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BEGIN:VEVENT
SUMMARY:Chongchun Zeng (Georgia Tech)
DTSTART:20200528T193000Z
DTEND:20200528T203000Z
DTSTAMP:20260404T094533Z
UID:MO_Analysis/1
DESCRIPTION:Title: On the dynamics of the focusing energy critical NLS with invers
e square potential\nby Chongchun Zeng (Georgia Tech) as part of MU-MST
joint analysis seminar\n\n\nAbstract\nWe consider the focusing energy cri
tical NLS with inverse square potential in dim 3\, 4\, and 5. We character
ize solutions on the energy surface of the ground state. We prove that sol
utions with kinetic energy less that that of the ground state must scatter
to zero or belong to the stable/unstable manifolds of the ground state. I
n the latter case they converge to the ground state exponentially in the e
nergy space as $t\\to \\pm \\infty$. (In 3-dim without radial assumption\,
this holds under the compactness assumption of non-scattering solutions o
n the energy surface.) When the kinetic energy is greater than that of the
ground state\, we show that radial $H^1$ solutions either blow up in fini
te time or again belong to the stable/unstable manifold of the ground stat
e. The proof relies on the detailed spectral analysis\, local invariant ma
nifold theory\, and a global virial analysis. This is a joint work with Ka
i Yang and Xiaoyi Zhang.\n
LOCATION:https://stable.researchseminars.org/talk/MO_Analysis/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zaher Hani (University of Michigan)
DTSTART:20200604T193000Z
DTEND:20200604T203000Z
DTSTAMP:20260404T094533Z
UID:MO_Analysis/2
DESCRIPTION:Title: On the rigorous derivation of the wave kinetic equations\nb
y Zaher Hani (University of Michigan) as part of MU-MST joint analysis sem
inar\n\n\nAbstract\nWave turbulence theory conjectures that the behavior o
f “generic" solutions of nonlinear dispersive equations is governed (at
least over certain long timescales) by the so-called wave kinetic equation
(WKE). This approximation is supposed to hold in the limit when the size
L of the domain goes to infinity\, and the strength \\alpha of the nonline
arity goes to 0. We will discuss some recent progress towards settling thi
s conjecture\, focusing on a recent joint work with Yu Deng (USC)\, in whi
ch we show that the answer seems to depend on the “scaling law” with w
hich the limit is taken. More precisely\, we identify two favorable scalin
g laws for which we justify rigorously this kinetic picture for very large
times that are arbitrarily close to the kinetic time scale (i.e. within $
L^\\epsilon$ for arbitrarily small $\\epsilon$). These two scaling laws ar
e similar to how the Boltzmann-Grad scaling law is imposed in the derivati
on of Boltzmann's equation. We also give counterexamples showing certain d
ivergences for other scaling laws.\n
LOCATION:https://stable.researchseminars.org/talk/MO_Analysis/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maciej Zworski (University of California Berkeley)
DTSTART:20200611T193000Z
DTEND:20200611T203000Z
DTSTAMP:20260404T094533Z
UID:MO_Analysis/3
DESCRIPTION:Title: Viscosity limits for 0th order operators\nby Maciej Zworski
(University of California Berkeley) as part of MU-MST joint analysis semi
nar\n\n\nAbstract\nFor self-adjoint pseudodifferential operators of order
0\,\nColin de Verdiere and Saint-Raymond introduced natural dynamical\ncon
ditions (motivated by the study of internal waves in fluids)\nguaranteeing
absolute continuity of the spectrum. I will present an\nalter-native appr
oach to obtaining such results based on Melrose’s\nradial propagation es
timates from scattering theory (joint work with\nS. Dyatlov). I will then
explain how an adaptation of the\nHelffer–Sjoestrand theory of scatterin
g resonances shows that in a\ncomplex neighbourhood of the continuous spec
trum viscosity\neigenvalues have limits as viscosity goes to 0. Here the v
iscosity\neigenvalues are the eigenvalues of the original operator to whic
h an\nanti-self-adjoint elliptic 2nd order operator is added. This justifi
es\nclaims made in the physics literature (joint work with J Galkowski).\n
LOCATION:https://stable.researchseminars.org/talk/MO_Analysis/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fabio Pusateri (University of Toronto)
DTSTART:20200625T193000Z
DTEND:20200625T203000Z
DTSTAMP:20260404T094533Z
UID:MO_Analysis/4
DESCRIPTION:Title: Multilinear Harmonic analysis for nonlinear PDEs with potential
s\nby Fabio Pusateri (University of Toronto) as part of MU-MST joint a
nalysis seminar\n\n\nAbstract\nMotivated by questions on the stability of
topological\nsolitons\, we study some nonlinear dispersive PDEs with poten
tials in\nboth 1 and 3 dimensions. Our approach is based on the distorted\
nFourier transform and multilinear harmonic analysis in this setting.\n
