BEGIN:VCALENDAR
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BEGIN:VEVENT
SUMMARY:Chongchun Zeng (Georgia Tech)
DTSTART:20200528T193000Z
DTEND:20200528T203000Z
DTSTAMP:20260422T212602Z
UID:MO_Analysis/1
DESCRIPTION:Title: On the dynamics of the focusing energy critical NLS with inverse squar
e potential\nby Chongchun Zeng (Georgia Tech) as part of MU-MST joint
analysis seminar\n\n\nAbstract\nWe consider the focusing energy critical N
LS with inverse square potential in dim 3\, 4\, and 5. We characterize sol
utions on the energy surface of the ground state. We prove that solutions
with kinetic energy less that that of the ground state must scatter to zer
o or belong to the stable/unstable manifolds of the ground state. In the l
atter case they converge to the ground state exponentially in the energy s
pace as $t\\to \\pm \\infty$. (In 3-dim without radial assumption\, this h
olds under the compactness assumption of non-scattering solutions on the e
nergy surface.) When the kinetic energy is greater than that of the ground
state\, we show that radial $H^1$ solutions either blow up in finite time
or again belong to the stable/unstable manifold of the ground state. The
proof relies on the detailed spectral analysis\, local invariant manifold
theory\, and a global virial analysis. This is a joint work with Kai Yang
and Xiaoyi Zhang.\n
LOCATION:https://researchseminars.org/talk/MO_Analysis/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zaher Hani (University of Michigan)
DTSTART:20200604T193000Z
DTEND:20200604T203000Z
DTSTAMP:20260422T212602Z
UID:MO_Analysis/2
DESCRIPTION:Title: On the rigorous derivation of the wave kinetic equations\nby Zaher
Hani (University of Michigan) as part of MU-MST joint analysis seminar\n\
n\nAbstract\nWave turbulence theory conjectures that the behavior of “ge
neric" solutions of nonlinear dispersive equations is governed (at least o
ver 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 th
e domain goes to infinity\, and the strength \\alpha of the nonlinearity g
oes to 0. We will discuss some recent progress towards settling this conje
cture\, focusing on a recent joint work with Yu Deng (USC)\, in which we s
how that the answer seems to depend on the “scaling law” with which th
e limit is taken. More precisely\, we identify two favorable scaling 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 $L^\\eps
ilon$ for arbitrarily small $\\epsilon$). These two scaling laws are simil
ar to how the Boltzmann-Grad scaling law is imposed in the derivation of B
oltzmann's equation. We also give counterexamples showing certain divergen
ces for other scaling laws.\n
LOCATION:https://researchseminars.org/talk/MO_Analysis/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maciej Zworski (University of California Berkeley)
DTSTART:20200611T193000Z
DTEND:20200611T203000Z
DTSTAMP:20260422T212602Z
UID:MO_Analysis/3
DESCRIPTION:Title: Viscosity limits for 0th order operators\nby Maciej Zworski (Unive
rsity of California Berkeley) as part of MU-MST joint analysis seminar\n\n
\nAbstract\nFor self-adjoint pseudodifferential operators of order 0\,\nCo
lin de Verdiere and Saint-Raymond introduced natural dynamical\nconditions
(motivated by the study of internal waves in fluids)\nguaranteeing absolu
te continuity of the spectrum. I will present an\nalter-native approach to
obtaining such results based on Melrose’s\nradial propagation estimates
from scattering theory (joint work with\nS. Dyatlov). I will then explain
how an adaptation of the\nHelffer–Sjoestrand theory of scattering reson
ances shows that in a\ncomplex neighbourhood of the continuous spectrum vi
scosity\neigenvalues have limits as viscosity goes to 0. Here the viscosit
y\neigenvalues are the eigenvalues of the original operator to which an\na
nti-self-adjoint elliptic 2nd order operator is added. This justifies\ncla
ims made in the physics literature (joint work with J Galkowski).\n
LOCATION:https://researchseminars.org/talk/MO_Analysis/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fabio Pusateri (University of Toronto)
DTSTART:20200625T193000Z
DTEND:20200625T203000Z
DTSTAMP:20260422T212602Z
UID:MO_Analysis/4
DESCRIPTION:Title: Multilinear Harmonic analysis for nonlinear PDEs with potentials\n
by Fabio Pusateri (University of Toronto) as part of MU-MST joint analysis
seminar\n\n\nAbstract\nMotivated by questions on the stability of topolog
