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CALSCALE:GREGORIAN
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BEGIN:VEVENT
SUMMARY:Maciej Zworski (UC Berkeley) (UC Berkeley)
DTSTART:20200908T200000Z
DTEND:20200908T210000Z
DTSTAMP:20260422T212609Z
UID:PDEAnalysis/1
DESCRIPTION:Title: Mathematics of magic angles for bilayer graphene\nby Maciej Zworsk
i (UC Berkeley) (UC Berkeley) as part of PDE Analysis Seminar\n\n\nAbstrac
t\nMagic angles are a hot topic in condensed matter physics: when two shee
ts of graphene\nare twisted by those angles the resulting material is supe
rconducting. Please do not be\nscared by the physics though: I will presen
t a very simple operator whose spectral properties\nare thought to determi
ne which angles are magical. It comes from a recent PR Letter\nby Tarnopol
sky–Kruchkov–Vishwanath. The mathematics behind this is an elementary\
nblend of representation theory (of the Heisenberg group in characteristic
three)\, Jacobi\ntheta functions and spectral instability of non-self-adj
oint operators (involving Hörmander’s\nbracket condition in a very simp
le setting). The results will be illustrated by colourful\nnumerics which
suggest some open problems. The talk is based on a “summer relaxation\np
roject” with S. Becker\, M. Embree and J. Wittsten.\n
LOCATION:https://researchseminars.org/talk/PDEAnalysis/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ruoxuan Yang (MIT Mathematics)
DTSTART:20200915T200000Z
DTEND:20200915T210000Z
DTSTAMP:20260422T212609Z
UID:PDEAnalysis/2
DESCRIPTION:Title: Shock Formation for the Burgers-Hilbert Equation\nby Ruoxuan Yang
(MIT Mathematics) as part of PDE Analysis Seminar\n\n\nAbstract\nWe will t
alk about the shock formation for the Burgers–Hilbert (BH) equation. We
begin with previous studies on BH equation\, including the vorticity disco
ntinuity model\, initial value problems and blowup results. Then we introd
uce the technique of modulated self-similarity\, show its background and a
pply it to the BH equation. Finally we sketch the proof and discuss its di
fficulty.\n\nZoom link: https://mit.zoom.us/j/94123420042?pwd=R2I3aG53b0N
HZk1wa1JPU3J5TXZKZz09\n\nZoom password: 577126\n
LOCATION:https://researchseminars.org/talk/PDEAnalysis/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Malo Jézéquel (MIT)
DTSTART:20210914T200000Z
DTEND:20210914T210000Z
DTSTAMP:20260422T212609Z
UID:PDEAnalysis/3
DESCRIPTION:Title: Real-analytic FBI transform and Anosov flows\nby Malo Jézéquel (
MIT) as part of PDE Analysis Seminar\n\n\nAbstract\nAnosov flows form an e
xtensively studied class of chaotic dynamical systems. In this talk\, I wi
ll explain how PDE techniques developed by Helffer and Sj¨ostrand in the
80s-90s can be used to study the statistical properties of real-analytic A
nosov flows\, and the complex-analytic properties of associated zeta funct
ions. This is a joint work with Yannick Guedes Bonthonneau.\n
LOCATION:https://researchseminars.org/talk/PDEAnalysis/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Thomas Hou (Caltech)
DTSTART:20211005T200000Z
DTEND:20211005T210000Z
DTSTAMP:20260422T212609Z
UID:PDEAnalysis/4
DESCRIPTION:Title: Potential singularity of 3D incompressible Euler equations and the nea
rly singular behavior of 3D Navier-Stokes equations\nby Thomas Hou (Ca
ltech) as part of PDE Analysis Seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/PDEAnalysis/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maciej Zworski (UC Berkeley)
DTSTART:20211019T200000Z
DTEND:20211019T210000Z
DTSTAMP:20260422T212609Z
UID:PDEAnalysis/5
DESCRIPTION:Title: Title to be announced\nby Maciej Zworski (UC Berkeley) as part of
PDE Analysis Seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/PDEAnalysis/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sylvia Serfaty (NYU Courant)
