
UID:UCLAAnalysisSeminar/7
DESCRIPTION:Title: Ellipsephic efficient congruencing for the moment curve
\nby Kirsti Biggs (Chalmers U. Technology) as part of UCLA analysis and PD
E seminar\n\nLecture held in https://ucla.zoom.us/j/9264073849.\n\nAbstrac
t\nAn ellipsephic set is a subset of the natural numbers whose elements ha
ve digital restrictions in some fixed prime base. Such sets have a fractal
structure and can be viewed as p-adic Cantor sets. The particular ellipse
phic sets that interest us have certain additive properties - for example\
, the set of integers whose digits are squares forms a key motivating exam
ple\, because there are few representations of an integer as the sum of tw
o squares.\n\n\nWe obtain discrete restriction estimates for the moment cu
rve over ellipsephic sets—in number theoretic terms\, we bound the numbe
r of ellipsephic solutions to a Vinogradov system of equations—using Woo
ley’s nested efficient congruencing method. These results generalise pre
vious work of the speaker\, on the quadratic case of this problem\, to the
moment curve of arbitrary degree.\n
LOCATION:Lecture held in https://ucla.zoom.us/j/9264073849
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mihailis Kolountzakis (U. Crete)
DTSTART;VALUE=DATE-TIME:20200602T160000Z
DTEND;VALUE=DATE-TIME:20200602T165000Z
DTSTAMP;VALUE=DATE-TIME:20210120T055524Z
UID:UCLAAnalysisSeminar/8
DESCRIPTION:Title: Orthogonal Fourier analysis on domains: methods\, resul
ts and open problems\nby Mihailis Kolountzakis (U. Crete) as part of UCLA
analysis and PDE seminar\n\nLecture held in https://caltech.zoom.us/j/7472
42458.\n\nAbstract\nWe all know how to do Fourier Analysis on an interval\
, on {\\mathbb R}^d\, or other groups. But what if our functions live on a
subset 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
domain? In other words\, can we select a set of frequencies \\lambda such
that the corresponding exponentials form an orthogonal basis for L^2 of ou
r domain? It turns out that the existence of such an orthogonal basis depe
nds heavily on the domain. So the answer is yes\, we can find an orthogona
l basis 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
1970s that the existence of such an exponential basis is equivalent to the
domain being able to tile space by translations (the hexagon\, that we me
ntioned\, indeed can tile\, while the disk cannot). In this talk we will t
rack 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
successes in our efforts to understand exponential bases. We will emphasiz
e several problems that are still open.\n
LOCATION:Lecture held in https://caltech.zoom.us/j/747242458
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yakov Shlapentokh-Rothman (Princeton)
DTSTART;VALUE=DATE-TIME:20200602T170000Z
DTEND;VALUE=DATE-TIME:20200602T180000Z
DTSTAMP;VALUE=DATE-TIME:20210120T055524Z
UID:UCLAAnalysisSeminar/9
DESCRIPTION:Title: Naked Singularities for the Einstein Vacuum Equations:
The Exterior Solution\nby Yakov Shlapentokh-Rothman (Princeton) as part of
UCLA analysis and PDE seminar\n\nLecture held in https://caltech.zoom.us/
j/747242458.\nAbstract: TBA\n\nWe will start by recalling the weak cosmic
censorship conjecture. Then we will review Christodoulou's construction of
naked singularities for the spherically symmetric Einstein-scalar field s
ystem. Finally\, we will discuss joint work with Igor Rodnianski which con
structs spacetimes corresponding to the exterior region of a naked singula
rity for the Einstein vacuum equations.\n
LOCATION:Lecture held in https://caltech.zoom.us/j/747242458
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kevin Hughes (U. Bristol)
DTSTART;VALUE=DATE-TIME:20200519T220000Z
DTEND;VALUE=DATE-TIME:20200519T230000Z
DTSTAMP;VALUE=DATE-TIME:20210120T055524Z
UID:UCLAAnalysisSeminar/10
DESCRIPTION:Title: Discrete restriction estimates\nby Kevin Hughes (U. Bri
stol) as part of UCLA analysis and PDE seminar\n\nLecture held in https://
ucla.zoom.us/j/9264073849.\n\nAbstract\nWe will discuss Wooley's Efficient
Congruencing approach to discrete restriction estimates for translation-d
ilation invariant systems of equations. Then we will discuss recent estima
tes for the curve (X\,X^3) which lie just outside of this framework as wel
l as that of Decoupling.\n
LOCATION:Lecture held in https://ucla.zoom.us/j/9264073849
END:VEVENT
BEGIN:VEVENT
SUMMARY:Stefan Steinerberger (U. Washington)
DTSTART;VALUE=DATE-TIME:20201006T220000Z
DTEND;VALUE=DATE-TIME:20201006T230000Z
DTSTAMP;VALUE=DATE-TIME:20210120T055524Z
UID:UCLAAnalysisSeminar/11
DESCRIPTION:Title: Roots of polynomials under repeated differentiation: a
nonlocal evolution equation with infinitely many conservation laws (and so
me universality phenomena)\nby Stefan Steinerberger (U. Washington) as par
t of UCLA analysis and PDE seminar\n\n\nAbstract\nSuppose you have a polyn