ical\nsolitons\, we study some nonlinear dispersive PDEs with potentials i
n\nboth 1 and 3 dimensions. Our approach is based on the distorted\nFourie
r transform and multilinear harmonic analysis in this setting.\n
LOCATION:https://researchseminars.org/talk/MO_Analysis/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Benjamin Harrop-Griffiths (University of California Los Angeles)
DTSTART:20200702T193000Z
DTEND:20200702T203000Z
DTSTAMP:20260422T212602Z
UID:MO_Analysis/5
DESCRIPTION:Title: Sharp well-posedness for the cubic NLS and mKdV on the line\nby Be
njamin Harrop-Griffiths (University of California Los Angeles) as part of
MU-MST joint analysis seminar\n\n\nAbstract\nIn this talk we consider the
cubic nonlinear Schrödinger and modified Korteweg-de Vries equations on t
he real line. We present a proof of global well-posedness for both equatio
ns with initial data in any subcritical Sobolev space. An essential ingred
ient in our arguments is the demonstration of a local smoothing effect for
both equations\, which in turn rests on the discovery of a one-parameter
family of microscopic conservation laws that remain meaningful at low regu
larity. This is joint work with Rowan Killip and Monica Visan.\n
LOCATION:https://researchseminars.org/talk/MO_Analysis/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gabriela Jaramillo (University of Houston)
DTSTART:20200723T193000Z
DTEND:20200723T203000Z
DTSTAMP:20260422T212602Z
UID:MO_Analysis/6
DESCRIPTION:Title: A Numerical Method for a Diffusive Class of Nonlocal Operators\nby
Gabriela Jaramillo (University of Houston) as part of MU-MST joint analys
is seminar\n\n\nAbstract\nIn this talk I will present results proving the
existence of solution to integro-differential\nequations involving convolu
tion kernels of diffusive type\, and establishing the decay of these solut
ions at infinity. I will show how these results can then be used to const
ruct a numerical method based on quadratures to solve nonlocal equations p
osed on the whole real line\, as well as in bounded domains with nonlocal
Dirichlet and Neumann boundary conditions.\n
LOCATION:https://researchseminars.org/talk/MO_Analysis/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Benoit Pausader (Brown University)
DTSTART:20200716T193000Z
DTEND:20200716T203000Z
DTSTAMP:20260422T212602Z
UID:MO_Analysis/7
DESCRIPTION:Title: Stability of Minkowski space for the Einstein-Klein-Gordon system\
nby Benoit Pausader (Brown University) as part of MU-MST joint analysis se
minar\n\n\nAbstract\nI will present a recent joint work with A. Ionescu on
the Einstein-Klein-Gordon system\, which is one of the simplest models th
at tries to incorporate the effect of matter in General relativity (by mod
eling it with a Klein-Gordon field). We consider the asymptotic behavior o
f 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 some descr
iption of the spacetime thus constructed.\n
LOCATION:https://researchseminars.org/talk/MO_Analysis/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ming Chen (University of Pittsburgh)
DTSTART:20200709T193000Z
DTEND:20200709T203000Z
DTSTAMP:20260422T212602Z
UID:MO_Analysis/8
DESCRIPTION:Title: Strong instability of Novikov peakons\nby Ming Chen (University of
Pittsburgh) as part of MU-MST joint analysis seminar\n\n\nAbstract\nIn th
is talk we consider a quasilinear dispersive equation with cubic nonlinear
ities which arises from integrable systems and shallow water modeling. A c
haracteristic feature of this equation is its ability to support solitary
waves with corner singularities\, called peakons. These peakons have been
shown to be orbitally and asymptotically stable in $H^1$. However it is al
so 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 find a f
unction space more suitable for the well-posedness theory for the peakons\
, and prove that a single peakon fails to be stable in this finer topology
. Indeed we show that perturbation in this class leads to finite-time blow
-up of the corresponding solutions. This is a joint work with Dmitry Pelin
ovsky.\n
LOCATION:https://researchseminars.org/talk/MO_Analysis/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Huy Nguyen (Brown University)
DTSTART:20200730T193000Z
DTEND:20200730T203000Z
DTSTAMP:20260422T212602Z
UID:MO_Analysis/9
DESCRIPTION:Title: Proof of modulational instability of Stokes waves in deep water\nb
