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BEGIN:VEVENT
SUMMARY:Sir John Ball (Heriot-Watt University\, Edinburgh)
DTSTART:20200604T153000Z
DTEND:20200604T163000Z
DTSTAMP:20260424T235201Z
UID:SIAM-PDE/1
DESCRIPTION:Title: Some energy minimization problems for liquid crystals\nby Sir
John Ball (Heriot-Watt University\, Edinburgh) as part of Seminar In the A
nalysis and Methods of PDE (SIAM PDE)\n\n\nAbstract\nThe talk will discuss
some energy minimization problems for liquid crystals described at differ
ent levels of detail by the probability density function of molecular orie
ntations\, by a tensor average of this function (the de Gennes Q tensor th
eory)\, and by the expected orientation of molecules (the Oseen-Frank theo
ry).\n
LOCATION:https://stable.researchseminars.org/talk/SIAM-PDE/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Benoit Perthame (Sorbonne University\, France)
DTSTART:20200702T153000Z
DTEND:20200702T163000Z
DTSTAMP:20260424T235201Z
UID:SIAM-PDE/2
DESCRIPTION:Title: Multiphase models of living tissues and the Hele-Shaw limit
\nby Benoit Perthame (Sorbonne University\, France) as part of Seminar In
the Analysis and Methods of PDE (SIAM PDE)\n\n\nAbstract\nThe mechanical m
odeling of living tissues has attracted much attention in the last decade
. Applications include tissue repair and growth models of solid tumors. T
hese models contain several levels of complexity\, both in terms of the bi
ological and mechanical effects\, and therefore in their mathematical desc
ription. Multiphase models describe the dynamics of several types of cells
\, liquid\, fibers (extra-cellular matrix) and both compressible and incom
pressible models are used in the literature.\n\nIn this talk I shall discu
ss the analysis of multiphase models based on Darcy's assumption. The comp
actness issue leads us to use Aronson-Benilan estimate and to build new va
riants. I shall also discuss the incompressible limit in special cases and
the associated free boundary problem.\n
LOCATION:https://stable.researchseminars.org/talk/SIAM-PDE/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Felix Otto (Max Planck Institute for Mathematics in the Sciences\,
Leipzig\, Germany)
DTSTART:20200903T153000Z
DTEND:20200903T163000Z
DTSTAMP:20260424T235201Z
UID:SIAM-PDE/3
DESCRIPTION:Title: The thresholding scheme for mean curvature flow and De Giorgi's id
eas for gradient flows\nby Felix Otto (Max Planck Institute for Mathem
atics in the Sciences\, Leipzig\, Germany) as part of Seminar In the Analy
sis and Methods of PDE (SIAM PDE)\n\n\nAbstract\nFlow of interfaces by mea
n curvature\, in its multi-phase version\,\nwas first formulated in the co
ntext of grain growth in polycrystalline materials. \nThe computationally
efficient and very popular thresholding scheme\nfor mean curvature flow by
Osher et. al. can be naturally extended \nto such a multi-phase situation
\, even for surface tensions that depend on \nthe lattice mismatch between
the adjacent grains.\n\nThis extension relies on the gradient flow struct
ure of mean curvature flow\,\nand the interpretation of the thresholding s
cheme\nas a corresponding "minimizing movements'' scheme\, that is\, a seq
uence of variational problems\nnaturally attached to the implicit time dis
cretization of a gradient flow.\n\nThis interpretation also allows for a (
conditional) convergence proof based on De Giorgi's ideas\nfor gradient fl
ows in metric spaces. The approach is similar to\nthe convergence proof fo
r the minimizing movement scheme by Almgren\, Taylor and Wang\,\nas given
by Luckhaus et. al. \n\nThis is joint work with S. Esedoglu and T. Laux.\n
LOCATION:https://stable.researchseminars.org/talk/SIAM-PDE/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Laure Saint-Raymond (ENS Lyon\, France)
DTSTART:20201008T153000Z
DTEND:20201008T163000Z
DTSTAMP:20260424T235201Z
UID:SIAM-PDE/4
DESCRIPTION:Title: Fluctuation theory in the Boltzmann-Grad limit\nby Laure Saint
-Raymond (ENS Lyon\, France) as part of Seminar In the Analysis and Method
s of PDE (SIAM PDE)\n\n\nAbstract\nIn this talk\, I will discuss a long te
rm project with T. Bodineau\, I. Gallagher and S. Simonella on hard-sphere
gases. In the low density limit\, the empirical density obeys a law of la
rge numbers and the dynamics is governed asymptotically by the (kinetic) B
oltzmann equation. Deviations from this behavior are described by dynamica
l correlations\, which we can fully characterize for short times. This pro
vides both a fluctuating Boltzmann equation and large deviation asymptotic
s.\n
LOCATION:https://stable.researchseminars.org/talk/SIAM-PDE/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vlad Vicol (Courant Institute of Mathematical Sciences\, NYU)
DTSTART:20201105T163000Z
DTEND:20201105T173000Z
DTSTAMP:20260424T235201Z
UID:SIAM-PDE/5
DESCRIPTION:Title: Shock formation and vorticity creation for compressible Euler\
nby Vlad Vicol (Courant Institute of Mathematical Sciences\, NYU) as part
of Seminar In the Analysis and Methods of PDE (SIAM PDE)\n\n\nAbstract\nIn
this talk\, I will discuss a long term project\, joint with Tristan Buckm
aster and Steve Shkoller\, concerning the formation of singularities (shoc
ks) for the compressible Euler equations with the ideal gas law. We provid
e a constructive proof of stable shock formation from smooth initial datum
\, of finite energy\, and with no vacuum regions. Via modulated self-simil
ar variables\, the blow-up time and location can be explicitly computed\,
and at the blow-up time\, the solutions can be shown to have precisely Hol
der 1/3 regularity. Additionally\, for the non-isentropic problem sounds w
aves interact with entropy waves to produce vorticity at the shock.\n
LOCATION:https://stable.researchseminars.org/talk/SIAM-PDE/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alessio Figalli (ETH Zurich\, Switzerland)
DTSTART:20201203T163000Z
DTEND:20201203T173000Z
DTSTAMP:20260424T235201Z
UID:SIAM-PDE/6
DESCRIPTION:Title: Generic regularity in obstacle problems\nby Alessio Figalli (E
TH Zurich\, Switzerland) as part of Seminar In the Analysis and Methods of
PDE (SIAM PDE)\n\n\nAbstract\nThe classical obstacle problem consists of
finding the equilibrium position of an elastic membrane whose boundary is
held fixed and constrained to lie above a given obstacle. By classical res
ults of Caffarelli\, the free boundary is smooth outside a set of singular
points. Explicit examples show that the singular set could be in general