omial of degree $p_n$ whose $n$ real roots are roughly distributed like a
Gaussian (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
that $(t\\cdot n)$-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 shrink
ing semicircle and a family of Marchenko-Pastur distributions (this sounds
like random matrix theory and we make some remarks in that direction). Mo
reover\, the underlying evolution satisfies an infinite number of conserva
tion laws that one can write down explicitly. This suggests a lot of quest
ions: Sean O'Rourke and I proposed an analogous equation for complex-value
d polynomials. Motivated by some numerical simulations\, Jeremy Hoskins a
nd I conjectured that $t=1$\, just before the polynomial disappears\, the
shape of the remaining roots is a semicircle and we prove that for a class
of random polynomials. I promise lots of open problems and pretty pictur
es.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bjoern Bringmann (UCLA)
DTSTART;VALUE=DATE-TIME:20201006T230000Z
DTEND;VALUE=DATE-TIME:20201007T000000Z
DTSTAMP;VALUE=DATE-TIME:20210120T055524Z
UID:UCLAAnalysisSeminar/12
DESCRIPTION:Title: Invariant Gibbs measures for the three-dimensional wave
equation with a Hartree nonlinearity\nby Bjoern Bringmann (UCLA) as part
of UCLA analysis and PDE seminar\n\n\nAbstract\nIn this talk\, we discuss
the construction and invariance of the Gibbs measure for a three-\ndimensi
onal wave equation with a Hartree-nonlinearity.\n\nIn the first part of th
e talk\, we construct the Gibbs measure and examine its properties. We dis
cuss the mutual singularity of the Gibbs measure and the so-called Gaussia
n free field. In contrast\, the Gibbs measure for one or two-dimensional w
ave equations is absolutely continuous with respect to the Gaussian free f
ield.\n\nIn the second part of the talk\, we discuss the probabilistic wel
l-posedness of the corresponding nonlinear wave equation\, which is needed
in the proof of invariance. At the moment\, this is the only theorem prov
ing the invariance of any singular Gibbs measure under a dispersive equati
on.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Khang Huynh (UCLA)
DTSTART;VALUE=DATE-TIME:20201020T220000Z
DTEND;VALUE=DATE-TIME:20201020T230000Z
DTSTAMP;VALUE=DATE-TIME:20210120T055524Z
UID:UCLAAnalysisSeminar/13
DESCRIPTION:Title: A geometric trapping approach to global regularity for
2D Navier-Stokes on manifolds\nby Khang Huynh (UCLA) as part of UCLA analy
sis and PDE seminar\n\n\nAbstract\nWe use frequency decomposition techniqu
es to give a direct proof of global existence and regularity for the Navie
r-Stokes equations on two-dimensional Riemannian manifolds without boundar
y. Our techniques are inspired by an approach of Mattingly and Sinai which
was developed in the context of periodic boundary conditions on a flat ba
ckground\, and which is based on a maximum principle for Fourier coefficie
nts. The extension to general manifolds requires several new ideas\, conne
cted to the less favorable spectral localization properties in our setting
. Our arguments make use of frequency projection operators\, multilinear e
stimates that originated in the study of the non-linear Schrodinger equati
on\, and ideas from microlocal analysis.\n\nThis is joint work with Aynur
Bulut.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jaemin Park (Georgia Tech)
DTSTART;VALUE=DATE-TIME:20201013T210000Z
DTEND;VALUE=DATE-TIME:20201013T220000Z
DTSTAMP;VALUE=DATE-TIME:20210120T055524Z
UID:UCLAAnalysisSeminar/14
DESCRIPTION:Title: Radial symmetry in stationary/uniformly-rotating soluti
ons to 2D Euler equation\nby Jaemin Park (Georgia Tech) as part of UCLA an
alysis and PDE seminar\n\n\nAbstract\nIn this talk\, I will discuss whethe
r all stationary/uniformly-rotating solutions of 2D Euler equation must be
radially symmetric\, if the vorticity is compactly supported. For a stati
onary solution that is either smooth or of patch type\, we prove that if t
he vorticity does not change sign\, it must be radially symmetric up to a
translation. It turns out that the fixed-sign condition is necessary for r
adial symmetry result: indeed\, we are able to find non-radial sign changi
ng stationary solution with compact support. We have also obtained some sh
arp criteria on symmetry for uniformly-rotating solutions for 2D Euler equ
ation and the SQG equation. The symmetry results are mainly obtained by ca
lculus of variations and elliptic equation techniques\, and the constructi
on of non-radial solution is obtained from bifurcation theory. Part of thi
s talk is based on joint work with Javier Gomez-Serrano\, Jia Shi and Yao
Yao\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Thomas Bloom (Cambridge)
DTSTART;VALUE=DATE-TIME:20201103T180000Z
DTEND;VALUE=DATE-TIME:20201103T190000Z
DTSTAMP;VALUE=DATE-TIME:20210120T055524Z
UID:UCLAAnalysisSeminar/15