LOCATION:https://stable.researchseminars.org/talk/MO_Analysis/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Benjamin Harrop-Griffiths (University of California Los Angeles)
DTSTART:20200702T193000Z
DTEND:20200702T203000Z
DTSTAMP:20260404T094533Z
UID:MO_Analysis/5
DESCRIPTION:Title: Sharp well-posedness for the cubic NLS and mKdV on the line
\nby Benjamin Harrop-Griffiths (University of California Los Angeles) as p
art of MU-MST joint analysis seminar\n\n\nAbstract\nIn this talk we consid
er the cubic nonlinear Schrödinger and modified Korteweg-de Vries equatio
ns on the real line. We present a proof of global well-posedness for both
equations with initial data in any subcritical Sobolev space. An essential
ingredient in our arguments is the demonstration of a local smoothing eff
ect for both equations\, which in turn rests on the discovery of a one-par
ameter family of microscopic conservation laws that remain meaningful at l
ow regularity. This is joint work with Rowan Killip and Monica Visan.\n
LOCATION:https://stable.researchseminars.org/talk/MO_Analysis/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gabriela Jaramillo (University of Houston)
DTSTART:20200723T193000Z
DTEND:20200723T203000Z
DTSTAMP:20260404T094533Z
UID:MO_Analysis/6
DESCRIPTION:Title: A Numerical Method for a Diffusive Class of Nonlocal Operators<
/a>\nby Gabriela Jaramillo (University of Houston) as part of MU-MST joint
analysis seminar\n\n\nAbstract\nIn this talk I will present results provi
ng the existence of solution to integro-differential\nequations involving
convolution kernels of diffusive type\, and establishing the decay of thes
e solutions at infinity. I will show how these results can then be used t
o construct a numerical method based on quadratures to solve nonlocal equa
tions posed on the whole real line\, as well as in bounded domains with no
nlocal Dirichlet and Neumann boundary conditions.\n
LOCATION:https://stable.researchseminars.org/talk/MO_Analysis/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Benoit Pausader (Brown University)
DTSTART:20200716T193000Z
DTEND:20200716T203000Z
DTSTAMP:20260404T094533Z
UID:MO_Analysis/7
DESCRIPTION:Title: Stability of Minkowski space for the Einstein-Klein-Gordon syst
em\nby Benoit Pausader (Brown University) as part of MU-MST joint anal
ysis seminar\n\n\nAbstract\nI will present a recent joint work with A. Ion
escu on the Einstein-Klein-Gordon system\, which is one of the simplest mo
dels that tries to incorporate the effect of matter in General relativity
(by modeling it with a Klein-Gordon field). We consider the asymptotic beh
avior of spacetime which start as small perturbation of an empty Minkowski
space and show that they remain globally smooth and relax to equilibrium
through a modified scattering that we describe precisely. We also give som
e description of the spacetime thus constructed.\n
LOCATION:https://stable.researchseminars.org/talk/MO_Analysis/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ming Chen (University of Pittsburgh)
DTSTART:20200709T193000Z
DTEND:20200709T203000Z
DTSTAMP:20260404T094533Z
UID:MO_Analysis/8
DESCRIPTION:Title: Strong instability of Novikov peakons\nby Ming Chen (Univer
sity of Pittsburgh) as part of MU-MST joint analysis seminar\n\n\nAbstract
\nIn this talk we consider a quasilinear dispersive equation with cubic no
nlinearities which arises from integrable systems and shallow water modeli
ng. A characteristic feature of this equation is its ability to support so
litary waves with corner singularities\, called peakons. These peakons hav
e been shown to be orbitally and asymptotically stable in $H^1$. However i
t is also known that the equation loses continuous dependence on data (and
hence is not well-posed in the Hadamard sense) in $H^1$. We are able to f
ind a function space more suitable for the well-posedness theory for the p
eakons\, and prove that a single peakon fails to be stable in this finer t
opology. Indeed we show that perturbation in this class leads to finite-ti
me blow-up of the corresponding solutions. This is a joint work with Dmitr
y Pelinovsky.\n
LOCATION:https://stable.researchseminars.org/talk/MO_Analysis/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Huy Nguyen (Brown University)
DTSTART:20200730T193000Z
DTEND:20200730T203000Z
DTSTAMP:20260404T094533Z
UID:MO_Analysis/9
DESCRIPTION:Title: Proof of modulational instability of Stokes waves in deep water
\nby Huy Nguyen (Brown University) as part of MU-MST joint analysis se
minar\n\n\nAbstract\nIt is proven that small-amplitude steady periodic wat
er waves with infinite depth are unstable with respect to long-wave pertur
bations. This modulational instability was first observed more than half a
