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BEGIN:VEVENT
SUMMARY:Sir John Ball (Heriot-Watt University\, Edinburgh)
DTSTART;VALUE=DATE-TIME:20200604T153000Z
DTEND;VALUE=DATE-TIME:20200604T163000Z
DTSTAMP;VALUE=DATE-TIME:20230529T060254Z
UID:SIAM-PDE/1
DESCRIPTION:Title: Some energy minimization problems for liquid crystals\nby Sir John Ba
ll (Heriot-Watt University\, Edinburgh) as part of Seminar In the Analysis
and Methods of PDE (SIAM PDE)\n\n\nAbstract\nThe talk will discuss some e
nergy minimization problems for liquid crystals described at different lev
els of detail by the probability density function of molecular orientation
s\, by a tensor average of this function (the de Gennes Q tensor theory)\,
and by the expected orientation of molecules (the Oseen-Frank theory).\n
LOCATION:https://researchseminars.org/talk/SIAM-PDE/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Benoit Perthame (Sorbonne University\, France)
DTSTART;VALUE=DATE-TIME:20200702T153000Z
DTEND;VALUE=DATE-TIME:20200702T163000Z
DTSTAMP;VALUE=DATE-TIME:20230529T060254Z
UID:SIAM-PDE/2
DESCRIPTION:Title: Multiphase models of living tissues and the Hele-Shaw limit\nby Be
noit Perthame (Sorbonne University\, France) as part of Seminar In the Ana
lysis and Methods of PDE (SIAM PDE)\n\n\nAbstract\nThe mechanical modeling
of living tissues has attracted much attention in the last decade. Appli
cations include tissue repair and growth models of solid tumors. These mo
dels contain several levels of complexity\, both in terms of the biologica
l and mechanical effects\, and therefore in their mathematical description
. Multiphase models describe the dynamics of several types of cells\, liqu
id\, fibers (extra-cellular matrix) and both compressible and incompressib
le models are used in the literature.\n\nIn this talk I shall discuss the
analysis of multiphase models based on Darcy's assumption. The compactness
issue leads us to use Aronson-Benilan estimate and to build new variants.
I shall also discuss the incompressible limit in special cases and the a
ssociated free boundary problem.\n
LOCATION:https://researchseminars.org/talk/SIAM-PDE/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Felix Otto (Max Planck Institute for Mathematics in the Sciences\,
Leipzig\, Germany)
DTSTART;VALUE=DATE-TIME:20200903T153000Z
DTEND;VALUE=DATE-TIME:20200903T163000Z
DTSTAMP;VALUE=DATE-TIME:20230529T060254Z
UID:SIAM-PDE/3
DESCRIPTION:Title: The thresholding scheme for mean curvature flow and De Giorgi's ideas for
gradient flows\nby Felix Otto (Max Planck Institute for Mathematics i
n the Sciences\, Leipzig\, Germany) as part of Seminar In the Analysis and
Methods of PDE (SIAM PDE)\n\n\nAbstract\nFlow of interfaces by mean curva
ture\, in its multi-phase version\,\nwas first formulated in the context o
f grain growth in polycrystalline materials. \nThe computationally efficie
nt 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 ad
jacent grains.\n\nThis extension relies on the gradient flow structure of
mean curvature flow\,\nand the interpretation of the thresholding scheme\n
as a corresponding "minimizing movements'' scheme\, that is\, a sequence o
f variational problems\nnaturally attached to the implicit time discretiza
tion of a gradient flow.\n\nThis interpretation also allows for a (conditi
onal) convergence proof based on De Giorgi's ideas\nfor gradient flows in
metric spaces. The approach is similar to\nthe convergence proof for the m
inimizing movement scheme by Almgren\, Taylor and Wang\,\nas given by Luck
haus et. al. \n\nThis is joint work with S. Esedoglu and T. Laux.\n
LOCATION:https://researchseminars.org/talk/SIAM-PDE/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Laure Saint-Raymond (ENS Lyon\, France)
DTSTART;VALUE=DATE-TIME:20201008T153000Z
DTEND;VALUE=DATE-TIME:20201008T163000Z
DTSTAMP;VALUE=DATE-TIME:20230529T060254Z
UID:SIAM-PDE/4
DESCRIPTION:Title: Fluctuation theory in the Boltzmann-Grad limit\nby Laure Saint-Raymon
d (ENS Lyon\, France) as part of Seminar In the Analysis and Methods of PD
E (SIAM PDE)\n\n\nAbstract\nIn this talk\, I will discuss a long term proj
ect with T. Bodineau\, I. Gallagher and S. Simonella on hard-sphere gases.