(n-1)-dimensional — that is\, as large as the regular set. In a recent p
aper with Ros-Oton and Serra we show that\, generically\, the singular set
has codimension 3 inside the free boundary\, solving a conjecture of Scha
effer in dimension $n\\leq 4$. This talk aims to give an overview of these
results.\n
LOCATION:https://stable.researchseminars.org/talk/SIAM-PDE/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrzej Swiech (Georgia Tech\, USA)
DTSTART:20210204T163000Z
DTEND:20210204T173000Z
DTSTAMP:20260424T235201Z
UID:SIAM-PDE/7
DESCRIPTION:Title: Finite dimensional approximations of Hamilton-Jacobi-Bellman equat
ions in spaces of probability measures. (Featured Article in SIAM Journal
on Mathematical Analysis)\nby Andrzej Swiech (Georgia Tech\, USA) as p
art of Seminar In the Analysis and Methods of PDE (SIAM PDE)\n\n\nAbstract
\nWe will discuss how certain Hamilton-Jacobi-Bellman (HJB) equations in s
paces of probability measures can be approximated by finite dimensional eq
uations. The most interesting cases are convergence of viscosity solutions
of HJB equations corresponding either to deterministic optimal control pr
oblems for systems of $n$ particles or to stochastic optimal control probl
ems for systems of $n$ particles with a common noise\, to the viscosity so
lution of a limiting HJB equation in the space of probability measures. Th
e limiting HJB equation is interpreted in its ``lifted" form in a Hilbert
space\, which has a unique viscosity solution. When the Hamiltonian is con
vex in the gradient variable and equations are of first order\, it can be
proved that the viscosity solutions of the finite dimensional problems con
verge to the value function of a variational problem in $\\mathcal{P}_2(\\
R^d)$ thus providing a representation formula for the solution of the limi
ting first order HJB equation. The talk will also contain an overview of e
xisting works and various approaches to partial differential equations in
abstract spaces\, including spaces of probability measures and Hilbert spa
ces. The talk is based on a joint work with W. Gangbo and S. Mayorga.\n\nF
eatured Article Authors: W. Gangbo\, S. Mayorga\, A. Swiech\n
LOCATION:https://stable.researchseminars.org/talk/SIAM-PDE/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sergei Chernyshenko (Imperial College London\, UK)
DTSTART:20210304T163000Z
DTEND:20210304T173000Z
DTSTAMP:20260424T235201Z
UID:SIAM-PDE/8
DESCRIPTION:Title: Auxiliary functionals: a path to solving the problem of turbulence
\nby Sergei Chernyshenko (Imperial College London\, UK) as part of Sem
inar In the Analysis and Methods of PDE (SIAM PDE)\n\n\nAbstract\nThe prob
lem of turbulence is the greatest unsolved problem of classical fluid dyna
mics. It is quite old. Similarly\, the problem of optimizing over the con
e of nonnegative polynomials was long believed to be too hard\,\nuntil at
the start of the millennium a breakthrough paved a way by linking it\, thr
ough sum-of-squares polynomial optimisation\, to semidefinite programming.
And only a few years ago\, auxiliary functionals were proposed with an \n
ultimate goal of applying the fruits of this breakthrough to solving the p
roblem of turbulence. The essence of these ideas is remarkably simple. The
talk will cover the basics\, and then a few questions will be reviewed de
eper\, including applications to systems of equations with energy-conservi
ng quadratic nonlinearities\, such as the Kuramoto–Sivashinsky and the N
avier-Stokes equations.\n
LOCATION:https://stable.researchseminars.org/talk/SIAM-PDE/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sylvia Serfaty (Courant Institute of Mathematical Sciences\, NYU)
DTSTART:20210401T153000Z
DTEND:20210401T163000Z
DTSTAMP:20260424T235201Z
UID:SIAM-PDE/9
DESCRIPTION:Title: Ginzburg-Landau\, old and new\nby Sylvia Serfaty (Courant Inst
itute of Mathematical Sciences\, NYU) as part of Seminar In the Analysis a
nd Methods of PDE (SIAM PDE)\n\n\nAbstract\nThis talk will review older an
d more recent results on the analysis of vortices in the Ginzburg-Landau m
odel of superconductivity\, including description of energy minimizers and
their vortex patterns in both two and three dimensions\, and description
of vortex dynamics.\n
LOCATION:https://stable.researchseminars.org/talk/SIAM-PDE/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gigliola Staffilani (MIT)
DTSTART:20210506T153000Z
DTEND:20210506T163000Z
DTSTAMP:20260424T235201Z
UID:SIAM-PDE/10
DESCRIPTION:Title: How much math do you need to know to “solve" an initial value p
roblem?\nby Gigliola Staffilani (MIT) as part of Seminar In the Analys
is and Methods of PDE (SIAM PDE)\n\n\nAbstract\nIn this talk I will presen
t some recent results concerning periodic solutions to nonlinear Schroding
er equations\, and in doing so I will introduce a variety of mathematical
techniques that range from harmonic and Fourier analysis to dynamical syst
ems\, from number theory to probability. \n\nI will start with a derivatio
n of this type of equation from a many body system\, and I will discuss ho
w Hamiltonian structures can be mapped through this derivation process. I
will then move to the study of the long time dynamics of associated initia
l value problems\, in particular I will concentrate on the notion of energ
y transfer. I will show how ideas from dynamical systems are fundamental t
o work through this analysis to obtain even relatively soft statements\,
and I will present some more recent results on the rigorous derivation of
a wave kinetic equation for a certain multidimensional KdV type equation u
sing a variety of tools such as Feynman diagrams\, sharp dispersive estima
tes and improved combinatorial lemmata.\n
LOCATION:https://stable.researchseminars.org/talk/SIAM-PDE/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yann Brenier (École Normale Supérieure\, Paris)
DTSTART:20210603T153000Z
DTEND:20210603T163000Z
DTSTAMP:20260424T235201Z
UID:SIAM-PDE/11
DESCRIPTION:Title: On optimal transport of matrix-valued measures\nby Yann Breni
er (École Normale Supérieure\, Paris) as part of Seminar In the Analysis
and Methods of PDE (SIAM PDE)\n\n\nAbstract\nWe suggest a way of defining
optimal transport of\npositive-semidefinite matrix-valued measures\, insp
ired by a recent\nrendering of the incompressible Euler equations and rela
ted conservative\nsystems as concave maximization problems. The main outpu
t of our work is a\nmatricial analogue of the Hellinger-Kantorovich metric