y Huy Nguyen (Brown University) as part of MU-MST joint analysis seminar\n
\n\nAbstract\nIt is proven that small-amplitude steady periodic water wave
s with infinite depth are unstable with respect to long-wave perturbations
. This modulational instability was first observed more than half a centur
y ago by Benjamin and Feir. It has never been proven rigorously except in
the case of finite depth. We provide a completely different and self-conta
ined approach to prove the spectral modulational instability for water wav
es in both the finite and infinite depth cases. Our linearization retains
the physical variables and is compatible with energy estimates for the non
linear problem.\n
LOCATION:https://researchseminars.org/talk/MO_Analysis/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Taryn Flock (Macalester College)
DTSTART:20200813T193000Z
DTEND:20200813T203000Z
DTSTAMP:20260422T212602Z
UID:MO_Analysis/10
DESCRIPTION:Title: A nonlinear Brascamp-Lieb inequality\nby Taryn Flock (Macalester
College) as part of MU-MST joint analysis seminar\n\n\nAbstract\nInequalit
ies play a central role in harmonic analysis. However\, in many cases the
fundamental question "When and how can one achieve equality?" is left unan
swered. Answering these questions opens the door to proving stronger or pe
rturbed versions of the inequality. The focus of the talk will be a nonli
near generalization of the classical Brascamp–Lieb inequality in a gener
al setting. A first step in this analysis is understanding the regularit
y of the sharp constant in the Brascamp-Lieb inequality. Time permitting\
, 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://researchseminars.org/talk/MO_Analysis/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hao Jia (University of Minnesota)
DTSTART:20201002T200000Z
DTEND:20201002T210000Z
DTSTAMP:20260422T212602Z
UID:MO_Analysis/11
DESCRIPTION:Title: Long time dynamics of 2d Euler and nonlinear inviscid damping\nby
Hao Jia (University of Minnesota) as part of MU-MST joint analysis semina
r\n\n\nAbstract\nIn this talk\, we will discuss some joint work with Alexa
ndru Ionescu on the nonlinear inviscid damping near point vortex and monot
one shear flows in a finite channel. We will put these results in the cont
ext of long time behavior of 2d Euler equations and indicate further impor
tant open problems in the field.\n
LOCATION:https://researchseminars.org/talk/MO_Analysis/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vera Mikyoung Hur (University of Illinois Urbana Champaign)
DTSTART:20201016T200000Z
DTEND:20201016T210000Z
DTSTAMP:20260422T212602Z
UID:MO_Analysis/12
DESCRIPTION:Title: Unstable Stokes waves: A periodic Evans function approach\nby Ver
a Mikyoung Hur (University of Illinois Urbana Champaign) as part of MU-MST
joint analysis seminar\n\n\nAbstract\nI will discuss spectral instability
of a Stokes wave of small amplitude in the finite depth. Analysis of the
periodic Evans function near the origin of the spectral plane offers an al
ternative proof of the Benjamin-Feir instability. Analysis near a pair of
resonance frequencies reveals spectral instability when 0.8644...<(wave nu
mber)x(depth)<1.0079.... The Benjamin-Feir instability occurs when (wave n
umber)x(depth)>1.3627...\, so new unstable waves are found. This seems the
first rigorous proof of the high-frequency instability. Joint work with Z
. Yang.\n
LOCATION:https://researchseminars.org/talk/MO_Analysis/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sameer Iyer (Princeton University)
DTSTART:20201009T200000Z
DTEND:20201009T210000Z
DTSTAMP:20260422T212602Z
UID:MO_Analysis/13
DESCRIPTION:Title: Global in x Stability of Prandtl's Boundary Layer for 2D\, Stationary
Navier-Stokes Flows\nby Sameer Iyer (Princeton University) as part of
MU-MST joint analysis seminar\n\n\nAbstract\nIn this talk I will discuss
a recent work which proves stability of Prandtl's boundary layer in the va
nishing viscosity limit. The result is an asymptotic stability result of t
he background profile in two senses: asymptotic as the viscosity tends to
zero and asymptotic as x (which acts a time variable) goes to infinity. In
particular\, this confirms the lack of the "boundary layer separation" in
certain regimes which have been predicted to be stable. This is joint wor
k w. Nader Masmoudi (Courant Institute\, NYU).\n