DESCRIPTION:Title: Spectral structure and arithmetic progressions\nby Thom
as Bloom (Cambridge) as part of UCLA analysis and PDE seminar\n\n\nAbstrac
t\nHow much additive structure can we guarantee in sets of integers\, know
ing only their density? The study of which density thresholds are sufficie
nt to guarantee the existence of various kinds of additive structures is a
n old and fascinating subject with connections to analytic number theory\,
additive combinatorics\, and harmonic analysis.\n\nIn this talk we will d
iscuss recent progress on perhaps the most well-known of these thresholds:
how large do we need a set of integers to be to guarantee the existence o
f a three-term arithmetic progression? In recent joint work with Olof Sisa
sk we broke through the logarithmic density barrier for this problem\, est
ablishing in particular that if a set is dense enough such that the sum of
reciprocals diverges\, then it must contain a three-term arithmetic progr
ession\, establishing the first case of an infamous conjecture of Erdos.\n
\nWe will give an introduction to this problem and sketch some of the rece
nt ideas that have made this progress possible. We will pay particular att
ention to the ways we exploit 'spectral structure' - understanding combina
torially sets of large Fourier coefficients\, which we hope will have furt
her applications in number theory and harmonic analysis.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yao Yao (Georgia Tech)
DTSTART;VALUE=DATE-TIME:20201118T000000Z
DTEND;VALUE=DATE-TIME:20201118T010000Z
DTSTAMP;VALUE=DATE-TIME:20210120T055524Z
UID:UCLAAnalysisSeminar/16
DESCRIPTION:Title: Two results on the interaction energy\nby Yao Yao (Geor
gia Tech) as part of UCLA analysis and PDE seminar\n\n\nAbstract\nFor any
nonnegative density $f$ and radially decreasing interaction potential $W$\
, the celebrated Riesz rearrangement inequality shows the interaction ener
gy $E[f] = \\int f(x)f(y)W(x-y) dxdy$ satisfies $E[f] \\leq E[f^*]$\, wher
e $f^*$ is the radially decreasing rearrangement of $f$. It is a natural q
uestion to look for a quantitative version of this inequality: if its two
sides almost agree\, how close must $f$ be to a translation of $f^*$? Prev
iously the stability estimate was only known for characteristic functions.
I will discuss a recent work with Xukai Yan\, where we found a simple pro
of of stability estimates for general densities. \n\nI will also discuss a
nother work with Matias Delgadino and Xukai Yan\, where we constructed an
interpolation curve between any two radially decreasing densities with the
same mass\, and show that the interaction energy is convex along this int
erpolation. As an application\, this leads to uniqueness of steady states
in aggregation-diffusion equations with any attractive interaction potenti
al for diffusion power $m\\geq 2$\, where the threshold is sharp.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jared Speck (Vanderbilt)
DTSTART;VALUE=DATE-TIME:20201020T230000Z
DTEND;VALUE=DATE-TIME:20201021T000000Z
DTSTAMP;VALUE=DATE-TIME:20210120T055524Z
UID:UCLAAnalysisSeminar/17
DESCRIPTION:Title: Stable big bang formation in general relativity: the co
mplete sub-critical regime\nby Jared Speck (Vanderbilt) as part of UCLA an
alysis and PDE seminar\n\n\nAbstract\nThe celebrated theorems of Hawking a
nd Penrose show that under appropriate assumptions on the matter model\, a
large\, open set of initial data for Einstein's equations lead to geodesi
cally incomplete solutions. However\, these theorems are "soft" in that th
ey do not yield any information\nabout the nature of the incompleteness\,
leaving open the possibilities that \n\ni) it is tied to the blowup of som
e invariant quantity (such as curvature) or \n\nii) it is due to a more si
nister phenomenon\, such as\nincompleteness due to lack of information for
how to uniquely continue the solution (this is roughly\nknown as the form
ation of a Cauchy horizon). \n\nDespite the "general ambiguity" in the mat
hematical physics literature\, there are heuristic results\, going back 50
years\, suggesting that whenever a certain "sub-criticality" condition ho
lds\, the Hawking-Penrose incompleteness is caused by the formation of a B
ig Bang singularity\, that is\, curvature blowup along an entire spacelike
hypersurface. In\nrecent joint work with I. Rodnianski and G. Fournodavlo
s\, we have given a rigorous proof of the heuristics. More precisely\, our
results apply to Sobolev-class perturbations - without symmetry - of gene
ralized Kasner solutions whose exponents satisfy the sub-criticality condi
tion. Our main\ntheorem shows that - like the generalized Kasner solutions
- the perturbed solutions develop Big Bang singularities. \n\nIn this tal
k\, I will provide an overview of our result and explain how it is tied to