spaces.\n
LOCATION:https://stable.researchseminars.org/talk/SIAM-PDE/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Luis Silvestre (University of Chicago)
DTSTART:20210701T153000Z
DTEND:20210701T163000Z
DTSTAMP:20260424T235201Z
UID:SIAM-PDE/12
DESCRIPTION:Title: Gaussian lower bounds for the Boltzmann equation without cut-off<
/a>\nby Luis Silvestre (University of Chicago) as part of Seminar In the A
nalysis and Methods of PDE (SIAM PDE)\n\n\nAbstract\nThe Boltzmann equatio
n models the evolution of densities of particles in a gas. Its global well
posedness is a major open problem\, facing comparable difficulties as sim
ilar questions for equations in fluids. With current techniques\, we canno
t rule out the possibility of a spontaneous emergence of a singularity in
the form of infinite mass or energy density concentrating at some point in
space. This work is part of a series of a priori estimates for the inhomo
geneous non-cutoff Boltzmann equation that are conditional to bounds on ma
croscopic quantities. We establish a Gaussian lower bound for solutions to
the Boltzmann equation without cutoff\, in the case of hard and moderatel
y soft potentials\, with spatial periodic conditions\, and under the sole
assumption that hydrodynamic quantities (local mass\, local energy and loc
al entropy density) remain bounded. In the talk\, we will discuss how this
lower bound fits in the larger program of conditional estimates.\n
LOCATION:https://stable.researchseminars.org/talk/SIAM-PDE/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Roman Shvydkoy (University of Illinois\, Chicago)
DTSTART:20210902T153000Z
DTEND:20210902T163000Z
DTSTAMP:20260424T235201Z
UID:SIAM-PDE/13
DESCRIPTION:Title: Analytical aspects of emergent dynamics in systems of collective
behavior\nby Roman Shvydkoy (University of Illinois\, Chicago) as part
of Seminar In the Analysis and Methods of PDE (SIAM PDE)\n\n\nAbstract\nO
ne of the challenging problems in the field of collective behavior is to u
nderstand global emergent phenomena arising from purely local communicatio
n between agents. In the context of alignment dynamics examples of such gl
obal phenomena include flock formations\, reaching consensus of opinions
\, emergence of leaders\, etc. For models based on purely local interacti
ons the assumption of graph-\, chain-\, or hydrodynamic connectivity of th
e flock is often necessary\, but not always guaranteed\, to ensure collect
ive outcome. In this talk we will give an overview of the subject and hig
hlight two new approaches to alignment dynamics in disconnected or weakly
connected flocks. One is based on a topological fractional diffusion that
resembles the closest neighbor rule originating in various empirical studi
es\, and another based on the use of random fluctuations and the hypocoerc
ivity property for the resulting kinetic Fokker-Planck-Alignment equation.
\n
LOCATION:https://stable.researchseminars.org/talk/SIAM-PDE/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Monica Visan (UCLA)
DTSTART:20211007T153000Z
DTEND:20211007T163000Z
DTSTAMP:20260424T235201Z
UID:SIAM-PDE/14
DESCRIPTION:Title: Determinants\, commuting flows\, and recent progress on completel
y integrable systems\nby Monica Visan (UCLA) as part of Seminar In the
Analysis and Methods of PDE (SIAM PDE)\n\n\nAbstract\nWe will survey a nu
mber of recent developments in the\ntheory of completely integrable nonlin
ear dispersive PDE. These\ninclude a priori bounds\, the orbital stability
of multisolitons\,\nwell-posedness at optimal regularity\, and the existe
nce of dynamics\nfor Gibbs distributed initial data. I will describe the b
asic objects\nthat tie together these disparate results\, as well as the d
iverse\nideas required for each problem.\n
LOCATION:https://stable.researchseminars.org/talk/SIAM-PDE/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Theodore Drivas (Stony Brook University)
DTSTART:20211104T153000Z
DTEND:20211104T163000Z
DTSTAMP:20260424T235201Z
UID:SIAM-PDE/15
DESCRIPTION:Title: Compressible fluids\, entropy hierarchies\, and flocking\nby
Theodore Drivas (Stony Brook University) as part of Seminar In the Analysi
s and Methods of PDE (SIAM PDE)\n\n\nAbstract\nWe will discuss two types o
f one-dimensional compressible fluid equations\; Navier-Stokes models with
local dissipation in which the viscosity depends degenerately on the dens
ity and nonlocal models for collective dynamics which exhibit flocking beh
avior. For the local models\, we prove large data global regularity for a
class of equations covering viscous shallow water. Another result proves a
conjecture of Peter Constantin on singularity formation for a model descr
ibing slender axisymmetric fluid jets. For the non-local models\, we esta
blish a continuation criterion which says that smooth solutions exist so l
ong as no vacuum states form. The method of proof involves introducing a
hierarchy of entropies to control the solution in terms of the minimum den
sity. We also show that any weak solutions which obeying an entropy inequ
ality exhibit flocking. This reports on joint work with P. Constantin\, H
. Nguyen\, F. Pasqualotto and R. Shvydkoy.\n
LOCATION:https://stable.researchseminars.org/talk/SIAM-PDE/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yao Yao (National University of Singapore)
DTSTART:20211202T163000Z
DTEND:20211202T173000Z
DTSTAMP:20260424T235201Z
UID:SIAM-PDE/16
DESCRIPTION:Title: Symmetry and uniqueness via a variational approach\nby Yao Ya
o (National University of Singapore) as part of Seminar In the Analysis an
d Methods of PDE (SIAM PDE)\n\n\nAbstract\nFor some nonlocal PDEs\, their
steady states can be seen as critical points of some associated energy fun
ctional. Therefore\, if one can construct perturbations around a function
such that the energy decreases to first order along the perturbation\, thi
s function cannot be a steady state. In this talk\, I will discuss how thi
s simple variational approach has led to some recent progress in the follo
wing equations\, where the key is to carefully construct a suitable pertur
bation. \n\nI will start with the aggregation-diffusion equation\, which i
s a nonlocal PDE driven by two competing effects: nonlinear diffusion and
long-range attraction. We show that all steady states are radially symmetr
ic up to a translation (joint with Carrillo\, Hittmeir and Volzone)\, and
give some criteria on the uniqueness/non-uniqueness of steady states withi