DTSTART:20211026T200000Z
DTEND:20211026T210000Z
DTSTAMP:20260422T212609Z
UID:PDEAnalysis/6
DESCRIPTION:Title: Title to be announced\nby Sylvia Serfaty (NYU Courant) as part of
PDE Analysis Seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/PDEAnalysis/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yaiza Canzani (UNC Chapel Hill)
DTSTART:20211130T210000Z
DTEND:20211130T220000Z
DTSTAMP:20260422T212609Z
UID:PDEAnalysis/7
DESCRIPTION:Title: Title to be announced\nby Yaiza Canzani (UNC Chapel Hill) as part
of PDE Analysis Seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/PDEAnalysis/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Isabelle Gallagher (Ecole Normale Supérieure)
DTSTART:20220405T200000Z
DTEND:20220405T210000Z
DTSTAMP:20260422T212609Z
UID:PDEAnalysis/8
DESCRIPTION:Title: Dynamics of dilute gases at equilibrium: from the atomistic descriptio
n to fluctuating hydrodynamics\nby Isabelle Gallagher (Ecole Normale S
upérieure) as part of PDE Analysis Seminar\n\n\nAbstract\nWe consider the
low density limit of a deterministic system of particles. Lanford’s the
orem in 1974 states that the empirical distribution converges in law to th
e solution to the Boltzmann equation\, for short times. Recently\, the flu
ctuation field has been shown to converge to a Gaussian process\, and this
convergence holds for arbitrarily long times if the gas is at equilibrium
. In this talk we will explain the main ideas of the proof\, and show how
linear fluctuating hydrodynamics can be derived from this model at equilib
rium.\n\nhttps://mit.zoom.us/j/96019944889?pwd=em5VVFJab1o2NlZtWGZVdDRQWmx
QQT09\nZoom password: 140860\n
LOCATION:https://researchseminars.org/talk/PDEAnalysis/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yaiza Canzani (UNC)
DTSTART:20220419T191500Z
DTEND:20220419T200500Z
DTSTAMP:20260422T212609Z
UID:PDEAnalysis/9
DESCRIPTION:Title: COUNTING CLOSED GEODESICS AND IMPROVING WEYL’S LAW FOR PREDOMINANT S
ETS OF METRICS\nby Yaiza Canzani (UNC) as part of PDE Analysis Seminar
\n\n\nAbstract\nWe discuss the typical behavior of two important quantitie
s on compact manifolds with a Riemannian metric g: the number\, c(T\,g)\,
of primitive closed geodesics of length smaller than T\, and the error\, E
(L\,g)\, in the Weyl law for counting the number of Laplace eigenvalues th
at are smaller than L. For Baire generic metrics\, the qualitative behavio
r of both of these quantities has been understood since the 1970’s and 1
980’s. In terms of quantitative behavior\, the only available result is
due to Contreras and it says that an exponential lower bound on c(T\,g) ho
lds for g in a Baire-generic set. Until now\, no upper bounds on c(T\,g) o
r quantitative improvements on E(L\,g) were known to hold for most metrics
\, not even for a dense set of metrics. In this talk\, we will introduce t
he concept of predominance in the space of Riemannian metrics. This is a n
otion that is analogous to having full Lebesgue measure in finite dimensio
ns\, and which\, in particular\, implies density. We will then give stretc
hed exponential upper bounds for c(T\,g) and logarithmic improvements for
E(L\,g) that hold for a predominant set of metrics. This is based on joint
work with J. Galkowski.\n
LOCATION:https://researchseminars.org/talk/PDEAnalysis/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hao Jia (University of Minnesota)
DTSTART:20220426T200000Z
DTEND:20220426T210000Z
DTSTAMP:20260422T212609Z
UID:PDEAnalysis/10
DESCRIPTION:Title: VORTEX SYMMETRIZATION PROBLEM FOR THE 2D EULER EQUATION\nby Hao J
ia (University of Minnesota) as part of PDE Analysis Seminar\n\nLecture he
ld in Room 2-147 in the Simons Building.\n\nAbstract\nThe 2d incompressibl
e Euler equation is globally well posed for smooth initial data. However t