some of the main themes of investigation by the mathematical general rela
tivity community\, including the remarkable work of Dafermos-Luk on the st
ability of Kerr Cauchy horizons. I will also discuss the new gauge that we
used in our work\, as well as intriguing connections to other problems co
ncerning stable singularity formation.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aleksandr Logunov (Princeton)
DTSTART;VALUE=DATE-TIME:20201215T190000Z
DTEND;VALUE=DATE-TIME:20201215T200000Z
DTSTAMP;VALUE=DATE-TIME:20210120T055524Z
UID:UCLAAnalysisSeminar/18
DESCRIPTION:Title: Zero sets of Laplace eigenfunctions\nby Aleksandr Logun
ov (Princeton) as part of UCLA analysis and PDE seminar\n\n\nAbstract\nIn
the beginning of 19th century Napoleon set a prize for the best mathematic
al explanation of Chladni’s resonance experiments. Nodal geometry studie
s the zeroes of solutions to elliptic differential equations such as the v
isible curves that appear in these physical experiments. We will discuss g
eometrical and analytic properties of zero sets of harmonic functions and
eigenfunctions of the Laplace operator. For harmonic functions on the plan
e there is an interesting relation between local length of the zero set an
d the growth of harmonic functions. The larger the zero set is\, the faste
r the growth of harmonic function should be and vice versa. Zero sets of L
aplace eigenfunctions on surfaces are unions of smooth curves with equiang
ular intersections. Topology of the zero set could be quite complicated\,
but Yau conjectured that the total length of the zero set is comparable to
the square root of the eigenvalue for all eigenfunctions. We will start w
ith open questions about spherical harmonics and explain some methods to s
tudy nodal sets.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Cristian Gonzales-Riquelme (IMPA)
DTSTART;VALUE=DATE-TIME:20201117T230000Z
DTEND;VALUE=DATE-TIME:20201118T000000Z
DTSTAMP;VALUE=DATE-TIME:20210120T055524Z
UID:UCLAAnalysisSeminar/19
DESCRIPTION:Title: BV and Sobolev continuity for maximal operators\nby Cri
stian Gonzales-Riquelme (IMPA) as part of UCLA analysis and PDE seminar\n\
n\nAbstract\nThe regularity of maximal operators has been a topic of\ninte
rest in harmonic analysis over the past decades. In this topic we are inte
rested in what can be said about the variation of a maximal function Mf gi
ven some information about the original function f. In this talk we presen
t\nsome recent results about the continuity of the map $f \\mapsto \\nabla
Mf$ 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. Madr
id (radial case).\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Paata Ivanisvili (NC State)
DTSTART;VALUE=DATE-TIME:20201201T230000Z
DTEND;VALUE=DATE-TIME:20201202T000000Z
DTSTAMP;VALUE=DATE-TIME:20210120T055524Z
UID:UCLAAnalysisSeminar/20
DESCRIPTION:Title: Sharpening the triangle inequality in Lp spaces\nby Paa
ta Ivanisvili (NC State) as part of UCLA analysis and PDE seminar\n\n\nAbs
tract\nThe classical triangle inequality in Lp estimates the norm of the s
um of two functions in terms of the sums of the norms of these functions.
Perhaps one drawback of this estimate is that it does not see how "orthogo
nal" these functions are. For example\, if f and g are not identically zer
o and they have disjoint supports then the triangle inequality is pretty s
trict (say for p>1).\n\nMotivated by the L2 case\, where one has a trivial
inequality ||f+g||^2 \\leq ||f||^2 + ||g||^2 + 2 |fg|_1\, one can think a
bout 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
talk will be based on a joint work with Carlen\, Frank and Lieb where we
obtain one extension of this estimate in Lp\, thereby proving and improvin
g the suggested possible estimates by Carbery\, and another work with Moon
ey where we further refine these estimates. The estimates will be provided
for all real p's.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Emanuel Carneiro (ICTP)
DTSTART;VALUE=DATE-TIME:20201215T180000Z
DTEND;VALUE=DATE-TIME:20201215T190000Z
DTSTAMP;VALUE=DATE-TIME:20210120T055524Z
UID:UCLAAnalysisSeminar/21
DESCRIPTION:Title: Uncertain signs\nby Emanuel Carneiro (ICTP) as part of
UCLA analysis and PDE seminar\n\n\nAbstract\nWe consider a generalized ver
sion of the sign uncertainty\nprinciple for the Fourier transform\, first
proposed by Bourgain\, Clozel and\nKahane in 2010 and revisited by Cohn an
d Gonçalves in 2019\, in connection\nto the sphere packing problem. In ou
r 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 k
now if and how soon this resonance can\nhappen\, when facing a suitable co
mpeting weighted integral condition. The\noriginal version of the problem
corresponds 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 wo
rk with Oscar Quesada-Herrera\n(IMPA - Rio de Janeiro).\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Damanik (Rice)