n the radial class (joint with Delgadino and Yan). I will also discuss the
2D Euler equation\, where we aim to understand under what condition must
a stationary/uniformly-rotating solution be radially symmetric. Using a va
riational approach\, we settle some open questions on the radial symmetry
of rotating patches\, and also show that any smooth stationary solution wi
th compactly supported and nonnegative vorticity must be radial (joint wit
h Gómez-Serrano\, Park and Shi).\n
LOCATION:https://stable.researchseminars.org/talk/SIAM-PDE/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:François Golse (École polytechnique\, France)
DTSTART:20220203T163000Z
DTEND:20220203T173000Z
DTSTAMP:20260424T235201Z
UID:SIAM-PDE/17
DESCRIPTION:Title: Quantum Dynamics and Optimal Transport\nby François Golse (
École polytechnique\, France) as part of Seminar In the Analysis and Meth
ods of PDE (SIAM PDE)\n\n\nAbstract\nIn 1979\, Dobrushin explained how Mon
ge’s theory of optimal transport (1781)\ncan be used to prove the mean-f
ield limit for the classical dynamics of large particle\nsystems. Is it po
ssible to compare two quantum states\, or a quantum state and a\nclassical
phase space density by some quantum analogue of optimal transport? and th
e\naffirmative\, can one use such ideas to study the mean-field and the cl
assical limits of\nquantum dynamics? This talk will review some recent res
ults in this direction\, based on\njoint works with E. Caglioti\, C. Mouho
t and T. Paul.\n
LOCATION:https://stable.researchseminars.org/talk/SIAM-PDE/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Barbara Niethammer (University of Bonn\, Germany)
DTSTART:20220303T163000Z
DTEND:20220303T173000Z
DTSTAMP:20260424T235201Z
UID:SIAM-PDE/18
DESCRIPTION:Title: An obstacle problem for cell polarization\nby Barbara Nietham
mer (University of Bonn\, Germany) as part of Seminar In the Analysis and
Methods of PDE (SIAM PDE)\n\n\nAbstract\nWe investigate a model for cell p
olarization under external stimulus where a diffusion equation in the inne
r cell is coupled to reaction diffusion equations on the cell membrane. In
certain scaling limits we rigorously derive generalized obstacle type pr
oblems. For these limit systems we prove global stability of steady states
and characterize the parameter regime for the onset of polarization. (Jo
int work with Anna Logioti (Bonn) Matthias Roeger (TU Dortmund) and Juan
Velazquez (U Bonn)).\n\nFeatured Article: A parabolic free boundary proble
m arising in a model of cell polarization. SIAM J. Math. Anal. 53-1 (2021
)\nFeatured Article Authors: A.Logioti\, B. Niethammer\, M. Röger and J.
L. Velázquez\n
LOCATION:https://stable.researchseminars.org/talk/SIAM-PDE/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Martin Hairer (Imperial College London\, UK)
DTSTART:20220407T153000Z
DTEND:20220407T163000Z
DTSTAMP:20260424T235201Z
UID:SIAM-PDE/19
DESCRIPTION:Title: Directed mean curvature flow in noisy environment\nby Martin
Hairer (Imperial College London\, UK) as part of Seminar In the Analysis a
nd Methods of PDE (SIAM PDE)\n\n\nAbstract\nWe consider the directed mean
curvature flow on the plane in a weak Gaussian random environment and show
that\, when started from a sufficiently flat initial condition\, a rescal
ed and recentred solution converges in a suitable scaling limit to the sol
ution of the KPZ equation. This result follows from the analysis of a more
general system of nonlinear stochastic PDEs driven by inhomogeneous noise
s\, using the theory of regularity structures. This is joint work with And
ris Gerasimovics (U. Bath) and Konstantin Matetski (U. Columbia).\n
LOCATION:https://stable.researchseminars.org/talk/SIAM-PDE/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrea Nahmod (University of Massachusetts Amherst -- USA)
DTSTART:20220505T153000Z
DTEND:20220505T163000Z
DTSTAMP:20260424T235201Z
UID:SIAM-PDE/20
DESCRIPTION:Title: Gibbs measures and propagation of randomness under the flow of no
nlinear dispersive PDE\nby Andrea Nahmod (University of Massachusetts
Amherst -- USA) as part of Seminar In the Analysis and Methods of PDE (SIA
M PDE)\n\n\nAbstract\nIn groundbreaking work\, Bourgain ’96 put forward
a random data theory to study the existence of strong solutions on the sta
tistical ensemble of Gibbs measures associated to dispersive equations. De
spite numerous follow-up works to those of Bourgain’s\, fundamental ques
tions remained open. How does a given initial random data get transported
by a nonlinear flow ? If it is Gaussian initially\, how does this Gaussia
nity propagate? What is the description of the solution beyond the linear
evolution?\n\nIn recent work\, joint with Yu Deng and Haitian Yue\, we dev
eloped the theory of random tensors\, a powerful new framework which allow
s us to unravel the propagation of randomness under the NLS flow beyond th
e linear evolution of random data\, and answer these questions in an optim
al range relative to what we define as the probabilistic scaling. In part
icular\, we establish the invariance of Gibbs measures for 2D NLS and 3D H
artree NLS equations using the method of random averaging operators\, a fi
rst order approximation to the full random tensor theory. \n\nIn this talk
we will describe these results\, and explain the ideas behind them. We co
nclude with some open problems and within this context present new work\,
joint with Bjoern Bringmann\, Yu Deng and Haitian Yue establishing the i
nvariance of the 3D Gibbs measure under the flow of the nonlinear wave equ
ation.\n\nBio Andrea R. Nahmod is Professor of Mathematics at the Universi
ty of Massachusetts Amherst. Her research lies at the interface of nonline
ar Fourier and harmonic analysis\, and the theory of partial differential
equations. Some of her recent work aims at gaining a quantitative understa
nding of the propagation of randomness under the nonlinear evolution of di
spersive PDE. Nahmod is a Fellow of the American Mathematical Society\; a
recipient of the Sargent-Faull Fellowship at Harvard’s Radcliffe Instit
ute for Advanced Study\, and of a Simons Foundation Fellowship. Nahmod wa
s twice a member of the Institute for Advanced Study at Princeton and held
Simons’ Professorships at MSRI\, Berkeley and at CRM Montreal. She deli
vered an invited address at the 2021 Joint Mathematical Meetings of the AM
S.\n
LOCATION:https://stable.researchseminars.org/talk/SIAM-PDE/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Kiselev (Duke University)