he long term dynamics of general solutions is difficult to understand due
to the lack of global relaxation mechanisms. Numerical simulations and phy
sical experiments show that vortices (steady solutions with radial vortici
ty functions) play an important role in the global dynamics\, through a pr
ocess called vortex symmetrization of small perturbations. In this talk\,
I will discuss some recent progress on this problem\, including a full non
linear symmetrization result near a special point vortex and precise linea
rized symmetrization result near general vortices. Difficulties of full no
nlinear vortex symmetrization around general vortices will also be discuss
ed. Joint work with Alexandru Ionescu.\n
LOCATION:https://researchseminars.org/talk/PDEAnalysis/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tuomas Orponen (University of Jyväskylä)
DTSTART:20220503T190000Z
DTEND:20220503T200000Z
DTSTAMP:20260422T212609Z
UID:PDEAnalysis/11
DESCRIPTION:Title: On the dimension of A + BC\nby Tuomas Orponen (University of Jyv
äskylä) as part of PDE Analysis Seminar\n\n\nAbstract\nLet A\,B\,C be co
mpact subsets of [0\,1]. What is the (Hausdorff) dimension of A + BC? The
problem is open\, but I will discuss the current partial results. After br
iefly discussing the case of general compact sets\, I will focus on the ca
se where A\,B are Ahlfors-regular.\n\nZoom link: https://mit.zoom.us/j/960
19944889?pwd=em5VVFJab1o2NlZtWGZVdDRQWmxQQT09\nZoom password: 140860\n
LOCATION:https://researchseminars.org/talk/PDEAnalysis/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zaher Hani (University of Michigan)
DTSTART:20220510T200000Z
DTEND:20220510T210000Z
DTSTAMP:20260422T212609Z
UID:PDEAnalysis/12
DESCRIPTION:Title: Title to be announced\nby Zaher Hani (University of Michigan) as
part of PDE Analysis Seminar\n\n\nAbstract\nAbstract to be shared\n
LOCATION:https://researchseminars.org/talk/PDEAnalysis/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jani Lukkarinen (U Helsinki)
DTSTART:20220927T190000Z
DTEND:20220927T200000Z
DTSTAMP:20260422T212609Z
UID:PDEAnalysis/13
DESCRIPTION:Title: Estimation of propagation of chaos via cumulant hierarchies in two ex
ample models\nby Jani Lukkarinen (U Helsinki) as part of PDE Analysis
Seminar\n\nLecture held in Room 2 - 136 in the Simons Building.\n\nAbstrac
t\nPropagation and generation of “chaos” is an important ingredient in
rigorous control of applicability of kinetic theory\, in general. Chaos c
an here be understood as sufficient statistical independence of random var
iables related to the “kinetic” observables of the system. Cumulant hi
erarchy of these random variables thus often gives a way of controlling th
e evolution and the degree of such independence\, i.e.\, the amount of “
chaos” in the system. In this talk\, we will consider two\, qualitativel
y different\, example cases for which kinetic theory is believed to be app
licable: the discrete nonlinear Schrodinger evolution (DNLS) with suitable
random\, spatially homogeneous initial data\, and the stochastic Kac mode
l. In both cases\, we set up suitable random variables and propose methods
to control the evolution of their cumulant hierarchies. The talk is based
on joint work with Aleksis Vuoksenmaa\, and earlier works with Matteo Mar
cozzi\, Alessia Nota\, and Herbert Spohn.\n
LOCATION:https://researchseminars.org/talk/PDEAnalysis/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shaoming Guo (U Wisconsin\, Madison)
DTSTART:20221018T190000Z
DTEND:20221018T200000Z
DTSTAMP:20260422T212609Z
UID:PDEAnalysis/14
DESCRIPTION:Title: A dichotomy for Hormander-type oscillatory integral operators\nby
Shaoming Guo (U Wisconsin\, Madison) as part of PDE Analysis Seminar\n\nL
ecture held in Room 2-136 in the Simon's Building.\n\nAbstract\nHormander