LOCATION:https://researchseminars.org/talk/MO_Analysis/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maria Ntekoume (Rice University)
DTSTART:20200925T200000Z
DTEND:20200925T210000Z
DTSTAMP:20260422T212602Z
UID:MO_Analysis/14
DESCRIPTION:Title: Symplectic non-squeezing for the KdV flow on the line\nby Maria N
tekoume (Rice University) as part of MU-MST joint analysis seminar\n\n\nAb
stract\nWe prove that the KdV flow on the line cannot squeeze a ball in $\
\dot H^{-\\frac 1 2}(\\mathbb R)$ into a cylinder of lesser radius. This i
s a PDE analogue of Gromov’s famous symplectic non-squeezing theorem for
an infinite dimensional PDE in infinite volume\n
LOCATION:https://researchseminars.org/talk/MO_Analysis/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Juhi Jang (University of Southern California)
DTSTART:20201204T210000Z
DTEND:20201204T220000Z
DTSTAMP:20260422T212602Z
UID:MO_Analysis/15
DESCRIPTION:Title: Dynamics of Newtonian stars\nby Juhi Jang (University of Southern
California) as part of MU-MST joint analysis seminar\n\n\nAbstract\nA cla
ssical model to describe the dynamics of Newtonian stars is the gravitatio
nal Euler-Poisson system. The Euler-Poisson system admits a wide range of
star solutions that are in equilibrium or expand for all time or collapse
in a finite time or rotate. In this talk\, I will discuss some recent prog
ress on those star solutions with focus on expansion and collapse.\n
LOCATION:https://researchseminars.org/talk/MO_Analysis/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gong Chen (Fields Institute)
DTSTART:20200918T200000Z
DTEND:20200918T210000Z
DTSTAMP:20260422T212602Z
UID:MO_Analysis/16
DESCRIPTION:Title: Long-time dynamics of the sine-Gordon equation\nby Gong Chen (Fie
lds Institute) as part of MU-MST joint analysis seminar\n\n\nAbstract\nIn
the first part of this talk\, I will illustrate how to compute the long-ti
me asymptotics of the sine-Gordon equation using its integrable structure
and nonlinear steepest descent. Then I will discuss the asymptotic stabili
ty of the sine-Gordon equation in weighted energy space. It is known that
the obstruction to the asymptotic stability of the sine-Gordon equation
in the energy space is the existence of small breathers which is also clo
sely related to the emergence of wobbling kinks. Our stability analysis
gives a criterion for the weight which is sharp up to the endpoint so tha
t the asymptotic stability holds.\n
LOCATION:https://researchseminars.org/talk/MO_Analysis/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mihaela Ifrim (University of Wisconsin Madison)
DTSTART:20201023T200000Z
DTEND:20201023T210000Z
DTSTAMP:20260422T212602Z
UID:MO_Analysis/17
DESCRIPTION:Title: Two dimensional gravity water waves at low regularity: global solutio
ns\nby Mihaela Ifrim (University of Wisconsin Madison) as part of MU-M
ST joint analysis seminar\n\n\nAbstract\nThis article represents the secon
d installment of a series of papers concerned with low regularity solution
s for the water wave equations in two space dimensions. Our focus here is
on global solutions for small and localized data. Such solutions have been
proved to exist earlier in much higher regularity. The goal of this talk
is to explain how these results were improved\, specifically show global w
ell-posedness under minimal regularity and decay assumptions for the initi
al data. One key ingredient here is represented by the balanced cubic esti
mates. Another is the nonlinear vector field Sobolev inequalities\, an ide
a first introduced by the last two authors in the context of the Benjamin-
Ono equations. This is joint work with Albert Ai and Daniel Tataru.\n
LOCATION:https://researchseminars.org/talk/MO_Analysis/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rui Han (Louisiana State University)
DTSTART:20201030T200000Z
DTEND:20201030T210000Z
DTSTAMP:20260422T212602Z
UID:MO_Analysis/18
DESCRIPTION:Title: Spectral gaps in graphene structures\nby Rui Han (Louisiana State
University) as part of MU-MST joint analysis seminar\n\n\nAbstract\nWe pr
esent a full analysis of the spectrum of graphene models on graphs in magn
etic fields with constant flux through every hexagonal comb. In particular
\, we provide a rigorous foundation for self-similarity by showing that fo
r irrational flux\, the spectrum of graphene is a zero measure Cantor set.