DTSTART:20220602T153000Z
DTEND:20220602T163000Z
DTSTAMP:20260424T235201Z
UID:SIAM-PDE/21
DESCRIPTION:Title: The flow of polynomial roots under differentiation\nby Alexan
der Kiselev (Duke University) as part of Seminar In the Analysis and Metho
ds of PDE (SIAM PDE)\n\n\nAbstract\nFeatured Article: "Global regularity
for a nonlocal PDE describing evolution of polynomial roots under differe
ntiation"\, to appear\, SIAM J Math Analysis \n\nFeatured Article Authors:
A. Kiselev\, Changhui Tan \n\nThe question of how roots of polynomials mo
ve under differentiation is classical. Contributions to this subject have
been made by Gauss\, Lucas\, Marcel Riesz\, Polya and many others. In 2018
\, Stefan Steinerberger derived formally a PDE that should describe the dy
namics of roots under differentiation in certain situations. The PDE in qu
estion is of hydrodynamic type and bears a striking resemblance to the mod
els used in mathematical biology to describe collective behavior and flock
ing of various species - such as fish\, birds or ants. The equation is cri
tical\, but due to strongly nonlinear form of its coefficients\, proving g
lobal regularity for its solutions is harder than for equations such as Bu
rgers\, SQG or Euler alignment model. I will discuss joint work with Chang
hui Tan in which we establish global regularity of Steinerberger's equatio
n and make a rigorous connection between its solutions and evolution of ro
ots under differentiation for a class of trigonometric polynomials.\n
LOCATION:https://stable.researchseminars.org/talk/SIAM-PDE/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Igor Rodnianski (Princeton University)
DTSTART:20220707T153000Z
DTEND:20220707T163000Z
DTSTAMP:20260424T235201Z
UID:SIAM-PDE/22
DESCRIPTION:Title: Linear and nonlinear stability problems for the Vlasov-Poisson eq
uations\nby Igor Rodnianski (Princeton University) as part of Seminar
In the Analysis and Methods of PDE (SIAM PDE)\n\n\nAbstract\nFeatured Arti
cle: "Plasma echoes near stable Penrose data"\, (SIAM J. Math. Anal. 54
(2022)\, pp. 940-953) joint with "\, to appear\, SIAM J Math Analysis \n\
nFeatured Article Authors: \nEmmanuel Grenier\, Toan T. Nguyen and Igor R
odnianski\n\n\nI will discuss the issues in and around problems of stabili
ty of spatially homogeneous equilibria in collisionless plasma\, including
Landau damping and plasma echos.\n
LOCATION:https://stable.researchseminars.org/talk/SIAM-PDE/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Scott Armstrong (Courant Institute/NYU\, United States)
DTSTART:20220901T153000Z
DTEND:20220901T163000Z
DTSTAMP:20260424T235201Z
UID:SIAM-PDE/23
DESCRIPTION:Title: Coarse-graining\, renormalization\, and quantitative homogenizati
on\nby Scott Armstrong (Courant Institute/NYU\, United States) as part
of Seminar In the Analysis and Methods of PDE (SIAM PDE)\n\n\nAbstract\nI
will present an overview of the theory of quantitative homogenization (st
ochastic as well as periodic) for elliptic and parabolic equations\, which
has been developed in the last ten years. A particular emphasis will be o
n the idea of "coarse-graining the coefficient field" with applications to
degenerate equations and other situations which require "renormalization\
," including some more recent applications to models in mathematical physi
cs. Time permitting\, I will discuss what I see as some of the most import
ant open problems in the subfield.\n
LOCATION:https://stable.researchseminars.org/talk/SIAM-PDE/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jacob Bedrossian (University of Maryland\, USA)
DTSTART:20221006T153000Z
DTEND:20221006T163000Z
DTSTAMP:20260424T235201Z
UID:SIAM-PDE/24
DESCRIPTION:Title: Landau damping and related effects in kinetic models of plasma ph
ysics\nby Jacob Bedrossian (University of Maryland\, USA) as part of S
eminar In the Analysis and Methods of PDE (SIAM PDE)\n\n\nAbstract\nFeatur
ed Article: "Linearized Wave-Damping Structure of Vlasov--Poisson in R3"
\, SIAM J. Math. Anal. 54(4) (2022)\, pp. 4379-4406 \n\nFeatured Artic
le Authors: Jacob Bedrossian\, Nader Masmoudi and Clément Mouhot\n\n\nIn
this talk I will attempt to overview past and recent progress in understa
nding asymptotic stability in collisionless and weakly collisional plasmas
. Results such as Landau damping\, plasma echoes\, and collision-enhanced
dissipation will be discussed followed by discussions of some open directi
ons.\n
LOCATION:https://stable.researchseminars.org/talk/SIAM-PDE/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Patrick Gérard (Université Paris-Saclay\, France)
DTSTART:20221103T163000Z
DTEND:20221103T173000Z
DTSTAMP:20260424T235201Z
UID:SIAM-PDE/25
DESCRIPTION:Title: A survey of the Benjamin-Ono equation with periodic boundary cond
itions\nby Patrick Gérard (Université Paris-Saclay\, France) as part
of Seminar In the Analysis and Methods of PDE (SIAM PDE)\n\n\nAbstract\nT
he Benjamin-Ono equation is a nonlinear dispersive wave equation in one sp
ace dimension\, introduced in 1967 as a model for long internal gravity wa
ves in a two layer fluid with infinite depth. In this talk\, I will show h
ow the use of a Lax pair provides a fairly complete picture of the dynamic
s with periodic boundary conditions. I will discuss an explicit formula fo
r the solutions\, global well posedness in sharp regularity\, long time d
ynamics\, the classification of traveling waves\, of multi-solitons and o
f doubly periodic solutions\, and the smoothing effect. This talk is inspi
red from a series of jointworks with Thomas Kappeler and Petar Topalov.\n
LOCATION:https://stable.researchseminars.org/talk/SIAM-PDE/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alberto Bressan (Penn State University\, USA)
DTSTART:20221201T163000Z
DTEND:20221201T173000Z
DTSTAMP:20260424T235201Z
UID:SIAM-PDE/26
DESCRIPTION:Title: On the optimal shape of tree roots and branches\nby Alberto B
ressan (Penn State University\, USA) as part of Seminar In the Analysis an
d Methods of PDE (SIAM PDE)\n\n\nAbstract\nFeatured Article: "Optimal Sh
apes for Tree Roots"\, SIAM J. Math. Anal. 54(4) (2022)\, pp. 4757-4784.\
n\nFeatured Article Authors: Alberto Bressan\, Sondre T. Galtung and Qing
Su.\n\n\nLiving organisms come in an immense variety of shapes.\nIn many
cases one can expect that\, through natural selection\, a ``best possible"
shape will have evolved. From a mathematical perspective\, it is thus of
