Organizing Committee
 Alexandru Ionescu
Princeton University  Yvan Martel
École Polytechnique  Kenji Nakanishi
Research Institute for Mathematical Sciences, Kyoto University  Monica Visan
University of California, Los Angeles
Abstract
Recent progress in the analysis of dispersive PDE's has revealed various aspects of longtime dynamics or behavior of solutions, from the basic three types (scattering, blowup, and solitons) to more complicated combinations, transitions, and oscillations among them, and so on. The goal of this workshop is for the participants to draw integrated landscapes of those diverse phenomena, aiming towards more a complete description, classification, and prediction of global dynamics, as well as new phenomena and methods.
Confirmed Speakers & Participants
 Speaker
 Poster Presenter
 Attendee
 Virtual Attendee

Patricia Alonso Ruiz
Texas A&M University

Ioakeim Ampatzoglou
Courant Institute of Mathematical Sciences, New York University

Xinliang An
National University of Singapore

Aidan Backus
Brown University

ByeongHo Bahn
University of Massachusetts Amherst

Hajer Bahouri
Université ParisEst  Créteil

Weizhu Bao
National University of Singapore

Marius Beceanu
University at Albany SUNY

Bekarys Bekmaganbetov
Brown University

Massimiliano Berti
SISSA

Lydia Bieri
University of Michigan

Piotr Bizon
Jagiellonian University

Bjoern Bringmann
Institute for Advanced Study

Nicolas Camps
Université Paris Saclay

Andreia Chapouto
UCLA

Jehanzeb Chaudhary
University of New Mexico

Gong Chen
Fields institute

Brian Choi
Southern Methodist University

Diego Cordoba
ICMAT

Stefan Czimek
Brown University (ICERM)