For arbitrary rational flux\, we show the existence of Dirac cones. We al
so show that for trivial flux\, the spectral bands have nontrivial overlap
\, which leads to the proof of the discrete Bethe-Sommerfeld conjecture fo
r the hexagonal lattice. This talk is based on joint works with S. Becker\
, J. Fillman and S. Jitomirskaya.\n
LOCATION:https://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:20260422T212602Z
UID:MO_Analysis/19
DESCRIPTION:Title: Stability of kinks in one-dimensional Klein-Gordon equations\nby
Pierre Germain (Courant Institute of Mathematical Sciences\, New York Univ
ersity) as part of MU-MST joint analysis seminar\n\n\nAbstract\nKinks are
topological solitons\, which appear in (nonlinear) one-dimensional Klein-G
ordon equations\, the Phi-4 and Sine-Gordon equations being the most well-
known examples. I will present new results which give asymptotic stability
for kinks\, with an explicit decay rate\, in some cases. The proof relies
on the distorted Fourier transform associated to the linearized equation
around the soliton\; this method should be of interest for more general so
liton stability problems. This is joint work with Fabio Pusateri.\n
LOCATION:https://researchseminars.org/talk/MO_Analysis/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jacob Bedrossian (University of Maryland)
DTSTART:20201120T210000Z
DTEND:20201120T220000Z
DTSTAMP:20260422T212602Z
UID:MO_Analysis/20
DESCRIPTION:Title: Almost-sure exponential mixing in stochastic fluid mechanics and Batc
helor-regime passive scalar turbulence\nby Jacob Bedrossian (Universit
y of Maryland) as part of MU-MST joint analysis seminar\n\n\nAbstract\nIn
1959\, Batchelor predicted that passive scalars advected in incompressible
fluids with small diffusivity k should display a $|k|^{−1}$ power spect
rum in a statistically stationary experiment at scales small enough for th
e velocity to be effectively smooth. This prediction has since been tested
extensively in physics. Results obtained with Alex Blumenthal and Sam Pun
shon-Smith provide the first mathematically rigorous proof of this law in
the fixed Reynolds number case under stochastic forcing. We show that the
origin of the Batchelor spectrum is the existence of a uniform\, exponenti
al rate that all passive scalar fields are mixed at (up to a random prefac
tor)\, which we prove using ideas from random dynamical systems such as a
la Furstenberg and two-point geometric ergodicity for quenched correlation
decay.\n
LOCATION:https://researchseminars.org/talk/MO_Analysis/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Olga Trichtchenko (Western University)
DTSTART:20201113T210000Z
DTEND:20201113T220000Z
DTSTAMP:20260422T212602Z
UID:MO_Analysis/21
DESCRIPTION:Title: Stability of Periodic Solutions to Hamiltonian PDEs\nby Olga Tric
htchenko (Western University) as part of MU-MST joint analysis seminar\n\n
\nAbstract\nThis talk will focus on spectral stability of small-amplitude\
, periodic solutions to Hamiltonian\, dispersive partial differential equa
tions. In particular\, it has been shown in the past that periodic travell
ing wave solutions to the full Euler equations describing inviscid\, incom
pressible fluid flow\, exhibit high frequency instabilities. However\, som
e simpler model equations frequently used\, do not. We will examine the na
ture of these instabilities\, how they arise\, and present a general condi
tion for instability. In special cases\, this condition reduces to conside
ring the interval in which there are roots of a polynomial half the degree
of the polynomial describing the dispersion relation. We will illustrate
the method for computing spectral stability by considering solutions to th
e Korteweg-de Vries\, Kawahara\, Whitham and Boussinesq-Whitham equations.