century ago by Benjamin and Feir. It has never been proven rigorously exc
ept in the case of finite depth. We provide a completely different and sel
f-contained approach to prove the spectral modulational instability for wa
ter waves in both the finite and infinite depth cases. Our linearization r
etains the physical variables and is compatible with energy estimates for
the nonlinear problem.\n
LOCATION:https://stable.researchseminars.org/talk/MO_Analysis/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Taryn Flock (Macalester College)
DTSTART:20200813T193000Z
DTEND:20200813T203000Z
DTSTAMP:20260404T094533Z
UID:MO_Analysis/10
DESCRIPTION:Title: A nonlinear Brascamp-Lieb inequality\nby Taryn Flock (Maca
lester College) as part of MU-MST joint analysis seminar\n\n\nAbstract\nIn
equalities play a central role in harmonic analysis. However\, in many cas
es the fundamental question "When and how can one achieve equality?" is le
ft unanswered. Answering these questions opens the door to proving stronge
r or perturbed versions of the inequality. The focus of the talk will be
a nonlinear generalization of the classical Brascamp–Lieb inequality in
a general setting. A first step in this analysis is understanding the re
gularity of the sharp constant in the Brascamp-Lieb inequality. Time perm
itting\, I will highlight connections to computer science\, geometry\, and
number theory. (works discussed will include joint work with Jon Bennett\
, Neal Bez\, Stefan Buschenhenke\, Michael Cowling\, and Sanghyuk Lee).\n
LOCATION:https://stable.researchseminars.org/talk/MO_Analysis/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hao Jia (University of Minnesota)
DTSTART:20201002T200000Z
DTEND:20201002T210000Z
DTSTAMP:20260404T094533Z
UID:MO_Analysis/11
DESCRIPTION:Title: Long time dynamics of 2d Euler and nonlinear inviscid damping<
/a>\nby Hao Jia (University of Minnesota) as part of MU-MST joint analysis
seminar\n\n\nAbstract\nIn this talk\, we will discuss some joint work wit
h Alexandru Ionescu on the nonlinear inviscid damping near point vortex an
d monotone shear flows in a finite channel. We will put these results in t
he context of long time behavior of 2d Euler equations and indicate furthe
r important open problems in the field.\n
LOCATION:https://stable.researchseminars.org/talk/MO_Analysis/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vera Mikyoung Hur (University of Illinois Urbana Champaign)
DTSTART:20201016T200000Z
DTEND:20201016T210000Z
DTSTAMP:20260404T094533Z
UID:MO_Analysis/12
DESCRIPTION:Title: Unstable Stokes waves: A periodic Evans function approach\
nby Vera Mikyoung Hur (University of Illinois Urbana Champaign) as part of
MU-MST joint analysis seminar\n\n\nAbstract\nI will discuss spectral inst
ability of a Stokes wave of small amplitude in the finite depth. Analysis
of the periodic Evans function near the origin of the spectral plane offer
s an alternative proof of the Benjamin-Feir instability. Analysis near a p
air of resonance frequencies reveals spectral instability when 0.8644...<(
wave number)x(depth)<1.0079.... The Benjamin-Feir instability occurs when
(wave number)x(depth)>1.3627...\, so new unstable waves are found. This se
ems the first rigorous proof of the high-frequency instability. Joint work
with Z. Yang.\n
LOCATION:https://stable.researchseminars.org/talk/MO_Analysis/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sameer Iyer (Princeton University)
DTSTART:20201009T200000Z
DTEND:20201009T210000Z
DTSTAMP:20260404T094533Z
UID:MO_Analysis/13
DESCRIPTION:Title: Global in x Stability of Prandtl's Boundary Layer for 2D\, Sta
tionary Navier-Stokes Flows\nby Sameer Iyer (Princeton University) as
part of MU-MST joint analysis seminar\n\n\nAbstract\nIn this talk I will d
iscuss a recent work which proves stability of Prandtl's boundary layer in
the vanishing viscosity limit. The result is an asymptotic stability resu
lt of the background profile in two senses: asymptotic as the viscosity te
nds to zero and asymptotic as x (which acts a time variable) goes to infin
ity. In particular\, this confirms the lack of the "boundary layer separat
ion" in certain regimes which have been predicted to be stable. This is jo
int work w. Nader Masmoudi (Courant Institute\, NYU).\n
LOCATION:https://stable.researchseminars.org/talk/MO_Analysis/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maria Ntekoume (Rice University)
DTSTART:20200925T200000Z
DTEND:20200925T210000Z
DTSTAMP:20260404T094533Z
UID:MO_Analysis/14
DESCRIPTION:Title: Symplectic non-squeezing for the KdV flow on the line\nby
Maria Ntekoume (Rice University) as part of MU-MST joint analysis seminar\
n\n\nAbstract\nWe prove that the KdV flow on the line cannot squeeze a bal
l in $\\dot H^{-\\frac 1 2}(\\mathbb R)$ into a cylinder of lesser radius.