In the low density limit\, the empirical density obeys a law of large num
bers and the dynamics is governed asymptotically by the (kinetic) Boltzman
n equation. Deviations from this behavior are described by dynamical corre
lations\, which we can fully characterize for short times. This provides b
oth a fluctuating Boltzmann equation and large deviation asymptotics.\n
LOCATION:https://researchseminars.org/talk/SIAM-PDE/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vlad Vicol (Courant Institute of Mathematical Sciences\, NYU)
DTSTART;VALUE=DATE-TIME:20201105T163000Z
DTEND;VALUE=DATE-TIME:20201105T173000Z
DTSTAMP;VALUE=DATE-TIME:20230529T060254Z
UID:SIAM-PDE/5
DESCRIPTION:Title: Shock formation and vorticity creation for compressible Euler\nby Vla
d Vicol (Courant Institute of Mathematical Sciences\, NYU) as part of Semi
nar In the Analysis and Methods of PDE (SIAM PDE)\n\n\nAbstract\nIn this t
alk\, I will discuss a long term project\, joint with Tristan Buckmaster a
nd Steve Shkoller\, concerning the formation of singularities (shocks) for
the compressible Euler equations with the ideal gas law. We provide a con
structive proof of stable shock formation from smooth initial datum\, of f
inite energy\, and with no vacuum regions. Via modulated self-similar vari
ables\, the blow-up time and location can be explicitly computed\, and at
the blow-up time\, the solutions can be shown to have precisely Holder 1/3
regularity. Additionally\, for the non-isentropic problem sounds waves in
teract with entropy waves to produce vorticity at the shock.\n
LOCATION:https://researchseminars.org/talk/SIAM-PDE/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alessio Figalli (ETH Zurich\, Switzerland)
DTSTART;VALUE=DATE-TIME:20201203T163000Z
DTEND;VALUE=DATE-TIME:20201203T173000Z
DTSTAMP;VALUE=DATE-TIME:20230529T060254Z
UID:SIAM-PDE/6
DESCRIPTION:Title: Generic regularity in obstacle problems\nby Alessio Figalli (ETH Zuri
ch\, Switzerland) as part of Seminar In the Analysis and Methods of PDE (S
IAM PDE)\n\n\nAbstract\nThe classical obstacle problem consists of finding
the equilibrium position of an elastic membrane whose boundary is held fi
xed and constrained to lie above a given obstacle. By classical results 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)-d
imensional — that is\, as large as the regular set. In a recent paper wi
th Ros-Oton and Serra we show that\, generically\, the singular set has co
dimension 3 inside the free boundary\, solving a conjecture of Schaeffer i
n dimension $n\\leq 4$. This talk aims to give an overview of these result
s.\n
LOCATION:https://researchseminars.org/talk/SIAM-PDE/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrzej Swiech (Georgia Tech\, USA)
DTSTART;VALUE=DATE-TIME:20210204T163000Z
DTEND;VALUE=DATE-TIME:20210204T173000Z
DTSTAMP;VALUE=DATE-TIME:20230529T060254Z
UID:SIAM-PDE/7
DESCRIPTION:Title: Finite dimensional approximations of Hamilton-Jacobi-Bellman equations in
spaces of probability measures. (Featured Article in SIAM Journal on Math
ematical Analysis)\nby Andrzej Swiech (Georgia Tech\, USA) as part of
Seminar In the Analysis and Methods of PDE (SIAM PDE)\n\n\nAbstract\nWe wi
ll discuss how certain Hamilton-Jacobi-Bellman (HJB) equations in spaces o
f probability measures can be approximated by finite dimensional equations
. The most interesting cases are convergence of viscosity solutions of HJB
equations corresponding either to deterministic optimal control problems
for systems of $n$ particles or to stochastic optimal control problems for
systems of $n$ particles with a common noise\, to the viscosity solution
of a limiting HJB equation in the space of probability measures. The limit
ing HJB equation is interpreted in its ``lifted" form in a Hilbert space\,
which has a unique viscosity solution. When the Hamiltonian is convex in
the gradient variable and equations are of first order\, it can be proved
that the viscosity solutions of the finite dimensional problems converge t
o the value function of a variational problem in $\\mathcal{P}_2(\\R^d)$ t
hus providing a representation formula for the solution of the limiting fi
rst order HJB equation. The talk will also contain an overview of existing
works and various approaches to partial differential equations in abstrac
t spaces\, including spaces of probability measures and Hilbert spaces. Th
e talk is based on a joint work with W. Gangbo and S. Mayorga.\n\nFeatured
Article Authors: W. Gangbo\, S. Mayorga\, A. Swiech\n
LOCATION:https://researchseminars.org/talk/SIAM-PDE/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sergei Chernyshenko (Imperial College London\, UK)
DTSTART;VALUE=DATE-TIME:20210304T163000Z
DTEND;VALUE=DATE-TIME:20210304T173000Z
DTSTAMP;VALUE=DATE-TIME:20230529T060254Z
UID:SIAM-PDE/8
DESCRIPTION:Title: Auxiliary functionals: a path to solving the problem of turbulence\nb
y Sergei Chernyshenko (Imperial College London\, UK) as part of Seminar In
the Analysis and Methods of PDE (SIAM PDE)\n\n\nAbstract\nThe problem of
turbulence is the greatest unsolved problem of classical fluid dynamics.