\n
LOCATION:https://researchseminars.org/talk/MO_Analysis/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michael Weinstein (Columbia University)
DTSTART:20210312T210000Z
DTEND:20210312T220000Z
DTSTAMP:20260422T212602Z
UID:MO_Analysis/22
DESCRIPTION:Title: Continuum and discrete models of waves in 2D materials\nby Michae
l Weinstein (Columbia University) as part of MU-MST joint analysis seminar
\n\n\nAbstract\nWe discuss continuum Schroedinger operators which are basi
c models of 2D-materials\, like graphene\, in its bulk form or deformed by
edges (sharp terminations or domain walls). \nFor non-magnetic and strong
ly non-magnetic systems we discuss the relationship to effective \ntight b
inding (discrete) Hamiltonians through a result on strong resolvent conver
gence. An application of this convergence is a result on the equality of t
opological (Fredholm) indices\nassociated with continuum and discrete mode
ls (for bulk and edge systems). Finally\, we discuss the construction of e
dge states in continuum systems with domain walls.\n
LOCATION:https://researchseminars.org/talk/MO_Analysis/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Monica Visan (UCLA)
DTSTART:20210219T210000Z
DTEND:20210219T220000Z
DTSTAMP:20260422T212602Z
UID:MO_Analysis/23
DESCRIPTION:Title: Recent progress on well-posedness for integrable PDE\nby Monica V
isan (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 proving o
ptimal well-posedness for integrable PDE. I will\nfirst discuss this meth
od in the context of the Korteweg-de Vries\nequation. I will then discuss
subsequent developments (joint with\nHarrop-Griffiths and Killip) that ha
ve led to optimal well-posedness\nresults for the integrable nonlinear Sch
rödinger and the modified\nKorteweg-de Vries equations.\n
LOCATION:https://researchseminars.org/talk/MO_Analysis/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kevin O'Neill (UC Davis)
DTSTART:20210205T210000Z
DTEND:20210205T220000Z
DTSTAMP:20260422T212602Z
UID:MO_Analysis/24
DESCRIPTION:Title: A Nonnegative Version of Whitney's Extension Problem\nby Kevin O'
Neill (UC Davis) as part of MU-MST joint analysis seminar\n\n\nAbstract\nW
hitney's Extension Problem asks the following: Given a compact set $E\\sub
set\\mathbb{R}^n$ 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 classical
Whitney Extension theorem tells us that\, given potential Taylor polynomi
als $P^x$ at each $x\\in E$\, there is such an extension F if and only if
the $P^x$'s are compatible under Taylor's theorem. However\, this leaves o
pen the question of how to tell solely from $f$. A 2006 paper of Charles F
efferman answers this question. We explain some of the concepts of that pa
per\, as well as recent work of the speaker\, joint with Fushuai Jiang and
Garving K. Luli\, which establishes the analogous result when $f\\ge0$ an
d we require $F\\ge0$.\n
LOCATION:https://researchseminars.org/talk/MO_Analysis/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Steve Shkoller (UC Davis)
DTSTART:20210319T200000Z
DTEND:20210319T210000Z
DTSTAMP:20260422T212602Z
UID:MO_Analysis/25
DESCRIPTION:Title: Shock formation for the 3d Euler equations\nby Steve Shkoller (UC
Davis) as part of MU-MST joint analysis seminar\n\n\nAbstract\nIn this ta
lk\, I will discuss the shock formation process for the 3d compressible Eu
ler equations\, in which sounds waves interact with entropy waves to produ
ce vorticity. Smooth solutions form a generic stable shock with explicitl
y computable blowup time\, location\, and direction. Our method establishe
s the asymptotic stability of a generic shock profile in modulated self-si
milar variables\, controlling the interaction of wave families via: (i) po
intwise bounds along Lagrangian trajectories\, (ii) geometric vorticity st
ructure\, and (iii) high-order energy estimates in Sobolev spaces. This i
s joint work with T. Buckmaster and V. Vicol.\n
LOCATION:https://researchseminars.org/talk/MO_Analysis/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Svetlana Roudenko (Florida International University)
DTSTART:20210423T200000Z
DTEND:20210423T210000Z
DTSTAMP:20260422T212602Z
UID:MO_Analysis/26