This is a PDE analogue of Gromov’s famous symplectic non-squeezing theo
rem for an infinite dimensional PDE in infinite volume\n
LOCATION:https://stable.researchseminars.org/talk/MO_Analysis/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Juhi Jang (University of Southern California)
DTSTART:20201204T210000Z
DTEND:20201204T220000Z
DTSTAMP:20260404T094533Z
UID:MO_Analysis/15
DESCRIPTION:Title: Dynamics of Newtonian stars\nby Juhi Jang (University of S
outhern California) as part of MU-MST joint analysis seminar\n\n\nAbstract
\nA classical model to describe the dynamics of Newtonian stars is the gra
vitational Euler-Poisson system. The Euler-Poisson system admits a wide ra
nge of star solutions that are in equilibrium or expand for all time or co
llapse in a finite time or rotate. In this talk\, I will discuss some rece
nt progress on those star solutions with focus on expansion and collapse.\
n
LOCATION:https://stable.researchseminars.org/talk/MO_Analysis/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gong Chen (Fields Institute)
DTSTART:20200918T200000Z
DTEND:20200918T210000Z
DTSTAMP:20260404T094533Z
UID:MO_Analysis/16
DESCRIPTION:Title: Long-time dynamics of the sine-Gordon equation\nby Gong Ch
en (Fields Institute) as part of MU-MST joint analysis seminar\n\n\nAbstra
ct\nIn the first part of this talk\, I will illustrate how to compute the
long-time asymptotics of the sine-Gordon equation using its integrable str
ucture and nonlinear steepest descent. Then I will discuss the asymptotic
stability of the sine-Gordon equation in weighted energy space. It is kno
wn that the obstruction to the asymptotic stability of the sine-Gordon eq
uation in the energy space is the existence of small breathers which is a
lso closely related to the emergence of wobbling kinks. Our stability an
alysis gives a criterion for the weight which is sharp up to the endpoint
so that the asymptotic stability holds.\n
LOCATION:https://stable.researchseminars.org/talk/MO_Analysis/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mihaela Ifrim (University of Wisconsin Madison)
DTSTART:20201023T200000Z
DTEND:20201023T210000Z
DTSTAMP:20260404T094533Z
UID:MO_Analysis/17
DESCRIPTION:Title: Two dimensional gravity water waves at low regularity: global
solutions\nby Mihaela Ifrim (University of Wisconsin Madison) as part
of MU-MST joint analysis seminar\n\n\nAbstract\nThis article represents th
e second installment of a series of papers concerned with low regularity s
olutions for the water wave equations in two space dimensions. Our focus h
ere is on global solutions for small and localized data. Such solutions ha
ve been proved to exist earlier in much higher regularity. The goal of thi
s talk is to explain how these results were improved\, specifically show g
lobal well-posedness under minimal regularity and decay assumptions for th
e initial data. One key ingredient here is represented by the balanced cub
ic estimates. Another is the nonlinear vector field Sobolev inequalities\,
an idea first introduced by the last two authors in the context of the Be
njamin-Ono equations. This is joint work with Albert Ai and Daniel Tataru.
\n
LOCATION:https://stable.researchseminars.org/talk/MO_Analysis/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rui Han (Louisiana State University)
DTSTART:20201030T200000Z
DTEND:20201030T210000Z
DTSTAMP:20260404T094533Z
UID:MO_Analysis/18
DESCRIPTION:Title: Spectral gaps in graphene structures\nby Rui Han (Louisian
a State University) as part of MU-MST joint analysis seminar\n\n\nAbstract
\nWe present a full analysis of the spectrum of graphene models on graphs
in magnetic fields with constant flux through every hexagonal comb. In par
ticular\, we provide a rigorous foundation for self-similarity by showing
that for irrational flux\, the spectrum of graphene is a zero measure Cant
or set. For arbitrary rational flux\, we show the existence of Dirac cones
. We also show that for trivial flux\, the spectral bands have nontrivial
overlap\, which leads to the proof of the discrete Bethe-Sommerfeld conjec
ture for the hexagonal lattice. This talk is based on joint works with S.