It is quite old. Similarly\, the problem of optimizing over the cone of no
nnegative polynomials was long believed to be too hard\,\nuntil at the sta
rt of the millennium a breakthrough paved a way by linking it\, through su
m-of-squares polynomial optimisation\, to semidefinite programming. And on
ly a few years ago\, auxiliary functionals were proposed with an \nultimat
e goal of applying the fruits of this breakthrough to solving the problem
of turbulence. The essence of these ideas is remarkably simple. The talk w
ill cover the basics\, and then a few questions will be reviewed deeper\,
including applications to systems of equations with energy-conserving quad
ratic nonlinearities\, such as the Kuramoto–Sivashinsky and the Navier-S
tokes equations.\n
LOCATION:https://researchseminars.org/talk/SIAM-PDE/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sylvia Serfaty (Courant Institute of Mathematical Sciences\, NYU)
DTSTART;VALUE=DATE-TIME:20210401T153000Z
DTEND;VALUE=DATE-TIME:20210401T163000Z
DTSTAMP;VALUE=DATE-TIME:20230529T060254Z
UID:SIAM-PDE/9
DESCRIPTION:Title: Ginzburg-Landau\, old and new\nby Sylvia Serfaty (Courant Institute o
f Mathematical Sciences\, NYU) as part of Seminar In the Analysis and Meth
ods of PDE (SIAM PDE)\n\n\nAbstract\nThis talk will review older and more
recent results on the analysis of vortices in the Ginzburg-Landau model of
superconductivity\, including description of energy minimizers and their
vortex patterns in both two and three dimensions\, and description of vort
ex dynamics.\n
LOCATION:https://researchseminars.org/talk/SIAM-PDE/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gigliola Staffilani (MIT)
DTSTART;VALUE=DATE-TIME:20210506T153000Z
DTEND;VALUE=DATE-TIME:20210506T163000Z
DTSTAMP;VALUE=DATE-TIME:20230529T060254Z
UID:SIAM-PDE/10
DESCRIPTION:Title: How much math do you need to know to “solve" an initial value problem?
\nby Gigliola Staffilani (MIT) as part of Seminar In the Analysis and
Methods of PDE (SIAM PDE)\n\n\nAbstract\nIn this talk I will present some
recent results concerning periodic solutions to nonlinear Schrodinger equa
tions\, and in doing so I will introduce a variety of mathematical techniq
ues that range from harmonic and Fourier analysis to dynamical systems\, f
rom number theory to probability. \n\nI will start with a derivation of th
is type of equation from a many body system\, and I will discuss how Hamil
tonian structures can be mapped through this derivation process. I will th
en move to the study of the long time dynamics of associated initial value
problems\, in particular I will concentrate on the notion of energy trans
fer. I will show how ideas from dynamical systems are fundamental to work
through this analysis to obtain even relatively soft statements\, and I w
ill present some more recent results on the rigorous derivation of a wave
kinetic equation for a certain multidimensional KdV type equation using a
variety of tools such as Feynman diagrams\, sharp dispersive estimates and
improved combinatorial lemmata.\n
LOCATION:https://researchseminars.org/talk/SIAM-PDE/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yann Brenier (École Normale Supérieure\, Paris)
DTSTART;VALUE=DATE-TIME:20210603T153000Z
DTEND;VALUE=DATE-TIME:20210603T163000Z
DTSTAMP;VALUE=DATE-TIME:20230529T060254Z
UID:SIAM-PDE/11
DESCRIPTION:Title: On optimal transport of matrix-valued measures\nby Yann Brenier (Éc
ole Normale Supérieure\, Paris) as part of Seminar In the Analysis and Me
thods of PDE (SIAM PDE)\n\n\nAbstract\nWe suggest a way of defining optima
l transport of\npositive-semidefinite matrix-valued measures\, inspired by
a recent\nrendering of the incompressible Euler equations and related con
servative\nsystems as concave maximization problems. The main output of ou
r work is a\nmatricial analogue of the Hellinger-Kantorovich metric spaces
.\n
LOCATION:https://researchseminars.org/talk/SIAM-PDE/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Luis Silvestre (University of Chicago)
DTSTART;VALUE=DATE-TIME:20210701T153000Z
DTEND;VALUE=DATE-TIME:20210701T163000Z
DTSTAMP;VALUE=DATE-TIME:20230529T060254Z
UID:SIAM-PDE/12
DESCRIPTION:Title: Gaussian lower bounds for the Boltzmann equation without cut-off\nby
Luis Silvestre (University of Chicago) as part of Seminar In the Analysis
and Methods of PDE (SIAM PDE)\n\n\nAbstract\nThe Boltzmann equation model
s the evolution of densities of particles in a gas. Its global well posedn
ess is a major open problem\, facing comparable difficulties as similar qu
estions for equations in fluids. With current techniques\, we cannot rule
out the possibility of a spontaneous emergence of a singularity in the for
m 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 inhomogeneous
non-cutoff Boltzmann equation that are conditional to bounds on macroscop
ic quantities. We establish a Gaussian lower bound for solutions to the Bo
ltzmann equation without cutoff\, in the case of hard and moderately soft
potentials\, with spatial periodic conditions\, and under the sole assumpt