DTSTART;VALUE=DATE-TIME:20201202T000000Z
DTEND;VALUE=DATE-TIME:20201202T010000Z
DTSTAMP;VALUE=DATE-TIME:20210120T055524Z
UID:UCLAAnalysisSeminar/22
DESCRIPTION:Title: Proving Positive Lyapunov Exponents: Beyond Independenc
e\nby David Damanik (Rice) as part of UCLA analysis and PDE seminar\n\n\nA
bstract\nWe discuss the problem of proving the positivity of the Lyapunov
exponent for Schr\\"odinger operators with potentials defined by a hyperbo
lic base transformation and a H \\"older continuous sampling function. Pro
minent examples of such base transformations are given by the doubling map
and the Arnold cat map. The talk is based on joint work with Artur Avila
and Zhenghe Zhang.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shukun Wu (UIUC)
DTSTART;VALUE=DATE-TIME:20201027T210000Z
DTEND;VALUE=DATE-TIME:20201027T220000Z
DTSTAMP;VALUE=DATE-TIME:20210120T055524Z
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 impro
ve 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
some relations between wave packets at different scales.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yilin Wang (MIT)
DTSTART;VALUE=DATE-TIME:20201208T220000Z
DTEND;VALUE=DATE-TIME:20201208T230000Z
DTSTAMP;VALUE=DATE-TIME:20210120T055524Z
UID:UCLAAnalysisSeminar/24
DESCRIPTION:Title: SLE\, energy duality\, and foliations by Weil-Petersson
quasicircles\nby Yilin Wang (MIT) as part of UCLA analysis and PDE semina
r\n\n\nAbstract\nThe Loewner energy for Jordan curves first arises from th
e small-parameter large deviations of Schramm-Loewner evolution (SLE). It
is finite if and only if the curve is a Weil-Petersson quasicircle\, an in
teresting class of Jordan curves appearing in Teichmuller theory\, geometr
ic function theory\, and string theory with currently more than 20 equival
ent definitions. In this talk\, I will show that the large-parameter large
deviations of SLE gives rise to a new Loewner-Kufarev energy\, which is d
ual to the Loewner energy via foliations by Weil-Petersson quasicircles an
d exhibits remarkable features and symmetries. Based on joint works with M
orris Ang and Minjae Park (MIT) and with Fredrik Viklund (KTH).\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Thomas Beck (Fordham)
DTSTART;VALUE=DATE-TIME:20201103T190000Z
DTEND;VALUE=DATE-TIME:20201103T200000Z
DTSTAMP;VALUE=DATE-TIME:20210120T055524Z
UID:UCLAAnalysisSeminar/25
DESCRIPTION:Title: Two-phase free boundary problems and the Friedland-Haym
an inequality\nby Thomas Beck (Fordham) as part of UCLA analysis and PDE s
eminar\n\n\nAbstract\nThe Friedland-Hayman inequality provides a lower bou
nd on the first Dirichlet eigenvalues of complementary subsets of the sphe
re. In this talk\, we will describe a variant of this inequality to geodes
ically convex subsets of the sphere with mixed Dirichlet-Neumann boundary
conditions. Using this inequality\, we prove an almost-monotonicity formul
a and Lipschitz continuity up to the boundary for the minimizer of a two-p
hase free boundary problem. This is joint work with David Jerison and Sara
h Raynor.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Adrian Nachman (U. Toronto)
DTSTART;VALUE=DATE-TIME:20201110T220000Z
DTEND;VALUE=DATE-TIME:20201110T230000Z
DTSTAMP;VALUE=DATE-TIME:20210120T055524Z
UID:UCLAAnalysisSeminar/26
DESCRIPTION:Title: A Nonlinear Plancherel Theorem with Applications to Glo
bal Well-posedness for the Defocusing Davey-Stewartson Equation and to the
Inverse Boundary Value Problem of Calderon\nby Adrian Nachman (U. Toronto
) as part of UCLA analysis and PDE seminar\n\n\nAbstract\nThis is joint wo
rk with Idan Regev and Daniel Tataru.\n\nThe talk will aim to present our
solutions to 2+\\epsilon open problems.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Justin Forlano (UCLA)
DTSTART;VALUE=DATE-TIME:20201124T220000Z
DTEND;VALUE=DATE-TIME:20201124T230000Z
DTSTAMP;VALUE=DATE-TIME:20210120T055524Z
UID:UCLAAnalysisSeminar/27
DESCRIPTION:Title: Normal form approach to the one-dimensional cubic nonli
near Schr\\"{o}dinger equation in almost critical spaces\nby Justin Forlan
o (UCLA) as part of UCLA analysis and PDE seminar\n\n\nAbstract\nIn recent
years\, the normal form approach has provided an alternative method to es
tablishing 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-d
imensional cubic nonlinear Schr\\"{o}dinger equation (NLS) on the real-lin
e and prove local well-posedness in almost critical Fourier-amalgam spaces
. This involves using an infinite iteration of normal form reductions (nam
ely\, integration by parts in time) to derive the normal form equation\, w
hich behaves better than NLS for rough functions.\n\nThis is joint work wi
th Tadahiro Oh (U. Edinburgh).\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Dobner (UCLA)
DTSTART;VALUE=DATE-TIME:20210106T000000Z
DTEND;VALUE=DATE-TIME:20210106T010000Z