DESCRIPTION:Title: Toward soliton resolution in KdV-type equations\nby Svetlana Roud
enko (Florida International University) as part of MU-MST joint analysis s
eminar\n\n\nAbstract\nThe questions about soliton resolution\, soliton sta
bility or formation of blow-up in KdV-type equations have been intriguing
the researchers for quite some time. \nIn this talk we will look at a high
er dimensional version of the KdV equation\, called Zakharov-Kuznetsov (ZK
) equation and discuss \nbehavior of solutions in the 2d and 3d models as
those are physically relevant. \nIn particular\, we will examine the behav
ior of solutions close to solitons in different settings. \n Direct nume
rical simulations for the KdV-type equations\, such as ZK\, with generic d
ata show that solutions split into\nsolitons traveling in the positive x-d
irection and radiation dispersing in the negative x-direction (possibly at
a specific angle in dimension 2 and higher). \nIn the L^2-critical and su
percritical cases (for example\, 2d cubic ZK equation)\, some of the solit
ons\, traveling\nto the right\, blow-up in finite time.\n Analytically\,
we prove existence of blow-up solutions in the 2d cubic (critical) ZK equ
ation. \nIn subcritical case\, such as 3d quadratic ZK\, we obtain asympto
tic stability of solitons in finite energy space. \nThe talk is based on j
oint works with Luiz Gustavo Farah\, Justin Holmer\, Christian Klein\, Nik
ola Stoilov\, and Kai Yang.\n
LOCATION:https://researchseminars.org/talk/MO_Analysis/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zhiwu Lin (Georgia Tech)
DTSTART:20210305T210000Z
DTEND:20210305T220000Z
DTSTAMP:20260422T212602Z
UID:MO_Analysis/28
DESCRIPTION:Title: Stability of some stellar models\nby Zhiwu Lin (Georgia Tech) as
part of MU-MST joint analysis seminar\n\n\nAbstract\nI will discuss some r
esults on stability of non-rotating and rotating stars. First\, we proved
a turning point principle which states that the stability changes at the c
ritical points of the total mass for a family of nonrotating stars paramet
rized by the center density. This is joint with Chongchun Zeng. Then we wi
ll discuss some recent results with Yucong Wang on the stability and insta
bility of rotating stars with general angular velocity profiles.\n
LOCATION:https://researchseminars.org/talk/MO_Analysis/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ian Tice (Carnegie Mellon)
DTSTART:20210226T210000Z
DTEND:20210226T220000Z
DTSTAMP:20260422T212602Z
UID:MO_Analysis/29
DESCRIPTION:Title: Traveling wave solutions to the free boundary Navier-Stokes equations
\nby Ian Tice (Carnegie Mellon) as part of MU-MST joint analysis semin
ar\n\n\nAbstract\nConsider a layer of viscous incompressible fluid bounded
below\nby a flat rigid boundary and above by a moving boundary. The flui
d is\nsubject to gravity\, surface tension\, and an external stress that i
s\nstationary when viewed in coordinate system moving at a constant\nveloc
ity parallel to the lower boundary. The latter can model\, for\ninstance\
, a tube blowing air on the fluid while translating across the\nsurface.
In this talk we will detail the construction of traveling wave\nsolutions
to this problem\, which are themselves stationary in the same\ntranslating
coordinate system. While such traveling wave solutions to\nthe Euler equ
ations are well-known\, to the best of our knowledge this is\nthe first co
nstruction of such solutions with viscosity. This is joint\nwork with Gio
vanni Leoni.\n
LOCATION:https://researchseminars.org/talk/MO_Analysis/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bjoern Bringmann (UCLA)
DTSTART:20210212T210000Z
DTEND:20210212T220000Z
DTSTAMP:20260422T212602Z
UID:MO_Analysis/30
DESCRIPTION:Title: Invariant Gibbs measures for the three-dimensional wave equation 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 constr
uction and invariance of the Gibbs measure for a threedimensional wave equ
ation with a Hartree-nonlinearity.\nIn the first part of the talk\, we con
struct the Gibbs measure and examine its properties. We discuss the\nmutua
l singularity of the Gibbs measure and the so-called Gaussian free field.