ion that hydrodynamic quantities (local mass\, local energy and local entr
opy density) remain bounded. In the talk\, we will discuss how this lower
bound fits in the larger program of conditional estimates.\n
LOCATION:https://researchseminars.org/talk/SIAM-PDE/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Roman Shvydkoy (University of Illinois\, Chicago)
DTSTART;VALUE=DATE-TIME:20210902T153000Z
DTEND;VALUE=DATE-TIME:20210902T163000Z
DTSTAMP;VALUE=DATE-TIME:20230529T060254Z
UID:SIAM-PDE/13
DESCRIPTION:Title: Analytical aspects of emergent dynamics in systems of collective behavio
r\nby Roman Shvydkoy (University of Illinois\, Chicago) as part of Sem
inar In the Analysis and Methods of PDE (SIAM PDE)\n\n\nAbstract\nOne of t
he challenging problems in the field of collective behavior is to understa
nd global emergent phenomena arising from purely local communication betwe
en agents. In the context of alignment dynamics examples of such global ph
enomena include flock formations\, reaching consensus of opinions\, emer
gence of leaders\, etc. For models based on purely local interactions the
assumption of graph-\, chain-\, or hydrodynamic connectivity of the flock
is often necessary\, but not always guaranteed\, to ensure collective out
come. In this talk we will give an overview of the subject and highlight
two new approaches to alignment dynamics in disconnected or weakly connect
ed flocks. One is based on a topological fractional diffusion that resembl
es the closest neighbor rule originating in various empirical studies\, an
d another based on the use of random fluctuations and the hypocoercivity p
roperty for the resulting kinetic Fokker-Planck-Alignment equation.\n
LOCATION:https://researchseminars.org/talk/SIAM-PDE/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Monica Visan (UCLA)
DTSTART;VALUE=DATE-TIME:20211007T153000Z
DTEND;VALUE=DATE-TIME:20211007T163000Z
DTSTAMP;VALUE=DATE-TIME:20230529T060254Z
UID:SIAM-PDE/14
DESCRIPTION:Title: Determinants\, commuting flows\, and recent progress on completely integ
rable systems\nby Monica Visan (UCLA) as part of Seminar In the Analys
is and Methods of PDE (SIAM PDE)\n\n\nAbstract\nWe will survey a number of
recent developments in the\ntheory of completely integrable nonlinear dis
persive PDE. These\ninclude a priori bounds\, the orbital stability of mul
tisolitons\,\nwell-posedness at optimal regularity\, and the existence of
dynamics\nfor Gibbs distributed initial data. I will describe the basic ob
jects\nthat tie together these disparate results\, as well as the diverse\
nideas required for each problem.\n
LOCATION:https://researchseminars.org/talk/SIAM-PDE/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Theodore Drivas (Stony Brook University)
DTSTART;VALUE=DATE-TIME:20211104T153000Z
DTEND;VALUE=DATE-TIME:20211104T163000Z
DTSTAMP;VALUE=DATE-TIME:20230529T060254Z
UID:SIAM-PDE/15
DESCRIPTION:Title: Compressible fluids\, entropy hierarchies\, and flocking\nby Theodor
e Drivas (Stony Brook University) as part of Seminar In the Analysis and M
ethods of PDE (SIAM PDE)\n\n\nAbstract\nWe will discuss two types of one-d
imensional compressible fluid equations\; Navier-Stokes models with local
dissipation in which the viscosity depends degenerately on the density and
nonlocal models for collective dynamics which exhibit flocking behavior.
For the local models\, we prove large data global regularity for a class o
f equations covering viscous shallow water. Another result proves a conjec
ture of Peter Constantin on singularity formation for a model describing s
lender axisymmetric fluid jets. For the non-local models\, we establish a
continuation criterion which says that smooth solutions exist so long as
no vacuum states form. The method of proof involves introducing a hierarc
hy of entropies to control the solution in terms of the minimum density.
We also show that any weak solutions which obeying an entropy inequality e
xhibit flocking. This reports on joint work with P. Constantin\, H. Nguye
n\, F. Pasqualotto and R. Shvydkoy.\n
LOCATION:https://researchseminars.org/talk/SIAM-PDE/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yao Yao (National University of Singapore)
DTSTART;VALUE=DATE-TIME:20211202T163000Z
DTEND;VALUE=DATE-TIME:20211202T173000Z
DTSTAMP;VALUE=DATE-TIME:20230529T060254Z
UID:SIAM-PDE/16
DESCRIPTION:Title: Symmetry and uniqueness via a variational approach\nby Yao Yao (Nati
onal University of Singapore) as part of Seminar In the Analysis and Metho
ds of PDE (SIAM PDE)\n\n\nAbstract\nFor some nonlocal PDEs\, their steady
states can be seen as critical points of some associated energy functional
. Therefore\, if one can construct perturbations around a function such th
at the energy decreases to first order along the perturbation\, this funct
ion cannot be a steady state. In this talk\, I will discuss how this simpl
e variational approach has led to some recent progress in the following eq
uations\, where the key is to carefully construct a suitable perturbation.