DTSTAMP;VALUE=DATE-TIME:20210120T055524Z
UID:UCLAAnalysisSeminar/28
DESCRIPTION:Title: Extreme values of the argument of the zeta function\nby
Alexander Dobner (UCLA) as part of UCLA analysis and PDE seminar\n\n\nAbs
tract\nLet $S(t) = \\frac{1}{\\pi}\\Im \\log \\zeta(\\frac{1}{2}+it)$. The
behavior of this function is intimately connected to irregularities in th
e locations of the zeros of the zeta function. In particular $S(t)$ measur
es 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 abo
ut the distribution of $S(t)$ and prove a new unconditional lower bound on
how often $S(t)$ achieves large values.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eugenia Malinnikova (Stanford)
DTSTART;VALUE=DATE-TIME:20210126T220000Z
DTEND;VALUE=DATE-TIME:20210126T230000Z
DTSTAMP;VALUE=DATE-TIME:20210120T055524Z
UID:UCLAAnalysisSeminar/29
DESCRIPTION:Title: Landis’ conjecture on the decay of solutions to Schr
ödinger equations on the plane.\nby Eugenia Malinnikova (Stanford) as par
t of UCLA analysis and PDE seminar\n\nInteractive livestream: https://ucla
.zoom.us/j/9264073849\n\nAbstract\nWe consider a real-valued function on t
he plane for which the absolute value of the Laplacian is bounded by the a
bsolute value of the function at each point. In other words\, we look at s
olutions of the stationary Schrödinger equation with a bounded 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 dimensions the
corresponding problem is open.\n\n \n\nThe talk is based on the joint work
with A. Logunov\, N. Nadirashvili\, and F. Nazarov.\n
URL:https://ucla.zoom.us/j/9264073849
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yufei Zhao (MIT)
DTSTART;VALUE=DATE-TIME:20210120T000000Z
DTEND;VALUE=DATE-TIME:20210120T010000Z
DTSTAMP;VALUE=DATE-TIME:20210120T055524Z
UID:UCLAAnalysisSeminar/30
DESCRIPTION:Title: Joints of varieties\nby Yufei Zhao (MIT) as part of UCL
A analysis and PDE seminar\n\n\nAbstract\nWe generalize the Guth-Katz join
ts theorem from lines to varieties. A special case of our result says that
$N$ planes (2-flats) in 6 dimensions (over any field) have $O(N^{3/2})$ j
oints\, where a joint is a point contained in a triple of these planes not
all lying in some hyperplane. Our most general result gives upper bounds\
, tight up to constant factors\, for joints with multiplicities for severa
l sets of varieties of arbitrary dimensions (known as Carbery's conjecture
). Our main innovation is a new way to extend the polynomial method to hig
her dimensional objects.\n\nJoint work with Jonathan Tidor and Hung-Hsun H
ans Yu.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Georgis Moschidis (UC Berkeley)
DTSTART;VALUE=DATE-TIME:20210112T180000Z
DTEND;VALUE=DATE-TIME:20210112T190000Z
DTSTAMP;VALUE=DATE-TIME:20210120T055524Z
UID:UCLAAnalysisSeminar/31
DESCRIPTION:Title: The instability of Anti-de Sitter spacetime for the Ein
stein-scalar field system\nby Georgis Moschidis (UC Berkeley) as part of U
CLA analysis and PDE seminar\n\n\nAbstract\nhe AdS instability conjecture
provides an example of weak turbulence appearing in the dynamics of the Ei
nstein equations in the presence of a negative cosmological constant. The
conjecture claims the existence of arbitrarily small perturbations to the
initial data of Anti-de Sitter spacetime which\, under evolution by the va
cuum Einstein equations with reflecting boundary conditions at conformal
infinity\, lead to the formation of black holes after sufficiently long ti
me. \n In this talk\, I will present a rigorous proof of the AdS instab
ility conjecture in the setting of the spherically symmetric Einstein-sca
lar field system. The construction of the unstable initial data will requi
re carefully designing a family of initial configurations of localized mat
ter beams and estimating the exchange of energy taking place between inter
acting beams over long periods of time\, as well as estimating the decoher
ence rate of those beams. I will also discuss possible paths for extending
these ideas to the vacuum case.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Elena Giorgi (Princeton)
DTSTART;VALUE=DATE-TIME:20210116T000000Z
DTEND;VALUE=DATE-TIME:20210116T010000Z
DTSTAMP;VALUE=DATE-TIME:20210120T055524Z
UID:UCLAAnalysisSeminar/32
DESCRIPTION:Title: Electromagnetic-gravitational perturbations of Kerr-New
man spacetime\nby Elena Giorgi (Princeton) as part of UCLA analysis and PD
E seminar\n\n\nAbstract\nThe Kerr-Newman spacetime is the most general exp
licit black hole solution\, and represents a stationary rotating charged b
lack hole. Its stability to gravitational and electromagnetic perturbation
s has eluded a proof since the 80s in the black hole perturbation communit
y\, because of "the apparent indissolubility of the coupling between the s
pin-1 and spin-2 fields in the perturbed spacetime"\, as put by Chandrasek