Becker\, J. Fillman and S. Jitomirskaya.\n
LOCATION:https://stable.researchseminars.org/talk/MO_Analysis/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pierre Germain (Courant Institute of Mathematical Sciences\, New Y
ork University)
DTSTART:20201106T210000Z
DTEND:20201106T220000Z
DTSTAMP:20260404T094533Z
UID:MO_Analysis/19
DESCRIPTION:Title: Stability of kinks in one-dimensional Klein-Gordon equations\nby Pierre Germain (Courant Institute of Mathematical Sciences\, New Yo
rk University) as part of MU-MST joint analysis seminar\n\n\nAbstract\nKin
ks are topological solitons\, which appear in (nonlinear) one-dimensional
Klein-Gordon equations\, the Phi-4 and Sine-Gordon equations being the mos
t well-known examples. I will present new results which give asymptotic st
ability for kinks\, with an explicit decay rate\, in some cases. The proof
relies on the distorted Fourier transform associated to the linearized eq
uation around the soliton\; this method should be of interest for more gen
eral soliton stability problems. This is joint work with Fabio Pusateri.\n
LOCATION:https://stable.researchseminars.org/talk/MO_Analysis/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jacob Bedrossian (University of Maryland)
DTSTART:20201120T210000Z
DTEND:20201120T220000Z
DTSTAMP:20260404T094533Z
UID:MO_Analysis/20
DESCRIPTION:Title: Almost-sure exponential mixing in stochastic fluid mechanics a
nd Batchelor-regime passive scalar turbulence\nby Jacob Bedrossian (Un
iversity of Maryland) as part of MU-MST joint analysis seminar\n\n\nAbstra
ct\nIn 1959\, Batchelor predicted that passive scalars advected in incompr
essible fluids with small diffusivity k should display a $|k|^{−1}$ powe
r spectrum in a statistically stationary experiment at scales small enough
for the velocity to be effectively smooth. This prediction has since been
tested extensively in physics. Results obtained with Alex Blumenthal and
Sam Punshon-Smith provide the first mathematically rigorous proof of this
law in the fixed Reynolds number case under stochastic forcing. We show th
at the origin of the Batchelor spectrum is the existence of a uniform\, ex
ponential rate that all passive scalar fields are mixed at (up to a random
prefactor)\, which we prove using ideas from random dynamical systems suc
h as a la Furstenberg and two-point geometric ergodicity for quenched corr
elation decay.\n
LOCATION:https://stable.researchseminars.org/talk/MO_Analysis/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Olga Trichtchenko (Western University)
DTSTART:20201113T210000Z
DTEND:20201113T220000Z
DTSTAMP:20260404T094533Z
UID:MO_Analysis/21
DESCRIPTION:Title: Stability of Periodic Solutions to Hamiltonian PDEs\nby Ol
ga Trichtchenko (Western University) as part of MU-MST joint analysis semi
nar\n\n\nAbstract\nThis talk will focus on spectral stability of small-amp
litude\, periodic solutions to Hamiltonian\, dispersive partial differenti
al equations. In particular\, it has been shown in the past that periodic
travelling wave solutions to the full Euler equations describing inviscid\
, incompressible fluid flow\, exhibit high frequency instabilities. Howeve
r\, some simpler model equations frequently used\, do not. We will examine
the nature of these instabilities\, how they arise\, and present a genera
l condition for instability. In special cases\, this condition reduces to
considering the interval in which there are roots of a polynomial half the
degree of the polynomial describing the dispersion relation. We will illu
strate the method for computing spectral stability by considering solution
s to the Korteweg-de Vries\, Kawahara\, Whitham and Boussinesq-Whitham equ
ations.\n
LOCATION:https://stable.researchseminars.org/talk/MO_Analysis/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michael Weinstein (Columbia University)