\n\nI will start with the aggregation-diffusion equation\, which is a non
local PDE driven by two competing effects: nonlinear diffusion and long-ra
nge attraction. We show that all steady states are radially symmetric up t
o a translation (joint with Carrillo\, Hittmeir and Volzone)\, and give so
me criteria on the uniqueness/non-uniqueness of steady states within the r
adial class (joint with Delgadino and Yan). I will also discuss the 2D Eul
er equation\, where we aim to understand under what condition must a stati
onary/uniformly-rotating solution be radially symmetric. Using a variation
al approach\, we settle some open questions on the radial symmetry of rota
ting patches\, and also show that any smooth stationary solution with comp
actly supported and nonnegative vorticity must be radial (joint with Góme
z-Serrano\, Park and Shi).\n
LOCATION:https://researchseminars.org/talk/SIAM-PDE/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:François Golse (École polytechnique\, France)
DTSTART;VALUE=DATE-TIME:20220203T163000Z
DTEND;VALUE=DATE-TIME:20220203T173000Z
DTSTAMP;VALUE=DATE-TIME:20230529T060254Z
UID:SIAM-PDE/17
DESCRIPTION:Title: Quantum Dynamics and Optimal Transport\nby François Golse (École p
olytechnique\, France) as part of Seminar In the Analysis and Methods of P
DE (SIAM PDE)\n\n\nAbstract\nIn 1979\, Dobrushin explained how Monge’s t
heory of optimal transport (1781)\ncan be used to prove the mean-field lim
it for the classical dynamics of large particle\nsystems. Is it possible t
o compare two quantum states\, or a quantum state and a\nclassical phase s
pace density by some quantum analogue of optimal transport? and the\naffir
mative\, can one use such ideas to study the mean-field and the classical
limits of\nquantum dynamics? This talk will review some recent results in
this direction\, based on\njoint works with E. Caglioti\, C. Mouhot and T.
Paul.\n
LOCATION:https://researchseminars.org/talk/SIAM-PDE/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Barbara Niethammer (University of Bonn\, Germany)
DTSTART;VALUE=DATE-TIME:20220303T163000Z
DTEND;VALUE=DATE-TIME:20220303T173000Z
DTSTAMP;VALUE=DATE-TIME:20230529T060254Z
UID:SIAM-PDE/18
DESCRIPTION:Title: An obstacle problem for cell polarization\nby Barbara Niethammer (Un
iversity 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 polariza
tion under external stimulus where a diffusion equation in the inner cell
is coupled to reaction diffusion equations on the cell membrane. In certai
n scaling limits we rigorously derive generalized obstacle type problems.
For these limit systems we prove global stability of steady states and c
haracterize the parameter regime for the onset of polarization. (Joint wor
k with Anna Logioti (Bonn) Matthias Roeger (TU Dortmund) and Juan Velazqu
ez (U Bonn)).\n\nFeatured Article: A parabolic free boundary problem arisi
ng in a model of cell polarization. SIAM J. Math. Anal. 53-1 (2021)\nFeat
ured Article Authors: A.Logioti\, B. Niethammer\, M. Röger and J. L. Vel
ázquez\n
LOCATION:https://researchseminars.org/talk/SIAM-PDE/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Martin Hairer (Imperial College London\, UK)
DTSTART;VALUE=DATE-TIME:20220407T153000Z
DTEND;VALUE=DATE-TIME:20220407T163000Z
DTSTAMP;VALUE=DATE-TIME:20230529T060254Z
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 and Meth
ods of PDE (SIAM PDE)\n\n\nAbstract\nWe consider the directed mean curvatu
re flow on the plane in a weak Gaussian random environment and show that\,
when started from a sufficiently flat initial condition\, a rescaled and
recentred solution converges in a suitable scaling limit to the solution o
f the KPZ equation. This result follows from the analysis of a more genera
l system of nonlinear stochastic PDEs driven by inhomogeneous noises\, usi
ng the theory of regularity structures. This is joint work with Andris Ger
asimovics (U. Bath) and Konstantin Matetski (U. Columbia).\n
LOCATION:https://researchseminars.org/talk/SIAM-PDE/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrea Nahmod (University of Massachusetts Amherst -- USA)
DTSTART;VALUE=DATE-TIME:20220505T153000Z
DTEND;VALUE=DATE-TIME:20220505T163000Z
DTSTAMP;VALUE=DATE-TIME:20230529T060254Z
UID:SIAM-PDE/20
DESCRIPTION:Title: Gibbs measures and propagation of randomness under the flow of nonlinear
dispersive PDE\nby Andrea Nahmod (University of Massachusetts Amherst
-- USA) as part of Seminar In the Analysis and Methods of PDE (SIAM PDE)\
n\n\nAbstract\nIn groundbreaking work\, Bourgain ’96 put forward a rando
m data theory to study the existence of strong solutions on the statistica
l ensemble of Gibbs measures associated to dispersive equations. Despite n
umerous follow-up works to those of Bourgain’s\, fundamental questions r
emained open. How does a given initial random data get transported by a no
nlinear flow ? If it is Gaussian initially\, how does this Gaussianity pr
opagate? What is the description of the solution beyond the linear evoluti
on?\n\nIn recent work\, joint with Yu Deng and Haitian Yue\, we developed
the theory of random tensors\, a powerful new framework which allows us to
unravel the propagation of randomness under the NLS flow beyond the linea
r evolution of random data\, and answer these questions in an optimal rang
e relative to what we define as the probabilistic scaling. In particular\
, we establish the invariance of Gibbs measures for 2D NLS and 3D Hartree
NLS equations using the method of random averaging operators\, a first ord
er approximation to the full random tensor theory. \n\nIn this talk we wil
l describe these results\, and explain the ideas behind them. We conclude