interest to understand whether similar geometric shapes can be recovered a
s minimizers of suitable functionals.\n\nAs a step in this direction\, we
consider two functionals measuring the efficiency of roots and branches in
a tree. Namely: \n(i) a ``sunlight functional"\, modeling the total amoun
t of sunlight captured by the leaves of a tree\, and\n(ii) a ``harvest fun
ctional"\, modeling the amount of nutrients collected by the roots.\nThe a
bove functionals must be combined with a ``ramified transportation cost"\,
for transporting nutrients from the roots to the base of the trunk\, or f
rom the base of the trunk to the leaves.\n\nThe talk will address the semi
continuity of these functionals\, and the existence and properties of opti
mal solutions\, in a space of measures.\nOpen problems will also be discus
sed\, including computational issues and how these optimal shapes may depe
nd on various parameters.\n
LOCATION:https://stable.researchseminars.org/talk/SIAM-PDE/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michael Weinstein (Columbia University)
DTSTART:20220202T163000Z
DTEND:20220202T173000Z
DTSTAMP:20260424T235201Z
UID:SIAM-PDE/27
DESCRIPTION:by Michael Weinstein (Columbia University) as part of Seminar
In the Analysis and Methods of PDE (SIAM PDE)\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/SIAM-PDE/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:László Székelyhidi (Universitat Leipzig)
DTSTART:20220302T163000Z
DTEND:20220302T173000Z
DTSTAMP:20260424T235201Z
UID:SIAM-PDE/28
DESCRIPTION:by László Székelyhidi (Universitat Leipzig) as part of Semi
nar In the Analysis and Methods of PDE (SIAM PDE)\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/SIAM-PDE/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michael Weinstein (Columbia University)
DTSTART:20220202T163000Z
DTEND:20220202T173000Z
DTSTAMP:20260424T235201Z
UID:SIAM-PDE/29
DESCRIPTION:by Michael Weinstein (Columbia University) as part of Seminar
In the Analysis and Methods of PDE (SIAM PDE)\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/SIAM-PDE/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:László Székelyhidi (Universitat Leipzig)
DTSTART:20220302T163000Z
DTEND:20220302T173000Z
DTSTAMP:20260424T235201Z
UID:SIAM-PDE/30
DESCRIPTION:by László Székelyhidi (Universitat Leipzig) as part of Semi
nar In the Analysis and Methods of PDE (SIAM PDE)\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/SIAM-PDE/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michael Weinstein (Columbia University)
DTSTART:20230202T163000Z
DTEND:20230202T173000Z
DTSTAMP:20260424T235201Z
UID:SIAM-PDE/31
DESCRIPTION:Title: Effective gaps for time-periodic Hamiltonians modeling Floquet ma
terials\nby Michael Weinstein (Columbia University) as part of Seminar
In the Analysis and Methods of PDE (SIAM PDE)\n\n\nAbstract\nFeatured Art
icle: "Effective gaps in continuous Floquet Hamiltonians"\, SIAM J Math
Analysis 54 #1 2022. \n\nFeatured Article Authors: Amir Sagiv and Micha
el Weinstein\n\n\nFloquet media are a type of material\, in which time-per
iodic forcing is applied to alter the material’s energy transport proper
ties. Examples in classical and quantum physics include (i) applying a tim
e-oscillating electric field to a graphene sheet to influence quantum elec
tronic transport\, and (ii) replacing a periodic array of standard optical
waveguides by an array of helically coiled waveguides to influence the fl
ow of light propagation in the array. The ability to modify energy transpo
rt via time modulation is recognized as having great potential for applica
tions to information transfer\, information processing\, and other applica
tions. \n\nWe discuss Floquet materials governed by a class of parametrica
lly forced Schrödinger equations\, which arises in the above examples: \n
i ψt = Hε (t) ψ\, Hε(t) = H0 + ε W ( ε t \, -i ∇ ).
(1)\n\nThe operator H0 = - Δ + V ( x ) models a graphene-like static m
aterial\; the potential V has the symmetries of a honeycomb tiling of the
plane. The family of self-adjoint operators T ↦ W ( T\, -i ∇ ) is assu
med to be Tper – periodic. \n\nWhile the energy transport of the unforce
d system ( W ≡ 0 ) is governed by the band structure (Floquet-Bloch spec
tral theory) of H0 \, that of the forced system is characterized by the mo
nodromy operator\, the unitary mapping ψ0 ↦ ψ ( ε-1 Tper ) \, and its
associated quasi-energy spectrum. Gaps in the band spectrum and quasi-ene
rgy spectrum\, respectively\, of static and Floquet materials\, play an im
portant role in their transport properties. \n\nThe evolution under Hε (t
) of band-limited Dirac wave-packets (a natural model of physical excitati
ons) is well-approximated on very large time scales by an effective time-p
eriodic Dirac equation\, which has a gap in its quasi-energy spectrum. But
little is known about the nature of the quasi-energy spectrum of (1)\, an
d it is believed that no such quasi-energy gap occurs. \n\nWe explain how
to transfer quasi-energy gap information about the effective Dirac dynamic
s to conclusions about the full Schrödinger dynamics (1). In particular\,
we show that (1) has an effective quasi-energy gap\, an interval of quasi
-energies whose corresponding modes have only a very small spectral projec
tion onto the subspace of band-limited Dirac wave-packets. The notion of e
ffective quasi-energy gap is a physically relevant relaxation of the stric
t notion of quasi-energy spectral gap. Physically\, if a system is tuned t
o drive or measure at momenta and energies near the Dirac point of H0 \, t
hen the resulting modes in the effective quasi-energy gap will only be wea
kly excited and detected. \n\nThis lecture focuses on joint work with Amir
Sagiv (Columbia University) appearing in the article: Effective gaps in c
ontinuous Floquet Hamiltonians\, SIMA 54 #1 2022.\n
LOCATION:https://stable.researchseminars.org/talk/SIAM-PDE/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:László Székelyhidi (Universitat Leipzig)
DTSTART:20230302T163000Z
DTEND:20230302T173000Z
DTSTAMP:20260424T235201Z
UID:SIAM-PDE/33
DESCRIPTION:Title: Magnetohydrodynamic turbulence: weak solutions and conserved quan
tities\nby László Székelyhidi (Universitat Leipzig) as part of Semi
nar In the Analysis and Methods of PDE (SIAM PDE)\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/SIAM-PDE/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gautam Iyer (CMU)
DTSTART:20230406T213000Z
DTEND:20230406T223000Z