Magdalena Czubak
University of Colorado at Boulder

Joel Dahne
Uppsala University

David Damanik
RICE University

Pierre de Roubin
University of Edinburgh

Yu Deng
University of Southern California

Giuseppe Di Fazio
University of Catania

Benjamin Dodson
John Hopkins University

Michele Dolce
Imperial College London

Hongjie Dong
Brown University

Jinqiao Duan
Illinois Institute of Technology

Daniel Eceizabarrena
University of Massachusetts Amherst

Chenjie Fan
Academy of Mathematics and Systems Science, CAS

Allen Fang
Sorbonne University

Anxo Fariña Biasi
Jagiellonian University

Patrick Flynn
Brown

Luigi Forcella
HeriotWatt University

Rupert Frank
LMU Munich

Claudia García
Universitat de Barcelona

Eduardo GarciaJuarez
Universitat de Barcelona

Louise Gassot
Laboratoire de Mathématiques d'Orsay  Université ParisSaclay

Pierre Germain
NYU  Courant Institute

Elena Giorgi
Columbia University

Tainara Gobetti Borges
Brown University

Javier Gomez Serrano
Princeton University

Ricardo Grande Izquierdo
University of Michigan

Benoît Grébert
University of Nantes

Sandrine Grellier
Université d'Orléans

Zihua Guo
Monash University

Yan Guo
Brown University

Zaher Hani
University of Michigan

Benjamin HarropGriffiths
University of California, Los Angeles

Susanna Haziot
Brown University Mathematics

Jiao He
Laboratoire de Mathématiques d'Orsay

Sebastian Herr
Bielefeld University

Justin Holmer
Brown University

Slim IBRAHIM
University of Victoria

Alexandru Ionescu
Princeton University

Sameer Iyer
UC Davis

Hao Jia
University of Minnesota

Adilbek Kairzhan
University of Toronto

Thomas Kappeler
Universität Zürich

Dean Katsaros
UMass amherst

Panayotis Kevrekidis
University of Massachusetts Amherst

Friedrich Klaus
Karlsruhe Institute of Technology

Haram Ko
Brown University

Herbert Koch
University of Bonn

Oussama Landoulsi
Florida International University

Thierry Laurens
University of California, Los Angeles

Gyu Eun Lee
University of Edinburgh

Guopeng Li
University of Edinburgh

Yao Li
University of Massachusetts Amherst

Kyle Liss
University of Maryland, College Park

Ruoyuan Liu
University of Edinburgh

Jonas Luhrmann
Texas A&M University

Jani Lukkarinen
University of Helsinki

Yvan Martel
École Polytechnique

Jeremy Marzuola
University of North Carolina

Nader Masmoudi
Courant Institute of Mathematical Sciences at NYU

Peter Miller
University of Michigan

Joseph Miller
University of Texas at Austin

Adam Morgan
University of Toronto

Lin Mu
University of Georgia

Jason Murphy
Missouri University of Science and Technology

Andrea Nahmod
University of Massachusetts Amherst

Kenji Nakanishi
Research Institute for Mathematical Sciences, Kyoto University

Maria Ntekoume
Rice University

Tadahiro Oh
The University of Edinburgh

Ludivine Oruba
Sorbonne Universite

José Palacios
Institut Denis Poisson, Université de Tours

Jaemin Park
Universitat de Barcelona

Benoit Pausader
Brown University

Nataša Pavlovic
University of Texas at Austin

Dmitry Pelinovsky
McMaster University

Galina Perelman
LAMA

Leonardo Pollini
Politecnico di Torino

Fabio Pusateri
University of Toronto

Oscar Riano
Florida International University

Tristan Robert
Université de Lorraine

Igor Rodnianski
Princeton University

Casey Rodriguez
University of North Carolina

Matthew Rosenzweig
Massachusetts Institute of Technology

Svetlana Roudenko
Florida International University

Wilhelm Schlag
Yale University

Birgit Schoerkhuber
University of Innsbruck, Austria

Diaraf Seck
University Cheikh Anta Diop of Dakar

Anastassiya Semenova
ICERM, Brown University

Chengyang Shao
Massachusetts Institute of Technology

Yeonjong Shin
Brown University

Gigliola Staffilani
Massachusetts Institute of Technology

Noah Stevenson
Princeton University

Annalaura Stingo
University of California Davis

Walter Strauss
Brown University

Catherine Sulem
University of Toronto

Ruoci Sun
Karlsruhe Institute of Technology

changzhen Sun
University of ParisSaclay

Chenmin Sun
CY CergyParis Université

Tomoyuki Tanaka
Nagoya University

Maja Taskovic
Emory University

Daniel Tataru
University of California, Berkeley

Leonardo Tolomeo
Universität Bon

MinhBinh Tran
Southern Methodist University

Nikolay Tzvetkov
University of CergyPontoise

Paolo Ventura
SISSA

Mats Vermeeren
University of Leeds

Monica Visan
University of California, Los Angeles

Hong Wang
Institute for Advanced Study (IAS)

Yuzhao Wang
University of Birmingham

Weinan Wang
University of Arizona

Xuecheng Wang
Tsinghua University

Sijue Wu
University of Michigan

Zoe Wyatt
University of Cambridge

Zhuolun Yang
Brown University

Jiaqi Yang
ICERM

Jia Yin
Lawrence Berkeley National Laboratory

Xueying Yu
University of Washington

Haitian Yue
University of Southern California

Zhiyuan Zhang
New York University

Jiqiang Zheng
Institute of Applied Physics and Computational Mathematics

Guangqu Zheng
University of Edinburgh

SHIJUN ZHENG
Georgia Southern University

Younes Zine
University of Edinburgh
Workshop Schedule
Monday, December 6, 2021

8:55  9:00 am ESTWelcome11th Floor Lecture Hall
 Brendan Hassett, ICERM/Brown University

9:00  9:45 am ESTAsymptotic stability of the SineGordon kink under odd perturbations via supersymmetry11th Floor Lecture Hall
 Wilhelm Schlag, Yale University
Abstract
We will describe the recent asymptotic analysis with Jonas Luehrmann of the SineGordon evolution of odd data near the kink. We do not rely on the complete integrability of the problem in a direct way, in particular we do not use the inverse scattering transform.

10:00  10:30 am ESTCoffee Break11th Floor Collaborative Space

10:30  11:15 am ESTTimedependent BogoliubovdeGennes and GinzburgLandau equations11th Floor Lecture Hall
 Virtual Speaker
 Rupert Frank, LMU Munich
Abstract
We study the timedependent BogoliubovdeGennes equations for generic translationinvariant fermionic manybody systems. For initial states that are close to thermal equilibrium states at temperatures near the critical temperature, we show that the magnitude of the order parameter stays approximately constant in time and, in particular, does not follow a timedependent GinzburgLandau equation, which is often employed as a phenomenological description and predicts a decay of the order parameter in time.