with some open problems and within this context present new work\, joint
with Bjoern Bringmann\, Yu Deng and Haitian Yue establishing the invarian
ce of the 3D Gibbs measure under the flow of the nonlinear wave equation.\
n\nBio Andrea R. Nahmod is Professor of Mathematics at the University of M
assachusetts Amherst. Her research lies at the interface of nonlinear Four
ier and harmonic analysis\, and the theory of partial differential equatio
ns. Some of her recent work aims at gaining a quantitative understanding o
f the propagation of randomness under the nonlinear evolution of dispersiv
e PDE. Nahmod is a Fellow of the American Mathematical Society\; a recipi
ent of the Sargent-Faull Fellowship at Harvard’s Radcliffe Institute for
Advanced Study\, and of a Simons Foundation Fellowship. Nahmod was twice
a member of the Institute for Advanced Study at Princeton and held Simons
’ Professorships at MSRI\, Berkeley and at CRM Montreal. She delivered a
n invited address at the 2021 Joint Mathematical Meetings of the AMS.\n
LOCATION:https://researchseminars.org/talk/SIAM-PDE/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Kiselev (Duke University)
DTSTART;VALUE=DATE-TIME:20220602T153000Z
DTEND;VALUE=DATE-TIME:20220602T163000Z
DTSTAMP;VALUE=DATE-TIME:20230529T060254Z
UID:SIAM-PDE/21
DESCRIPTION:Title: The flow of polynomial roots under differentiation\nby Alexander Kis
elev (Duke University) as part of Seminar In the Analysis and Methods of P
DE (SIAM PDE)\n\n\nAbstract\nFeatured Article: "Global regularity for a
nonlocal PDE describing evolution of polynomial roots under differentiatio
n"\, to appear\, SIAM J Math Analysis \n\nFeatured Article Authors: A. Kis
elev\, Changhui Tan \n\nThe question of how roots of polynomials move unde
r differentiation is classical. Contributions to this subject have been ma
de by Gauss\, Lucas\, Marcel Riesz\, Polya and many others. In 2018\, Stef
an Steinerberger derived formally a PDE that should describe the dynamics
of roots under differentiation in certain situations. The PDE in question
is of hydrodynamic type and bears a striking resemblance to the models use
d in mathematical biology to describe collective behavior and flocking of
various species - such as fish\, birds or ants. The equation is critical\,
but due to strongly nonlinear form of its coefficients\, proving global r
egularity for its solutions is harder than for equations such as Burgers\,
SQG or Euler alignment model. I will discuss joint work with Changhui Tan
in which we establish global regularity of Steinerberger's equation and m
ake a rigorous connection between its solutions and evolution of roots und
er differentiation for a class of trigonometric polynomials.\n
LOCATION:https://researchseminars.org/talk/SIAM-PDE/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Igor Rodnianski (Princeton University)
DTSTART;VALUE=DATE-TIME:20220707T153000Z
DTEND;VALUE=DATE-TIME:20220707T163000Z
DTSTAMP;VALUE=DATE-TIME:20230529T060254Z
UID:SIAM-PDE/22
DESCRIPTION:Title: Linear and nonlinear stability problems for the Vlasov-Poisson equations
\nby Igor Rodnianski (Princeton University) as part of Seminar In the
Analysis and Methods of PDE (SIAM PDE)\n\n\nAbstract\nFeatured Article:
"Plasma echoes near stable Penrose data"\, (SIAM J. Math. Anal. 54 (2022)
\, pp. 940-953) joint with "\, to appear\, SIAM J Math Analysis \n\nFeatur
ed Article Authors: \nEmmanuel Grenier\, Toan T. Nguyen and Igor Rodnians
ki\n\n\nI will discuss the issues in and around problems of stability of s
patially homogeneous equilibria in collisionless plasma\, including Landau
damping and plasma echos.\n
LOCATION:https://researchseminars.org/talk/SIAM-PDE/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Scott Armstrong (Courant Institute/NYU\, United States)
DTSTART;VALUE=DATE-TIME:20220901T153000Z
DTEND;VALUE=DATE-TIME:20220901T163000Z
DTSTAMP;VALUE=DATE-TIME:20230529T060254Z
UID:SIAM-PDE/23
DESCRIPTION:Title: Coarse-graining\, renormalization\, and quantitative homogenization\
nby Scott Armstrong (Courant Institute/NYU\, United States) as part of Sem
inar In the Analysis and Methods of PDE (SIAM PDE)\n\n\nAbstract\nI will p
resent an overview of the theory of quantitative homogenization (stochasti
c as well as periodic) for elliptic and parabolic equations\, which has be
en developed in the last ten years. A particular emphasis will be on the i
dea of "coarse-graining the coefficient field" with applications to degene
rate equations and other situations which require "renormalization\," incl
uding some more recent applications to models in mathematical physics. Tim
e permitting\, I will discuss what I see as some of the most important ope
n problems in the subfield.\n
LOCATION:https://researchseminars.org/talk/SIAM-PDE/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jacob Bedrossian (University of Maryland\, USA)
DTSTART;VALUE=DATE-TIME:20221006T153000Z
DTEND;VALUE=DATE-TIME:20221006T163000Z
DTSTAMP;VALUE=DATE-TIME:20230529T060254Z
UID:SIAM-PDE/24
DESCRIPTION:Title: Landau damping and related effects in kinetic models of plasma physics\nby Jacob Bedrossian (University of Maryland\, USA) as part of Seminar
In the Analysis and Methods of PDE (SIAM PDE)\n\n\nAbstract\nFeatured Arti
cle: "Linearized Wave-Damping Structure of Vlasov--Poisson in R3"\, SIAM
J. Math. Anal. 54(4) (2022)\, pp. 4379-4406 \n\nFeatured Article Auth
ors: Jacob Bedrossian\, Nader Masmoudi and Clément Mouhot\n\n\nIn this t
alk I will attempt to overview past and recent progress in understanding a
symptotic stability in collisionless and weakly collisional plasmas. Resul
ts such as Landau damping\, plasma echoes\, and collision-enhanced dissipa