1973 proposed to study a generalized Fourier extension operator\, and aske
d whether the generalized operator satisfies the same L p bounds as that o
f the standard Fourier extension operator. Surprisingly\, Bourgain 1991 ga
ve a negative answer to Hormander’s question. In this talk\, I will disc
uss a modification of Hormander’s question whose answer may be affirmati
ve. This is a joint work with Hong Wang and Ruixiang Zhang.\n
LOCATION:https://researchseminars.org/talk/PDEAnalysis/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Philip Gressman (UPenn)
DTSTART:20221108T200000Z
DTEND:20221108T210000Z
DTSTAMP:20260422T212609Z
UID:PDEAnalysis/15
DESCRIPTION:Title: Title to be shared\nby Philip Gressman (UPenn) as part of PDE Ana
lysis Seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/PDEAnalysis/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Benoit Pausader (Brown)
DTSTART:20221115T200000Z
DTEND:20221115T210000Z
DTSTAMP:20260422T212609Z
UID:PDEAnalysis/16
DESCRIPTION:Title: Stability of a point charge for the repulsive Vlasov-Poisson system\nby Benoit Pausader (Brown) as part of PDE Analysis Seminar\n\nLecture
held in 2-136.\n\nAbstract\nWe consider solutions of the repulsive Vlasov-
Poisson systems which are a combination of a point charge and a small dens
ity with respect to Liouville measure (a “cloud”)\, and we show that t
hese solutions exist globally\, that the electric field decay at an optima
l rate and that the particle distribution converges along a modified scatt
ering dynamics. This follows by a Lagrangian study of the linearized equat
ion\, which is integrated by means of an asymptotic action-angle coordinat
e transformation\, and an Eulerian study of the nonlinear dynamic which ex
hibits the “mixing” mechanism responsible for the asymptotic behavior.
This is joint work with Klaus Widmayer (U. Zurich) and Jiaqi Yang (ICERM)
.\n
LOCATION:https://researchseminars.org/talk/PDEAnalysis/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Semyon Dyatlov (MIT)
DTSTART:20221025T200000Z
DTEND:20221025T210000Z
DTSTAMP:20260422T212609Z
UID:PDEAnalysis/17
DESCRIPTION:Title: MICROLOCAL ANALYSIS OF INTERNAL WAVES IN 2D AQUARIA\nby Semyon Dy
atlov (MIT) as part of PDE Analysis Seminar\n\nLecture held in Room 2-136
in the Simon's Building.\n\nAbstract\n\\noindent For a bounded smooth plan
ar domain Ω\, we study the forced evolution problem for the 4th order PDE
\n\n\\begin{equation}\n (\\partial^{2}_{t} \\Delta + \\partial^{2}_{x_
{2}} )u(t\,x)=f(x)cos(\\lambda t)\, t \\geq 0\, x \\in \\Omega\n\\end{equ
ation}\n\n\\vspace{1ex}\n\nwith homogeneous initial conditions and Dirichl
et boundary conditions on $\\partial \\Omega$. This is motivated by conce
ntration of fluid velocity on attractors for stratified fluids in effectiv
ely 2-dimensional aquaria\, first observed experimentally in 1997. \\\\\n\
n\\vspace{1ex}\n\n\\noindent The behavior of solutions to (1) is intimatel
y tied to the chess billiard map on the boundary $\\partial \\Omega$\, whi
ch depends on the forcing frequency λ. Under the natural assumption that
the chess billiard b has the Morse– Smale property\, we show that as $t
\\rightarrow \\infty $ the singular part of the solution u concentrates on
the attractive cycle of b. The proof combines various tools from microloc
al analysis\, scattering theory\, and hyperbolic dynamics. Joint work with
Jian Wang and Maciej Zworski. \\\\\n
LOCATION:https://researchseminars.org/talk/PDEAnalysis/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dominique Maldague (MIT Mathematics)
DTSTART:20221101T190000Z
DTEND:20221101T200000Z
DTSTAMP:20260422T212609Z
UID:PDEAnalysis/18
DESCRIPTION:Title: A SHARP SQUARE FUNCTION ESTIMATE FOR THE MOMENT CURVE IN $\\mathbb{R}
^{3}$\nby Dominique Maldague (MIT Mathematics) as part of PDE Analysis