DTSTART:20210312T210000Z
DTEND:20210312T220000Z
DTSTAMP:20260404T094533Z
UID:MO_Analysis/22
DESCRIPTION:Title: Continuum and discrete models of waves in 2D materials\nby
Michael Weinstein (Columbia University) as part of MU-MST joint analysis
seminar\n\n\nAbstract\nWe discuss continuum Schroedinger operators which a
re basic models of 2D-materials\, like graphene\, in its bulk form or defo
rmed by edges (sharp terminations or domain walls). \nFor non-magnetic and
strongly non-magnetic systems we discuss the relationship to effective \n
tight binding (discrete) Hamiltonians through a result on strong resolvent
convergence. An application of this convergence is a result on the equali
ty of topological (Fredholm) indices\nassociated with continuum and discre
te models (for bulk and edge systems). Finally\, we discuss the constructi
on of edge states in continuum systems with domain walls.\n
LOCATION:https://stable.researchseminars.org/talk/MO_Analysis/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Monica Visan (UCLA)
DTSTART:20210219T210000Z
DTEND:20210219T220000Z
DTSTAMP:20260404T094533Z
UID:MO_Analysis/23
DESCRIPTION:Title: Recent progress on well-posedness for integrable PDE\nby M
onica Visan (UCLA) as part of MU-MST joint analysis seminar\n\n\nAbstract\
nI will present the new method developed in joint work with\nKillip for pr
oving optimal well-posedness for integrable PDE. I will\nfirst discuss th
is method in the context of the Korteweg-de Vries\nequation. I will then
discuss subsequent developments (joint with\nHarrop-Griffiths and Killip)
that have led to optimal well-posedness\nresults for the integrable nonlin
ear Schrödinger and the modified\nKorteweg-de Vries equations.\n
LOCATION:https://stable.researchseminars.org/talk/MO_Analysis/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kevin O'Neill (UC Davis)
DTSTART:20210205T210000Z
DTEND:20210205T220000Z
DTSTAMP:20260404T094533Z
UID:MO_Analysis/24
DESCRIPTION:Title: A Nonnegative Version of Whitney's Extension Problem\nby K
evin O'Neill (UC Davis) as part of MU-MST joint analysis seminar\n\n\nAbst
ract\nWhitney's Extension Problem asks the following: Given a compact set
$E\\subset\\mathbb{R}^n$ and a function $f:E\\to\\mathbb{R}$\, how can we
tell if there exists $F\\in C^m(\\mathbb{R}^n)$ such that $F|_E=f$? The cl
assical Whitney Extension theorem tells us that\, given potential Taylor p
olynomials $P^x$ at each $x\\in E$\, there is such an extension F if and o
nly if the $P^x$'s are compatible under Taylor's theorem. However\, this l
eaves open the question of how to tell solely from $f$. A 2006 paper of Ch
arles Fefferman answers this question. We explain some of the concepts of
that paper\, as well as recent work of the speaker\, joint with Fushuai Ji
ang and Garving K. Luli\, which establishes the analogous result when $f\\
ge0$ and we require $F\\ge0$.\n
LOCATION:https://stable.researchseminars.org/talk/MO_Analysis/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Steve Shkoller (UC Davis)
DTSTART:20210319T200000Z
DTEND:20210319T210000Z
DTSTAMP:20260404T094533Z
UID:MO_Analysis/25
DESCRIPTION:Title: Shock formation for the 3d Euler equations\nby Steve Shkol
ler (UC Davis) as part of MU-MST joint analysis seminar\n\n\nAbstract\nIn
this talk\, I will discuss the shock formation process for the 3d compress
ible Euler equations\, in which sounds waves interact with entropy waves t
o produce vorticity. Smooth solutions form a generic stable shock with ex
plicitly computable blowup time\, location\, and direction. Our method est
ablishes the asymptotic stability of a generic shock profile in modulated
self-similar variables\, controlling the interaction of wave families via:
(i) pointwise bounds along Lagrangian trajectories\, (ii) geometric vorti
city structure\, and (iii) high-order energy estimates in Sobolev spaces.