tion will be discussed followed by discussions of some open directions.\n
LOCATION:https://researchseminars.org/talk/SIAM-PDE/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Patrick Gérard (Université Paris-Saclay\, France)
DTSTART;VALUE=DATE-TIME:20221103T163000Z
DTEND;VALUE=DATE-TIME:20221103T173000Z
DTSTAMP;VALUE=DATE-TIME:20230529T060254Z
UID:SIAM-PDE/25
DESCRIPTION:Title: A survey of the Benjamin-Ono equation with periodic boundary conditions<
/a>\nby Patrick Gérard (Université Paris-Saclay\, France) as part of Sem
inar In the Analysis and Methods of PDE (SIAM PDE)\n\n\nAbstract\nThe Benj
amin-Ono equation is a nonlinear dispersive wave equation in one space dim
ension\, introduced in 1967 as a model for long internal gravity waves in
a two layer fluid with infinite depth. In this talk\, I will show how the
use of a Lax pair provides a fairly complete picture of the dynamics with
periodic boundary conditions. I will discuss an explicit formula for the s
olutions\, global well posedness in sharp regularity\, long time dynamics
\, the classification of traveling waves\, of multi-solitons and of doubl
y periodic solutions\, and the smoothing effect. This talk is inspired fro
m a series of jointworks with Thomas Kappeler and Petar Topalov.\n
LOCATION:https://researchseminars.org/talk/SIAM-PDE/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alberto Bressan (Penn State University\, USA)
DTSTART;VALUE=DATE-TIME:20221201T163000Z
DTEND;VALUE=DATE-TIME:20221201T173000Z
DTSTAMP;VALUE=DATE-TIME:20230529T060254Z
UID:SIAM-PDE/26
DESCRIPTION:Title: On the optimal shape of tree roots and branches\nby Alberto Bressan
(Penn State University\, USA) as part of Seminar In the Analysis and Metho
ds of PDE (SIAM PDE)\n\n\nAbstract\nFeatured Article: "Optimal Shapes fo
r Tree Roots"\, SIAM J. Math. Anal. 54(4) (2022)\, pp. 4757-4784.\n\nFeat
ured Article Authors: Alberto Bressan\, Sondre T. Galtung and Qing Su.\n\
n\nLiving organisms come in an immense variety of shapes.\nIn many cases o
ne can expect that\, through natural selection\, a ``best possible" shape
will have evolved. From a mathematical perspective\, it is thus of interes
t to understand whether similar geometric shapes can be recovered as minim
izers of suitable functionals.\n\nAs a step in this direction\, we conside
r two functionals measuring the efficiency of roots and branches in a tree
. Namely: \n(i) a ``sunlight functional"\, modeling the total amount of su
nlight captured by the leaves of a tree\, and\n(ii) a ``harvest functional
"\, modeling the amount of nutrients collected by the roots.\nThe above fu
nctionals must be combined with a ``ramified transportation cost"\, for tr
ansporting nutrients from the roots to the base of the trunk\, or from the
base of the trunk to the leaves.\n\nThe talk will address the semicontinu
ity of these functionals\, and the existence and properties of optimal sol
utions\, in a space of measures.\nOpen problems will also be discussed\, i
ncluding computational issues and how these optimal shapes may depend on v
arious parameters.\n
LOCATION:https://researchseminars.org/talk/SIAM-PDE/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michael Weinstein (Columbia University)
DTSTART;VALUE=DATE-TIME:20220202T163000Z
DTEND;VALUE=DATE-TIME:20220202T173000Z
DTSTAMP;VALUE=DATE-TIME:20230529T060254Z
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://researchseminars.org/talk/SIAM-PDE/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:László Székelyhidi (Universitat Leipzig)
DTSTART;VALUE=DATE-TIME:20220302T163000Z
DTEND;VALUE=DATE-TIME:20220302T173000Z
DTSTAMP;VALUE=DATE-TIME:20230529T060254Z
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://researchseminars.org/talk/SIAM-PDE/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michael Weinstein (Columbia University)
DTSTART;VALUE=DATE-TIME:20220202T163000Z
DTEND;VALUE=DATE-TIME:20220202T173000Z
DTSTAMP;VALUE=DATE-TIME:20230529T060254Z
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://researchseminars.org/talk/SIAM-PDE/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:László Székelyhidi (Universitat Leipzig)
DTSTART;VALUE=DATE-TIME:20220302T163000Z
DTEND;VALUE=DATE-TIME:20220302T173000Z
DTSTAMP;VALUE=DATE-TIME:20230529T060254Z
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://researchseminars.org/talk/SIAM-PDE/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michael Weinstein (Columbia University)
DTSTART;VALUE=DATE-TIME:20230202T163000Z
DTEND;VALUE=DATE-TIME:20230202T173000Z
DTSTAMP;VALUE=DATE-TIME:20230529T060254Z
UID:SIAM-PDE/31
DESCRIPTION:Title: Effective gaps for time-periodic Hamiltonians modeling Floquet materials
\nby Michael Weinstein (Columbia University) as part of Seminar In the
Analysis and Methods of PDE (SIAM PDE)\n\n\nAbstract\nFeatured Article:
"Effective gaps in continuous Floquet Hamiltonians"\, SIAM J Math Analys
is 54 #1 2022. \n\nFeatured Article Authors: Amir Sagiv and Michael Wein
stein\n\n\nFloquet media are a type of material\, in which time-periodic f
orcing is applied to alter the material’s energy transport properties. E
xamples in classical and quantum physics include (i) applying a time-oscil
lating electric field to a graphene sheet to influence quantum electronic
transport\, and (ii) replacing a periodic array of standard optical wavegu
ides by an array of helically coiled waveguides to influence the flow of l
ight propagation in the array. The ability to modify energy transport via
time modulation is recognized as having great potential for applications t
o information transfer\, information processing\, and other applications.