Seminar\n\n\nAbstract\n\\noindent We will present recent work which prove
s a sharp $L^{7}$ square function estimate for the moment curve in $\\math
bb{R}^{3}$. Consider a function f with Fourier support in a small neighbor
hood of the moment curve. Partition the neighborhood into box-like subsets
and form a square function in the Fourier projections of f onto these box
-like regions. Bounding $f$ in $L_{p}$ by the square function in $L_{p}$ i
s an important way to quantify the cancellation that f has from its specia
lized Fourier support. As Guth\, Wang\, and Zhang did for the cone in 3 di
mensions\, this is another example of using ideas and techniques from deco
upling theory to prove a sharp square function estimate.\n
LOCATION:https://researchseminars.org/talk/PDEAnalysis/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lior Alon (MIT)
DTSTART:20221206T200000Z
DTEND:20221206T210000Z
DTSTAMP:20260422T212609Z
UID:PDEAnalysis/19
DESCRIPTION:Title: Fourier quasicrystals and stable polynomials\nby Lior Alon (MIT)
as part of PDE Analysis Seminar\n\nLecture held in Room 2-136 in the Simon
's Building.\n\nAbstract\nThe Poisson summation formula says that the coun
table sum of exp(int)\, over all integers $n$\, vanishes as long as t is n
ot an integer multiple of $2π$. Can we find a non-periodic discrete set A
\, such that the sum of exp(iat)\, over a in A\, vanishes for all t outsid
e of a discrete set? The surprising answer is yes. Yves Meyer called the a
tomic measure supported on such a set a crystalline measure. Crystalline m
easures provide another surprising connection between physics (quasicrysta
ls) and number theory (the zeros of the Zeta and L functions under GRH). A
recent work of Pavel Kurasov and Peter Sarnak provided a construction of
crystalline measures with ‘good’ convergence (Fourier quasicrystals) u
sing stable polynomials\, a family of multivariate polynomials that were p
reviously used in proving the Lee-Yang circle theorem and the Kadison-Sing
er conjecture. After providing the needed background\, I will discuss a re
cent work in progress with Cynthia Vinzant on the classification of these
Kurasov-Sarnak measures and their supporting sets. We prove that these set
s have well-defined gap distributions. We show that each Kurasov-Sarnak me
asure decomposes according to the irreducible decomposition of its associa
ted polynomial\, and the measures associated with each irreducible factor
is either supported on an arithmetic progression\, or its support has a bo
unded intersection with any arithmetic progression. Finally\, we construct
random Kurasov-Sarnak measures with gap distribution as close as we want
to the eigenvalues spacing of a random unitary matrix.\n
LOCATION:https://researchseminars.org/talk/PDEAnalysis/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hong Wang (UCLA)
DTSTART:20221213T200000Z
DTEND:20221213T210000Z
DTSTAMP:20260422T212609Z
UID:PDEAnalysis/20
DESCRIPTION:Title: Stick Kakeya sets in $R^3$\nby Hong Wang (UCLA) as part of PDE An
alysis Seminar\n\n\nAbstract\nA Kakeya set is a set of points in $\\mathbb
{R}^n$ which contains a unit line segment in every direction. The Kakeya c
onjecture states that the dimension of any Kakeya set is n. This conjectur
e remains wide open for all $n \\geq 3$. \\\\\n\nTogether with Josh Zahl\
, we study a special collection of the Kakeya sets\, namely the sticky Kak
eya sets\, where the line segments in nearby directions stay close. We pr
ove that sticky Kakeya sets in $\\mathbb{R}^3$ have dimension 3. In the ta
lk\, we will also discuss the connection to projection theory in geometric
measure theory\n
LOCATION:https://researchseminars.org/talk/PDEAnalysis/20/
END:VEVENT
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