DTSTAMP:20260424T235201Z
UID:SIAM-PDE/34
DESCRIPTION:Title: Using mixing to accelerate convergence of Langevin systems\, and
applications to Monte Carlo methods\nby Gautam Iyer (CMU) as part of S
eminar In the Analysis and Methods of PDE (SIAM PDE)\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/SIAM-PDE/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gunther Uhlmann (University of Washington\, USA\, and Hong Kong Un
iversity of Science and Technology\, Hong Kong)
DTSTART:20230504T153000Z
DTEND:20230504T163000Z
DTSTAMP:20260424T235201Z
UID:SIAM-PDE/35
DESCRIPTION:Title: The Calderon Problem: 40 Years Later\nby Gunther Uhlmann (Uni
versity of Washington\, USA\, and Hong Kong University of Science and Tech
nology\, Hong Kong) as part of Seminar In the Analysis and Methods of PDE
(SIAM PDE)\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/SIAM-PDE/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Isabelle Gallagher (École Normale Supérieure\, Paris\, France\,
on leave from Université Paris Cité)
DTSTART:20230601T153000Z
DTEND:20230601T163000Z
DTSTAMP:20260424T235201Z
UID:SIAM-PDE/36
DESCRIPTION:Title: From Newton to Boltzmann\, fluctuations and large deviations\
nby Isabelle Gallagher (École Normale Supérieure\, Paris\, France\, on l
eave from Université Paris Cité) as part of Seminar In the Analysis and
Methods of PDE (SIAM PDE)\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/SIAM-PDE/36/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrea Bertozzi (UCLA)
DTSTART:20230706T153000Z
DTEND:20230706T163000Z
DTSTAMP:20260424T235201Z
UID:SIAM-PDE/37
DESCRIPTION:Title: Undercompressive shocks in tears of wine\nby Andrea Bertozzi
(UCLA) as part of Seminar In the Analysis and Methods of PDE (SIAM PDE)\n\
nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/SIAM-PDE/37/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Christopher K.R.T. Jones (UNC-Chapel Hill (emeritus)\, George Mas
on University\, US\, and University of Reading\, UK)
DTSTART:20230907T153000Z
DTEND:20230907T163000Z
DTSTAMP:20260424T235201Z
UID:SIAM-PDE/38
DESCRIPTION:Title: Stability Indices for Nonlinear Waves and Patterns\nby Christ
opher K.R.T. Jones (UNC-Chapel Hill (emeritus)\, George Mason University\
, US\, and University of Reading\, UK) as part of Seminar In the Analysis
and Methods of PDE (SIAM PDE)\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/SIAM-PDE/38/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Irena Gamba (University of Texas\, Austin)
DTSTART:20231005T153000Z
DTEND:20231005T163000Z
DTSTAMP:20260424T235201Z
UID:SIAM-PDE/39
DESCRIPTION:Title: Weak turbulence modeled by quasilinear diffusion for electrostati
c and magnetized plasma systems\nby Irena Gamba (University of Texas\,
Austin) as part of Seminar In the Analysis and Methods of PDE (SIAM PDE)\
n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/SIAM-PDE/39/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eduard Feireisl (Czech Academy of Sciences and Charles University\
, Prague)
DTSTART:20231102T153000Z
DTEND:20231102T163000Z
DTSTAMP:20260424T235201Z
UID:SIAM-PDE/40
DESCRIPTION:Title: Dissipative systems in fluid dynamics\nby Eduard Feireisl (Cz
ech Academy of Sciences and Charles University\, Prague) as part of Semina
r In the Analysis and Methods of PDE (SIAM PDE)\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/SIAM-PDE/40/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Svitlana Mayboroda (Federal Institute of Technology - Eidgenössis
che Technische Hochschule (ETH) Zürich\, Switzerland)
DTSTART:20231207T163000Z
DTEND:20231207T173000Z
DTSTAMP:20260424T235201Z
UID:SIAM-PDE/41
DESCRIPTION:Title: Wave Localization and the Landscape Law\nby Svitlana Mayborod
a (Federal Institute of Technology - Eidgenössische Technische Hochschule
(ETH) Zürich\, Switzerland) as part of Seminar In the Analysis and Metho
ds of PDE (SIAM PDE)\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/SIAM-PDE/41/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Camillo De Lellis (Institute for Advanced Studies (IAS)\, Princeto
n University\, USA)
DTSTART:20240201T163000Z
DTEND:20240201T173000Z
DTSTAMP:20260424T235201Z
UID:SIAM-PDE/42
DESCRIPTION:Title: Area-minimizing integral currents: singularities and structure\nby Camillo De Lellis (Institute for Advanced Studies (IAS)\, Princeton
University\, USA) as part of Seminar In the Analysis and Methods of PDE (S
IAM PDE)\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/SIAM-PDE/42/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Luigi Ambrosio (Scuola Normale Superiore\, Pisa\, Italy)
DTSTART:20240307T163000Z
DTEND:20240307T173000Z
DTSTAMP:20260424T235201Z
UID:SIAM-PDE/43
DESCRIPTION:Title: On some variational problems involving functions with bounded Hes
sian\nby Luigi Ambrosio (Scuola Normale Superiore\, Pisa\, Italy) as p
art of Seminar In the Analysis and Methods of PDE (SIAM PDE)\n\nAbstract:
TBA\n
LOCATION:https://stable.researchseminars.org/talk/SIAM-PDE/43/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Guillaume Bal (University of Chicago)
DTSTART:20240404T153000Z
DTEND:20240404T163000Z
DTSTAMP:20260424T235201Z
UID:SIAM-PDE/44
DESCRIPTION:Title: Asymmetric interface transport and topological insulators\nby
Guillaume Bal (University of Chicago) as part of Seminar In the Analysis
and Methods of PDE (SIAM PDE)\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/SIAM-PDE/44/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nader Masmoudi (ew York University-Abu Dhabi\, UAE & Courant Insti
tute\, NYU\, USA)
DTSTART:20240502T153000Z
DTEND:20240502T163000Z
DTSTAMP:20260424T235201Z
UID:SIAM-PDE/45
DESCRIPTION:Title: Recent Progress in the Study of the Prandtl System and the Zero V
iscosity Limit\nby Nader Masmoudi (ew York University-Abu Dhabi\, UAE
& Courant Institute\, NYU\, USA) as part of Seminar In the Analysis and Me
thods of PDE (SIAM PDE)\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/SIAM-PDE/45/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kavita Ramanan (Brown University)
DTSTART:20240606T153000Z
DTEND:20240606T163000Z
DTSTAMP:20260424T235201Z
UID:SIAM-PDE/46
DESCRIPTION:Title: Long-time behavior of nonlinearly coupled measure-valued equation
s that model many-server systems\nby Kavita Ramanan (Brown University)
as part of Seminar In the Analysis and Methods of PDE (SIAM PDE)\n\nAbstr
act: TBA\n
LOCATION:https://stable.researchseminars.org/talk/SIAM-PDE/46/
END:VEVENT
BEGIN:VEVENT
SUMMARY:..... (....)