In contrast\, the Gibbs\nmeasure for one or two-dimensional wave equations
is absolutely continuous with respect to the Gaussian\nfree field.\n\n\nI
n the second part of the talk\, we discuss the probabilistic well-posednes
s of the corresponding nonlinear\nwave equation\, which is needed in the p
roof of invariance. At the moment\, this is the only theorem proving\nthe
invariance of any singular Gibbs measure under a dispersive equation.\n
LOCATION:https://researchseminars.org/talk/MO_Analysis/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anna Mazzucato (Penn State)
DTSTART:20210430T200000Z
DTEND:20210430T210000Z
DTSTAMP:20260422T212602Z
UID:MO_Analysis/31
DESCRIPTION:Title: Enhanced dissipation and global existence for the 2D Kuramoto-Sivash
insky equation\nby Anna Mazzucato (Penn State) as part of MU-MST joint
analysis seminar\n\n\nAbstract\nWe consider the Kuramoto-Sivashinsky equa
tion (KSE) on the two-dimensional torus in scalar form. We prove global ex
istence for small data in the absence of growing modes. If growing modes a
re present\, we show that global existence for arbitrary data holds for th
e advective KSE\, provided the advecting flow field induces a sufficient s
mall diffusion time for the linearized operator\, for example if the flow
is mixing with large amplitude. If the advecting flow is a shear flow\, t
hen we show global existence still holds by using pseudo-spectral estimate
s.\n
LOCATION:https://researchseminars.org/talk/MO_Analysis/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mat Johnson (University of Kansas)
DTSTART:20210409T200000Z
DTEND:20210409T210000Z
DTSTAMP:20260422T212602Z
UID:MO_Analysis/32
DESCRIPTION:Title: Dynamics of Periodic Lugiato-Lefever Waves\nby Mat Johnson (Unive
rsity of Kansas) as part of MU-MST joint analysis seminar\n\n\nAbstract\nI
n this talk\, we will consider the liner and nonlinear dynamics of perturb
ations of spectrally stable periodic stationary solutions of the Lugiato-L
efever equation (LLE)\, a damped nonlinear Schrodinger equation with forci
ng that arises in optics. It is known that spectrally stable T-periodic s
olutions 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 size of i
nitial perturbations both tend to zero as $N\\to\\infty$\, and hence such
subharmonic stability results are not uniform in N and are\, in fact\, emp
ty in the limit $N=\\infty$. The primary goal of this talk is to introduc
e a methodology\, in the context of the LLE\, by which a uniform in N stab
ility result for subharmonic perturbations may be achieved (at least at th
e linear level). The obtained uniform decay rates are shown to agree prec
isely with the polynomial decay rates of localized\, i.e. integrable on th
e line\, perturbations of such spectrally stable periodic solutions of LLE
. If time permits\, I will also discuss recent progress towards extending
these results for the LLE to the nonlinear level. This is joint with wit
h Mariana Haragus (Univ. Bourgogne Franche-Comtè)\, Wesley Perkins (KU) a
nd Bjorn de-Rijk (Stuttgart)\n
LOCATION:https://researchseminars.org/talk/MO_Analysis/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jon Wilkening (UC Berkeley)
DTSTART:20210326T200000Z
DTEND:20210326T210000Z
DTSTAMP:20260422T212602Z
UID:MO_Analysis/33
DESCRIPTION:Title: Quasi-periodic water waves\nby Jon Wilkening (UC Berkeley) as par
t of MU-MST joint analysis seminar\n\n\nAbstract\nWe present a framework t
o compute and study two-dimensional water waves that are quasi-periodic in
space and/or time. This means they can be represented as periodic functio
ns on a higher-dimensional torus by evaluating along irrational directions
. In the spatially quasi-periodic case\, the nonlocal Dirichlet-Neumann op
erator is computed using conformal mapping methods and a quasi-periodic va
riant of the Hilbert transform. In the temporally quasi-periodic case\, we
devise a shooting method to compute standing waves with 3 quasi-periods a
s well as hybrid traveling-standing waves that return to a spatial transla
tion of their initial condition at a later time. Many examples will be giv
en to illustrate the types of behavior that can occur.\n
LOCATION:https://researchseminars.org/talk/MO_Analysis/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maciej Zworski (UC Berkeley)
DTSTART:20210416T200000Z
DTEND:20210416T210000Z
DTSTAMP:20260422T212602Z
UID:MO_Analysis/34
DESCRIPTION:Title: Mathematics of magic angles for bilayer graphene\nby Maciej Zwors
ki (UC Berkeley) as part of MU-MST joint analysis seminar\n\n\nAbstract\nM
agic angles are a hot topic in condensed matter physics:\nwhen two sheets
of graphene are twisted by those angles the resulting\nmaterial is superco
nducting. I will present a very simple operator\nwhose spectral propertie
s are thought to determine which angles are magical.\nIt comes from a rece
nt PR Letter by Tarnopolsky--Kruchkov--Vishwanath.\nThe mathematics behind
this is an elementary blend of representation theory\n(of the Heisenberg
group in characteristic three)\, Jacobi theta functions and\nspectral inst
ability of non-self-adjoint operators (involving Hörmander's\nbracket con
dition in a very simple setting). The results will be illustrated by\ncolo
urful numerics which suggest some open problems (joint work\nwith S Becker
\, M Embree and J Wittsten).\n
LOCATION:https://researchseminars.org/talk/MO_Analysis/34/
END:VEVENT
END:VCALENDAR