11:30 am  12:15 pm ESTOn the wellposedness of the derivative nonlinear Schr\"odinger equation11th Floor Lecture Hall
 Maria Ntekoume, Rice University
Abstract
We consider the derivative nonlinear Schr\"odinger equation in one space dimension, posed both on the line and on the circle. This model is known to be completely integrable and $L^2$critical with respect to scaling. However, not much is known regarding the wellposendess of the equation below $H^{\frac 12}$. In this talk, we prove that this problem is globally wellposed for initial data in the Sobolev spaces $H^s$ for $\frac 1 6\leq s<\frac 12$. The key ingredient in our argument is proving that ensembles of orbits with $L^2$equicontinuous initial data remain equicontinuous under evolution. This is joint work with Rowan Killip and Monica Visan.

12:30  2:30 pm ESTLunch/Free Time

2:30  3:15 pm ESTQuantitative derivation and scattering of the 3D cubic NLS in the energy space11th Floor Lecture Hall
 Justin Holmer, Brown University
Abstract
We consider the derivation of the {defocusing cubic nonlinear Schr\"{o}dinger equation (NLS) on $\mathbb{R}^{3}$ from quantum $N$body dynamics. We reformat the hierarchy approach with KlainermanMachedon theory and prove a biscattering theorem for the NLS to obtain convergence rate estimates under $H^{1}$ regularity. The $H^{1}$ convergence rate estimate we obtain is almost optimal for $H^{1}$ datum, and immediately improves if we have any extra regularity on the limiting initial oneparticle state. This is joint work with Xuwen Chen (University of Rochester).

3:30  4:15 pm ESTLocal smoothing estimate for the cone in R^311th Floor Lecture Hall
 Virtual Speaker
 Hong Wang, Institute for Advanced Study (IAS)
Abstract
If u is a solution to the wave equation on R^n, a local smoothing inequality bounds $\u\_{L^p(\mathbb{R}^n\times [1,2])}$ in terms of the Sobolev norms of the initial data. We prove Sogge's local smoothing conjecture in 2+1 dimensions.
In the proof, we introduced an approximation of the $L^4$norm that works better for induction. Another key ingredient is an incidence estimate for points and tubes.
This is joint work with Larry Guth and Ruixiang Zhang. 
4:30  6:00 pm ESTWelcome ReceptionReception  11th Floor Collaborative Space
Tuesday, December 7, 2021

9:00  9:45 am ESTHighOrder Rogue Waves and Solitons, and Solutions Interpolating Between Them11th Floor Lecture Hall
 Virtual Speaker
 Peter Miller, University of Michigan
Abstract
A family of exact solutions to the focusing nonlinear Schrödinger equation is presented that contains fundamental rogue waves and multiplepole solitons of all orders. The family is indexed with a continuous parameter representing the "order" that allows one to continuously tune between rogue waves and solitons of different integer orders. In this scheme, solitons and rogue waves of increasing integer orders alternate as the continuous order parameter increases. For example, the Peregrine solution can be viewed as a soliton of order threehalves. We show that solutions in this family exhibit certain universal features in the limit of high (continuous) order. This is joint work with Deniz Bilman (Cincinnati).