DTSTART:20240704T153000Z
DTEND:20240704T163000Z
DTSTAMP:20260424T235201Z
UID:SIAM-PDE/47
DESCRIPTION:Title: Canceled due to Independence Day holiday\nby ..... (....) as
part of Seminar In the Analysis and Methods of PDE (SIAM PDE)\n\nAbstract:
TBA\n
LOCATION:https://stable.researchseminars.org/talk/SIAM-PDE/47/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kavita Ramanan (Brown University)
DTSTART:20240905T153000Z
DTEND:20240905T163000Z
DTSTAMP:20260424T235201Z
UID:SIAM-PDE/48
DESCRIPTION:Title: Long-time behavior of nonlinearly coupled measure-valued equation
s that model many-server systems\nby Kavita Ramanan (Brown University)
as part of Seminar In the Analysis and Methods of PDE (SIAM PDE)\n\nAbstr
act: TBA\n
LOCATION:https://stable.researchseminars.org/talk/SIAM-PDE/48/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Robert McCann (University of Toronto\, Canada)
DTSTART:20250226T150000Z
DTEND:20250226T160000Z
DTSTAMP:20260424T235201Z
UID:SIAM-PDE/49
DESCRIPTION:Title: The monopolist's free boundary problem in the plane: an excursion
into the economic value of private information\nby Robert McCann (Uni
versity of Toronto\, Canada) as part of Seminar In the Analysis and Method
s of PDE (SIAM PDE)\n\n\nAbstract\nThe principal-agent problem is an impor
tant paradigm in economic theory for studying the value of private informa
tion: the nonlinear pricing problem faced by a monopolist is one example\;
others include optimal taxation and auction design. For multidimensional
spaces of consumers (i.e. agents) and products\, Rochet and Chone (1998) r
eformulated this problem as a concave maximization over the set of convex
functions\, by assuming agent preferences are bilinear in the product and
agent parameters. This optimization corresponds mathematically to a convex
ity-constrained obstacle problem. The solution is divided into multiple re
gions\, according to the rank of the Hessian of the optimizer.\n\nApart fr
om four possible pathologies\, if the monopolist’s costs grow quadratic
ally with the product type we show that a smooth free boundary delineates
the region where it becomes efficient to customize products for individual
buyers. We give the first complete solution of the problem on square dom
ains\, and discover new transitions from unbunched to targeted and from ta
rgeted to blunt bunching as market conditions become more and more favorab
le to the seller.\n\nBased on work with Cale Rankin (Monash University) a
nd Kelvin Shuangjian Zhang (Fudan University) https://arxiv.org/abs/2412.1
5505.\n\nChair: Marcelo Disconzi\, marcelo.disconzi@vanderbilt.edu\n
LOCATION:https://stable.researchseminars.org/talk/SIAM-PDE/49/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chanwoo Kim (University of Wisconsin\, Madison)
DTSTART:20250226T163000Z
DTEND:20250226T173000Z
DTSTAMP:20260424T235201Z
UID:SIAM-PDE/50
DESCRIPTION:Title: Quantitative Theory of Hydrodynamic Limits Toward Incompressible
Euler Equations\nby Chanwoo Kim (University of Wisconsin\, Madison) as
part of Seminar In the Analysis and Methods of PDE (SIAM PDE)\n\n\nAbstra
ct\nIn this talk\, I will discuss quantitative convergence results for sca
led Boltzmann solutions approaching solutions of the incompressible Euler
equations as the Knudsen number tends to zero\, without requiring prior kn
owledge of the limiting solution.\n\nChair: Marcelo Disconzi\, marcelo.dis
conzi@vanderbilt.edu\n
LOCATION:https://stable.researchseminars.org/talk/SIAM-PDE/50/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tim Laux (University of Regensburg\, Germany)
DTSTART:20250227T150000Z
DTEND:20250227T160000Z
DTSTAMP:20260424T235201Z
UID:SIAM-PDE/51
DESCRIPTION:Title: The sharp-interface limit of the Allen-Cahn equation\nby Tim
Laux (University of Regensburg\, Germany) as part of Seminar In the Analys
is and Methods of PDE (SIAM PDE)\n\n\nAbstract\nThe Allen-Cahn equation is
one of the most basic reaction-diffusion equations\, modeling a large var
iety of phase transition problems. In a suitable scaling limit\, the trans
ition becomes sharp and the system follows a geometric evolution equation
- the mean curvature flow. The structure of this "sharp-interface limit" h
as received continuous attention from both the geometric and applied analy
sis communities over the last decades. In this talk\, I will give an overv
iew of some of the breakthroughs in this field and highlight a recent shor
t convergence analysis in a joint work with Julian Fischer and Theresa Sim
on. Our proof is based on a new relative entropy for diffuse interface pro
blems that allows us to prove the optimal convergence rate toward mean cur
vature flow.\n\nAtanas Stefanov\, University of Alabama\, Birminghan (stef
anov@uab.edu)\n
LOCATION:https://stable.researchseminars.org/talk/SIAM-PDE/51/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrew Lawrie (University of Maryland\, College Park)
DTSTART:20250227T163000Z
DTEND:20250227T173000Z
DTSTAMP:20260424T235201Z
UID:SIAM-PDE/52
DESCRIPTION:Title: Soliton dynamics for classical scalar fields\nby Andrew Lawri
e (University of Maryland\, College Park) as part of Seminar In the Analys
is and Methods of PDE (SIAM PDE)\n\n\nAbstract\nI will present some of my
recent work with Jacek Jendrej. We study classical scalar fields in dimens
ion 1+1 with a symmetric double-well self-interaction potential. Examples
of such equations are the phi-4 model and the sine-Gordon equation. These
nonlinear wave equations admit non-trivial static solutions called kinks a
nd antikinks\, which are amongst the simplest examples of topological soli
tons. We define an n-kink cluster to be a solution approaching\, for large
positive times\, a superposition of n alternating kinks and antikinks who
se velocities converge to zero and mutual distances grow to infinity. Our
main result is a determination of the leading order asymptotic behavior of
any n-kink cluster. We use this information to construct the n-dimensiona
l invariant manifold of n-kink clusters\, which plays the dynamical role o
f the stable/unstable manifold for an ideal "critical point at infinity”
given by well separated multi-kink configurations. In this context we als
o explain the role of kink clusters as universal profiles for the formatio
n/annihilation of multikink configurations.\n\nSession Chair: Atanas Stefa
nov\, University of Alabama\, Birminghan (stefanov@uab.edu)\n
LOCATION:https://stable.researchseminars.org/talk/SIAM-PDE/52/
END:VEVENT
END:VCALENDAR