This is joint work with T. Buckmaster and V. Vicol.\n
LOCATION:https://stable.researchseminars.org/talk/MO_Analysis/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Svetlana Roudenko (Florida International University)
DTSTART:20210423T200000Z
DTEND:20210423T210000Z
DTSTAMP:20260404T094533Z
UID:MO_Analysis/26
DESCRIPTION:Title: Toward soliton resolution in KdV-type equations\nby Svetla
na Roudenko (Florida International University) as part of MU-MST joint ana
lysis seminar\n\n\nAbstract\nThe questions about soliton resolution\, soli
ton stability or formation of blow-up in KdV-type equations have been intr
iguing the researchers for quite some time. \nIn this talk we will look at
a higher dimensional version of the KdV equation\, called Zakharov-Kuznet
sov (ZK) equation and discuss \nbehavior of solutions in the 2d and 3d mod
els as those are physically relevant. \nIn particular\, we will examine th
e behavior of solutions close to solitons in different settings. \n Dire
ct numerical simulations for the KdV-type equations\, such as ZK\, with ge
neric data show that solutions split into\nsolitons traveling in the posit
ive x-direction and radiation dispersing in the negative x-direction (poss
ibly at a specific angle in dimension 2 and higher). \nIn the L^2-critical
and supercritical cases (for example\, 2d cubic ZK equation)\, some of th
e solitons\, traveling\nto the right\, blow-up in finite time.\n Analyti
cally\, we prove existence of blow-up solutions in the 2d cubic (critical)
ZK equation. \nIn subcritical case\, such as 3d quadratic ZK\, we obtain
asymptotic stability of solitons in finite energy space. \nThe talk is bas
ed on joint works with Luiz Gustavo Farah\, Justin Holmer\, Christian Klei
n\, Nikola Stoilov\, and Kai Yang.\n
LOCATION:https://stable.researchseminars.org/talk/MO_Analysis/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zhiwu Lin (Georgia Tech)
DTSTART:20210305T210000Z
DTEND:20210305T220000Z
DTSTAMP:20260404T094533Z
UID:MO_Analysis/28
DESCRIPTION:Title: Stability of some stellar models\nby Zhiwu Lin (Georgia Te
ch) as part of MU-MST joint analysis seminar\n\n\nAbstract\nI will discuss
some results on stability of non-rotating and rotating stars. First\, we
proved a turning point principle which states that the stability changes a
t the critical points of the total mass for a family of nonrotating stars
parametrized by the center density. This is joint with Chongchun Zeng. The
n we will discuss some recent results with Yucong Wang on the stability an
d instability of rotating stars with general angular velocity profiles.\n
LOCATION:https://stable.researchseminars.org/talk/MO_Analysis/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ian Tice (Carnegie Mellon)
DTSTART:20210226T210000Z
DTEND:20210226T220000Z
DTSTAMP:20260404T094533Z
UID:MO_Analysis/29
DESCRIPTION:Title: Traveling wave solutions to the free boundary Navier-Stokes eq
uations\nby Ian Tice (Carnegie Mellon) as part of MU-MST joint analysi
s seminar\n\n\nAbstract\nConsider a layer of viscous incompressible fluid
bounded below\nby a flat rigid boundary and above by a moving boundary. T
he fluid is\nsubject to gravity\, surface tension\, and an external stress
that is\nstationary when viewed in coordinate system moving at a constant
\nvelocity parallel to the lower boundary. The latter can model\, for\nin
stance\, a tube blowing air on the fluid while translating across the\nsur
face. In this talk we will detail the construction of traveling wave\nsol
utions to this problem\, which are themselves stationary in the same\ntran
slating coordinate system. While such traveling wave solutions to\nthe Eu
ler equations are well-known\, to the best of our knowledge this is\nthe f
irst construction of such solutions with viscosity. This is joint\nwork w
ith Giovanni Leoni.\n
LOCATION:https://stable.researchseminars.org/talk/MO_Analysis/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bjoern Bringmann (UCLA)
DTSTART:20210212T210000Z
DTEND:20210212T220000Z
DTSTAMP:20260404T094533Z
UID:MO_Analysis/30
DESCRIPTION:Title: Invariant Gibbs measures for the three-dimensional wave equati
on with a Hartree nonlinearity\nby Bjoern Bringmann (UCLA) as part of
MU-MST joint analysis seminar\n\n\nAbstract\nIn this talk\, we discuss the
construction and invariance of the Gibbs measure for a threedimensional w
ave equation with a Hartree-nonlinearity.\nIn the first part of the talk\,
we construct the Gibbs measure and examine its properties. We discuss the
\nmutual singularity of the Gibbs measure and the so-called Gaussian free
field. In contrast\, the Gibbs\nmeasure for one or two-dimensional wave eq
uations is absolutely continuous with respect to the Gaussian\nfree field.