10:00  10:30 am ESTCoffee Break11th Floor Collaborative Space

10:30  11:15 am ESTLandau law and stability of 3D shocks11th Floor Lecture Hall
 Virtual Speaker
 Igor Rodnianski, Princeton University
Abstract
We will discuss stability and long term behavior of 3 dimensional compressible irrotational shocks arising in the compressible Euler equations.
In 1945, Landau argued that spherically symmetric solutions which form weak shocks will settle to a profile with 2 shocks decaying at the rate proportionate to 1/{t\sqrt{\log t}}. We address this conjecture by first identifying the asymptotic profile which exhibit 2 shocks, as a selfsimilar solution of a related Burgers equation, and then proving its stability and the conjectured rate of decay for general (nonspherically symmetric) perturbations. This is joint work with D. Ginsberg. 
11:30 am  12:15 pm ESTGround state in the energy supercritical GrossPitaevskii equation with a harmonic potential11th Floor Lecture Hall
 Virtual Speaker
 Dmitry Pelinovsky, McMaster University
Abstract
In order to prove the existence of a ground state (a positive, radially symmetric solution in the energy space), we develop the shooting method and deal with a oneparameter family of classical solutions to an initialvalue problem for the stationary equation. We prove that the solution curve (the graph of the eigenvalue parameter versus the supremum norm) is oscillatory below a threshold and monotone above a threshold. Compared to the existing literature, rigorous asymptotics are derived by constructing families of solutions to the stationary equation with functionalanalytic rather than geometric methods. The same analytical technique allows us to characterize the Morse index of the ground state.

12:30  2:00 pm ESTLunch/Free Time

2:00  2:45 pm ESTRigidity for solutions to the quintic NLS equation at the ground state level11th Floor Lecture Hall
 Benjamin Dodson, John Hopkins University
Abstract
In this talk, we will prove rigidity for solutions to the quintic nonlinear Schrodinger equation in one dimension, at the level of the ground state. Specifically, we show that the only solutions that fail to scatter are the solitons and the pseudoconformal transformation of the solitons.

3:00  4:30 pm ESTLightning Talks followed by Coffee Break and discussionsLightning Talks  11th Floor Lecture Hall
Wednesday, December 8, 2021

9:00  9:45 am ESTA Rigorous Derivation of the Hamiltonian Structure for the Nonlinear Schrodinger Equation11th Floor Lecture Hall
 Virtual Speaker
 Nataša Pavlovic, University of Texas at Austin
Abstract
Many mathematical works have focused on understanding the manner in which the dynamics of the nonlinear Schrodinger equation (NLS) arises as an effective equation. By effective equation, we mean that solutions of the NLS equation approximate solutions to an underlying physical equation in some topology in a particular asymptotic regime. For example, the cubic NLS is an effective equation for a system of N bosons interacting pairwise via a delta or approximate delta potential. In this talk, we will advance a new perspective on deriving an effective equation, which focuses on structure. In particular, we will show how the Hamiltonian structure for the cubic NLS in any dimension arises from corresponding structure at the Nparticle level. Also we will discuss what we have learned so far about understanding origins of integrability of the 1D cubic NLS. The talk is based on joint works with Dana Mendelson, Andrea Nahmod, Matthew Rosenzweig and Gigliola Staffilani.

10:00  10:30 am ESTCoffee Break11th Floor Collaborative Space

10:30  11:15 am ESTGibbs measures, canonical stochastic quantization, and singular stochastic wave equations11th Floor Lecture Hall
 Virtual Speaker
 Tadahiro Oh, The University of Edinburgh
Abstract
In this talk, I will discuss the (non)construction of the focusing Gibbs measures and the associated dynamical problems. This study was initiated by Lebowitz, Rose, and Speer (1988) and continued by Bourgain (1994), BrydgesSlade (1996), and CarlenFröhlichLebowitz (2016). In the onedimensional setting, we consider the masscritical case, where a critical mass threshold is given by the mass of the ground state on the real line. In this case, I will show that the Gibbs measure is indeed normalizable at the optimal mass threshold, thus answering an open question posed by Lebowitz, Rose, and Speer (1988).
In the three dimensionalsetting, I will first discuss the construction of the $\Phi^3_3$measure with a cubic interaction potential. This problem turns out to be critical, exhibiting a phase transition: normalizability in the weakly nonlinear regime and nonnormalizability in the strongly nonlinear regime. Then, I will discuss the dynamical problem for the canonical stochastic quantization of the $\Phi^3_3$measure, namely, the threedimensional stochastic damped nonlinear wave equation with a quadratic nonlinearity forced by an additive spacetime white noise (= the hyperbolic $\Phi^3_3$model). As for the local theory, I will describe the paracontrolled approach to study stochastic nonlinear wave equations, introduced in my work with Gubinelli and Koch (2018). In the globalization part, I introduce a new, conceptually simple and straightforward approach, where we directly work with the (truncated) Gibbs measure, using the variational formula and ideas from theory of optimal transport.
The first part of the talk is based on a joint work with Philippe Sosoe (Cornell) and Leonardo Tolomeo (Bonn), while the second part is based on a joint work with Mamoru Okamoto (Osaka) and Leonardo Tolomeo (Bonn). 
11:30 am  12:15 pm ESTMathematical Construction for Gravitational Collapse11th Floor Lecture Hall
 Yan Guo, Brown University
Abstract
We will discuss recent constructions of blowup solutions for describing gravitational collapse for EulerPoisson system.