har. We will present a derivation of the Teukolsky and Regge-Wheeler equat
ions in Kerr-Newman in physical space and use it to obtain a quantitative
proof of stability.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Betsy Stovall (UW-Madison)
DTSTART;VALUE=DATE-TIME:20210302T190000Z
DTEND;VALUE=DATE-TIME:20210302T200000Z
DTSTAMP;VALUE=DATE-TIME:20210120T055524Z
UID:UCLAAnalysisSeminar/33
DESCRIPTION:by Betsy Stovall (UW-Madison) as part of UCLA analysis and PDE
seminar\n\nInteractive livestream: https://caltech.zoom.us/j/99420414248\
nAbstract: TBA\n
URL:https://caltech.zoom.us/j/99420414248
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marta Lewicka (U. Pittsburgh)
DTSTART;VALUE=DATE-TIME:20210109T000000Z
DTEND;VALUE=DATE-TIME:20210109T010000Z
DTSTAMP;VALUE=DATE-TIME:20210120T055524Z
UID:UCLAAnalysisSeminar/34
DESCRIPTION:Title: Expansions of averaging operators and applications\nby
Marta Lewicka (U. Pittsburgh) as part of UCLA analysis and PDE seminar\n\n
\nAbstract\nhe following approach of finding solutions to a partial differ
ential equation Lu=0\, proved to be quite versatile:\n\n(i) develop an asy
mptotic expansion of a suitable family of averaging operators (to be appli
ed on u)\; the operators are parametrized by the radius \\epsilon of avera
ging\, and the coefficient in the expansion that multiplies the appropriat
e power of \\epsilon should equal Lu\, the "appropriate power" refers to t
he order of L\;\n\n(ii) study the related mean value equation by removing
higher order terms in the expansion\;\n\n(iii) interpret the mean value eq
uation as the dynamic programming principle of a two-player game incorpora
ting deterministic and stochastic components\;\n\n(iv) pass to the limit i
n 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
approach in the contexts of p-Laplacian and the non-local geometric p-Lap
lacian. Other applications include: Robin boundary conditions and weighted
Laplace-Beltrami operator on a manifold. In each case\, finding the appro
priate averaging principle is the key starting point in order to develop (
i)-(iv).\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Philip T. Gressman (UPenn)
DTSTART;VALUE=DATE-TIME:20210105T230000Z
DTEND;VALUE=DATE-TIME:20210106T000000Z
DTSTAMP;VALUE=DATE-TIME:20210120T055524Z
UID:UCLAAnalysisSeminar/35
DESCRIPTION:Title: Radon-like Transforms\, Geometric Measures\, and Invari
ant Theory\nby Philip T. Gressman (UPenn) as part of UCLA analysis and PDE
seminar\n\n\nAbstract\nFourier restriction\, Radon-like operators\, and d
ecoupling theory are three active areas of harmonic analysis which involve
submanifolds of Euclidean space in a fundamental way. In each case\, the
mapping properties of the objects of study depend in a fundamental way on
the "non-flatness" of the submanifold\, but with the exception of certain
extreme cases (primarily curves and hypersurfaces)\, it is not clear exact
ly how to quantify the geometry in an analytically meaningful way. In this
talk\, I will discuss a series of recent results which shed light on this
situation using tools from an unusually broad range of mathematical sourc
es.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sigurd Angenent (UW-Madison)
DTSTART;VALUE=DATE-TIME:20210202T230000Z
DTEND;VALUE=DATE-TIME:20210203T000000Z
DTSTAMP;VALUE=DATE-TIME:20210120T055524Z
UID:UCLAAnalysisSeminar/36
DESCRIPTION:by Sigurd Angenent (UW-Madison) as part of UCLA analysis and P
DE seminar\n\nInteractive livestream: https://caltech.zoom.us/j/9942041424
8\nAbstract: TBA\n
URL:https://caltech.zoom.us/j/99420414248
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:20210120T055524Z
UID:UCLAAnalysisSeminar/37
DESCRIPTION:by Cyrill Muratov (New Jersey Institute of Technology) as part
of UCLA analysis and PDE seminar\n\nInteractive livestream: https://calte
ch.zoom.us/j/99420414248\nAbstract: TBA\n
URL:https://caltech.zoom.us/j/99420414248
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hong Wang (IAS)
DTSTART;VALUE=DATE-TIME:20210115T230000Z
DTEND;VALUE=DATE-TIME:20210116T000000Z
DTSTAMP;VALUE=DATE-TIME:20210120T055524Z
UID:UCLAAnalysisSeminar/38
DESCRIPTION:Title: Restriction theory in Fourier analysis\nby Hong Wang (I
AS) as part of UCLA analysis and PDE seminar\n\n\nAbstract\nIf a function
has Fourier transform supported on a sphere\, what can we say about this f
unction?\n\nGiven a collection of long thin tubes pointing in different di
rections\, how much do they overlap?\n\nThese two questions are closely re
lated. In this talk\, we will discuss how understanding the second questio
n leads to progress on the first one. More precisely\, we will discuss Ste
in's restriction conjecture and Sogge's local smoothing conjecture for the
wave equation.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tsviqa Lakrec (U. Jerusalem)
DTSTART;VALUE=DATE-TIME:20210216T180000Z
DTEND;VALUE=DATE-TIME:20210216T190000Z