\n\nWe discuss Floquet materials governed by a class of parametrically for
ced Schrödinger equations\, which arises in the above examples: \ni 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 material
\; the potential V has the symmetries of a honeycomb tiling of the plane.
The family of self-adjoint operators T ↦ W ( T\, -i ∇ ) is assumed to
be Tper – periodic. \n\nWhile the energy transport of the unforced syste
m ( W ≡ 0 ) is governed by the band structure (Floquet-Bloch spectral th
eory) of H0 \, that of the forced system is characterized by the monodromy
operator\, the unitary mapping ψ0 ↦ ψ ( ε-1 Tper ) \, and its associ
ated quasi-energy spectrum. Gaps in the band spectrum and quasi-energy spe
ctrum\, respectively\, of static and Floquet materials\, play an important
role in their transport properties. \n\nThe evolution under Hε (t) of ba
nd-limited Dirac wave-packets (a natural model of physical excitations) is
well-approximated on very large time scales by an effective time-periodic
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)\, and it is
believed that no such quasi-energy gap occurs. \n\nWe explain how to tran
sfer quasi-energy gap information about the effective Dirac dynamics to co
nclusions about the full Schrödinger dynamics (1). In particular\, we sho
w that (1) has an effective quasi-energy gap\, an interval of quasi-energi
es whose corresponding modes have only a very small spectral projection on
to the subspace of band-limited Dirac wave-packets. The notion of effectiv
e quasi-energy gap is a physically relevant relaxation of the strict notio
n of quasi-energy spectral gap. Physically\, if a system is tuned to drive
or measure at momenta and energies near the Dirac point of H0 \, then the
resulting modes in the effective quasi-energy gap will only be weakly exc
ited and detected. \n\nThis lecture focuses on joint work with Amir Sagiv
(Columbia University) appearing in the article: Effective gaps in continuo
us Floquet Hamiltonians\, SIMA 54 #1 2022.\n
LOCATION:https://researchseminars.org/talk/SIAM-PDE/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:László Székelyhidi (Universitat Leipzig)
DTSTART;VALUE=DATE-TIME:20230302T163000Z
DTEND;VALUE=DATE-TIME:20230302T173000Z
DTSTAMP;VALUE=DATE-TIME:20230529T060254Z
UID:SIAM-PDE/33
DESCRIPTION:Title: Magnetohydrodynamic turbulence: weak solutions and conserved quantities<
/a>\nby László Székelyhidi (Universitat Leipzig) as part of Seminar In
the Analysis and Methods of PDE (SIAM PDE)\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/SIAM-PDE/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gautam Iyer (CMU)
DTSTART;VALUE=DATE-TIME:20230406T213000Z
DTEND;VALUE=DATE-TIME:20230406T223000Z
DTSTAMP;VALUE=DATE-TIME:20230529T060254Z
UID:SIAM-PDE/34
DESCRIPTION:Title: Using mixing to accelerate convergence of Langevin systems\, and applica
tions to Monte Carlo methods\nby Gautam Iyer (CMU) as part of Seminar
In the Analysis and Methods of PDE (SIAM PDE)\n\nAbstract: TBA\n
LOCATION:https://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;VALUE=DATE-TIME:20230504T153000Z
DTEND;VALUE=DATE-TIME:20230504T163000Z
DTSTAMP;VALUE=DATE-TIME:20230529T060254Z
UID:SIAM-PDE/35
DESCRIPTION:Title: The Calderon Problem: 40 Years Later\nby Gunther Uhlmann (University
of Washington\, USA\, and Hong Kong University of Science and Technology\
, Hong Kong) as part of Seminar In the Analysis and Methods of PDE (SIAM P
DE)\n\nAbstract: TBA\n
LOCATION:https://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;VALUE=DATE-TIME:20230601T153000Z
DTEND;VALUE=DATE-TIME:20230601T163000Z
DTSTAMP;VALUE=DATE-TIME:20230529T060254Z
UID:SIAM-PDE/36
DESCRIPTION:Title: From Newton to Boltzmann\, fluctuations and large deviations\nby Isa
belle Gallagher (École Normale Supérieure\, Paris\, France\, on leave fr
om Université Paris Cité) as part of Seminar In the Analysis and Methods
of PDE (SIAM PDE)\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/SIAM-PDE/36/
END:VEVENT
END:VCALENDAR