\n\n\nIn the second part of the talk\, we discuss the probabilistic well-p
osedness of the corresponding nonlinear\nwave equation\, which is needed i
n the proof of invariance. At the moment\, this is the only theorem provin
g\nthe invariance of any singular Gibbs measure under a dispersive equatio
n.\n
LOCATION:https://stable.researchseminars.org/talk/MO_Analysis/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anna Mazzucato (Penn State)
DTSTART:20210430T200000Z
DTEND:20210430T210000Z
DTSTAMP:20260404T094533Z
UID:MO_Analysis/31
DESCRIPTION:Title: Enhanced dissipation and global existence for the 2D Kuramoto
-Sivashinsky equation\nby Anna Mazzucato (Penn State) as part of MU-MS
T joint analysis seminar\n\n\nAbstract\nWe consider the Kuramoto-Sivashins
ky equation (KSE) on the two-dimensional torus in scalar form. We prove gl
obal existence for small data in the absence of growing modes. If growing
modes are present\, we show that global existence for arbitrary data holds
for the advective KSE\, provided the advecting flow field induces a suffi
cient small diffusion time for the linearized operator\, for example if t
he flow is mixing with large amplitude. If the advecting flow is a shear f
low\, then we show global existence still holds by using pseudo-spectral e
stimates.\n
LOCATION:https://stable.researchseminars.org/talk/MO_Analysis/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mat Johnson (University of Kansas)
DTSTART:20210409T200000Z
DTEND:20210409T210000Z
DTSTAMP:20260404T094533Z
UID:MO_Analysis/32
DESCRIPTION:Title: Dynamics of Periodic Lugiato-Lefever Waves\nby Mat Johnson
(University of Kansas) as part of MU-MST joint analysis seminar\n\n\nAbst
ract\nIn this talk\, we will consider the liner and nonlinear dynamics of
perturbations of spectrally stable periodic stationary solutions of the Lu
giato-Lefever equation (LLE)\, a damped nonlinear Schrodinger equation wit
h forcing that arises in optics. It is known that spectrally stable T-per
iodic solutions are nonlinearly stable to subharmonic perturbations\, i.e.
to NT-periodic perturbations for some integer N\, with exponential decay
rates. However\, both the exponential rates of decay and the allowable si
ze of initial perturbations both tend to zero as $N\\to\\infty$\, and henc
e such subharmonic stability results are not uniform in N and are\, in fac
t\, empty in the limit $N=\\infty$. The primary goal of this talk is to i
ntroduce a methodology\, in the context of the LLE\, by which a uniform in
N stability result for subharmonic perturbations may be achieved (at leas
t at the linear level). The obtained uniform decay rates are shown to agr
ee precisely with the polynomial decay rates of localized\, i.e. integrabl
e on the line\, perturbations of such spectrally stable periodic solutions
of LLE. If time permits\, I will also discuss recent progress towards ex
tending these results for the LLE to the nonlinear level. This is joint w
ith with Mariana Haragus (Univ. Bourgogne Franche-Comtè)\, Wesley Perkins
(KU) and Bjorn de-Rijk (Stuttgart)\n
LOCATION:https://stable.researchseminars.org/talk/MO_Analysis/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jon Wilkening (UC Berkeley)
DTSTART:20210326T200000Z
DTEND:20210326T210000Z
DTSTAMP:20260404T094533Z
UID:MO_Analysis/33
DESCRIPTION:Title: Quasi-periodic water waves\nby Jon Wilkening (UC Berkeley)
as part of MU-MST joint analysis seminar\n\n\nAbstract\nWe present a fram
ework to compute and study two-dimensional water waves that are quasi-peri
odic in space and/or time. This means they can be represented as periodic
functions on a higher-dimensional torus by evaluating along irrational dir
ections. In the spatially quasi-periodic case\, the nonlocal Dirichlet-Neu
mann operator is computed using conformal mapping methods and a quasi-peri
odic variant of the Hilbert transform. In the temporally quasi-periodic ca
se\, we devise a shooting method to compute standing waves with 3 quasi-pe
riods as well as hybrid traveling-standing waves that return to a spatial
translation of their initial condition at a later time. Many examples will
be given to illustrate the types of behavior that can occur.\n
LOCATION:https://stable.researchseminars.org/talk/MO_Analysis/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maciej Zworski (UC Berkeley)
DTSTART:20210416T200000Z
DTEND:20210416T210000Z
DTSTAMP:20260404T094533Z
UID:MO_Analysis/34
DESCRIPTION:Title: Mathematics of magic angles for bilayer graphene\nby Macie
j Zworski (UC Berkeley) as part of MU-MST joint analysis seminar\n\n\nAbst
ract\nMagic angles are a hot topic in condensed matter physics:\nwhen two
sheets of graphene are twisted by those angles the resulting\nmaterial is
superconducting. I will present a very simple operator\nwhose spectral pr
operties are thought to determine which angles are magical.\nIt comes from
a recent PR Letter by Tarnopolsky--Kruchkov--Vishwanath.\nThe mathematics
behind this is an elementary blend of representation theory\n(of the Heis
enberg group in characteristic three)\, Jacobi theta functions and\nspectr
al instability of non-self-adjoint operators (involving Hörmander's\nbrac
ket condition in a very simple setting). The results will be illustrated b
y\ncolourful numerics which suggest some open problems (joint work\nwith S
Becker\, M Embree and J Wittsten).\n
LOCATION:https://stable.researchseminars.org/talk/MO_Analysis/34/
END:VEVENT
END:VCALENDAR