DTSTAMP;VALUE=DATE-TIME:20210120T055524Z
UID:UCLAAnalysisSeminar/39
DESCRIPTION:by Tsviqa Lakrec (U. Jerusalem) as part of UCLA analysis and P
DE seminar\n\nInteractive livestream: https://ucla.zoom.us/j/9264073849\nA
bstract: TBA\n
URL:https://ucla.zoom.us/j/9264073849
END:VEVENT
BEGIN:VEVENT
SUMMARY:Benjamin Seeger (College de France)
DTSTART;VALUE=DATE-TIME:20210111T230000Z
DTEND;VALUE=DATE-TIME:20210112T000000Z
DTSTAMP;VALUE=DATE-TIME:20210120T055524Z
UID:UCLAAnalysisSeminar/40
DESCRIPTION:Title: Interpolation results for pathwise Hamilton-Jacobi equa
tions\nby Benjamin Seeger (College de France) as part of UCLA analysis and
PDE seminar\n\n\nAbstract\nI will show how interpolation methods can be u
sed to make sense of pathwise Hamilton-Jacobi equations for a wide range o
f Hamiltonians and driving paths. The various function spaces describe reg
ularity (including Sobolev\, Besov\, Holder\, and variation) as well as st
ructure. I will also discuss some criteria for a function to be representa
ble as a difference of convex functions\, a class which plays an important
role in the theory of pathwise Hamilton-Jacobi equations.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andreia Chapouto (U. Edinburgh)
DTSTART;VALUE=DATE-TIME:20210112T170000Z
DTEND;VALUE=DATE-TIME:20210112T180000Z
DTSTAMP;VALUE=DATE-TIME:20210120T055524Z
UID:UCLAAnalysisSeminar/41
DESCRIPTION:Title: Invariance of the Gibbs measures for the periodic gener
alized KdV equations\nby Andreia Chapouto (U. Edinburgh) as part of UCLA a
nalysis and PDE seminar\n\n\nAbstract\nIn this talk\, we consider the peri
odic generalized Korteweg-de Vries equations (gKdV). In particular\, we st
udy gKdV with the Gibbs measure initial data. The main difficulty lies in
constructing local-in-time dynamics in the support of the measure. Since g
KdV is analytically ill-posed in the $L^2$-based Sobolev support\, we inst
ead prove deterministic local well-posedness in some Fourier-Lebesgue spac
es containing the support of the Gibbs measures. New key ingredients are b
ilinear and trilinear Strichartz estimates adapted to the Fourier-Lebesgue
setting. Once we construct local-in-time dynamics\, we apply Bourgain's i
nvariant measure argument to prove almost sure global well-posedness of th
e defocusing gKdV with respect to the Gibbs measure and invariance of the
Gibbs measure under the gauged gKdV dynamics.\n\nThis talk is based on joi
nt work with Nobu Kishimoto (RIMS\, University of Kyoto).\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kihyun Kim (KAIST)
DTSTART;VALUE=DATE-TIME:20210129T230000Z
DTEND;VALUE=DATE-TIME:20210130T000000Z
DTSTAMP;VALUE=DATE-TIME:20210120T055524Z
UID:UCLAAnalysisSeminar/42
DESCRIPTION:Title: Blow-up dynamics for the self-dual Chern-Simons-Schröd
inger equation\nby Kihyun Kim (KAIST) as part of UCLA analysis and PDE sem
inar\n\nInteractive livestream: https://ucla.zoom.us/j/9264073849\n\nAbstr
act\nWe consider the blow-up dynamics of the self-dual Chern-Simons-Schrö
dinger equation (CSS) under equivariance symmetry. (CSS) is $L^2$-critical
\, has the pseudoconformal symmetry\, and admits a soliton $Q$ for each eq
uivariance index $m \\geq 0$. An application of the pseudoconformal transf
ormation to $Q$ yields an explicit finite-time blow-up solution $S(t)$ whi
ch contracts at the pseudoconformal rate $|t|$. In the high equivariance c
ase $m \\geq 1$\, the pseudoconformal blow-up for smooth finite energy sol
utions in fact occurs in a codimension one sense\; it is stable under a co
dimension one perturbation\, but also exhibits an instability mechanism. I
n the radial case $m=0$\, however\, $S(t)$ is no longer a finite energy bl
ow-up solution. Interestingly enough\, there are smooth finite energy blow
-up solutions whose blow-up rates differ from the pseudoconformal 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
URL:https://ucla.zoom.us/j/9264073849
END:VEVENT
BEGIN:VEVENT
SUMMARY:Adi Glucksam (U. Toronto)
DTSTART;VALUE=DATE-TIME:20210119T230000Z
DTEND;VALUE=DATE-TIME:20210120T000000Z
DTSTAMP;VALUE=DATE-TIME:20210120T055524Z
UID:UCLAAnalysisSeminar/43
DESCRIPTION:Title: Stationary random entire functions and related question
s\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 tr
anslations\, taking f(z) to f(z+w). B.Weiss showed in `97 that there exist
s a probability measure defined on the space of entire functions\, which i
s invariant under this action. In this talk I will present optimal bounds
on the minimal possible growth of functions in the support of such measure
s and discuss other growth-related problems inspired by this work. In part
icular\, I will focus on the question of minimal possible growth-rate of f
requently oscillating subharmonic functions.\nThe talk is partly based on
a joint work with L. Buhovsky\, A. Logunov\, and M. Sodin.\n
END:VEVENT
END:VCALENDAR