12:30  12:40 pm ESTGroup Photo11th Floor Lecture Hall

12:40  2:30 pm ESTLunch/Free Time

2:30  3:15 pm ESTInternal Modes and Radiation Damping for 3d KleinGordon equations11th Floor Lecture Hall
 Virtual Speaker
 Fabio Pusateri, University of Toronto
Abstract
We consider quadratic KleinGordon equations with an external potential $V$ in $3+1$ spacetime dimensions. We assume that $V$ is generic and decaying, and that the operator $\Delta + V + m^2$ has an eigenvalue $\lambda^2 < m^2$. This is a socalled ‘internal mode’ and gives rise to timeperiodic localized solutions of the linear flow. We address the question of whether such solutions persist under the full nonlinear flow. Our main result shows that small nonlinear solutions slowly decay as the energy is transferred from the internal mode to the continuous spectrum, provided a natural Fermi golden rule holds. Moreover, we obtain very precise asymptotic information including sharp rates of decay and the growth of weighted norms. These results extend the seminal work of SofferWeinstein for cubic nonlinearities to the case of any generic perturbation. This is joint work with Tristan Léger (Princeton University).

3:30  4:00 pm ESTCoffee Break11th Floor Collaborative Space

4:00  4:45 pm ESTSolutions to the KdV and Related Equations With Almost Periodic Initial Data11th Floor Lecture Hall
 David Damanik, RICE University
Abstract
We discuss recent work concerning the existence, uniqueness, and structure of solutions to the KdV equation, as well as related ones, with almost periodic initial data. The talk is based on several joint works with a variety of coauthors, including Ilia Binder, Michael Goldstein, Yong Li, Milivoje Lukic, Alexander Volberg, Fei Xu, and Peter Yuditskii.
Thursday, December 9, 2021

9:00  9:45 am ESTThe Quartic Integrability and Long Time Existence of Steep Water Waves in 2D11th Floor Lecture Hall
 Virtual Speaker
 Sijue Wu, University of Michigan
Abstract
Abstract. It is known since the work of Dyachenko & Zakharov in 1994 that for the weakly nonlinear 2d infinite depth water waves, there are no 3wave interactions and all of the 4wave interaction coefficients vanish on the non trivial resonant manifold. In this talk, I will present a recent result that proves this partial integrability from a different angle. We construct a sequence of energy functionals Ej (t), directly in the physical space, which are explicit in the Riemann mapping variable and involve material derivatives of order j of the solutions for the 2d water wave equation, so that ddtEj (t) is quintic or higher order. We show that if some scaling invariant norm, and a norm involving one spacial derivative above the scaling of the initial data are of size no more than ε, then the lifespan of the solution for the 2d water wave equation is at least of order O(ε−3), and the solution remains as regular as the initial data during this time. If only the scaling invariant norm of the data is of size ε, then the lifespan of the solution is at least of order O(ε−5/2). Our long time existence results do not impose size restrictions on the slope of the initial interface and the magnitude of the initial velocity, they allow the interface to have arbitrary large steepnesses and initial velocities to have arbitrary large magnitudes.

10:00  10:30 am ESTCoffee Break11th Floor Collaborative Space

10:30  11:15 am ESTGlobal wellposedness of the Zakharov System below the ground state11th Floor Lecture Hall
 Virtual Speaker
 Sebastian Herr, Bielefeld University
Abstract
We consider the Cauchy problem for the Zakharov system with a focus on the energycritical dimension d = 4 and prove that global wellposedness holds in the full (nonradial) energy space for any initial data with energy and wave mass below the ground state threshold. The result is based on a uniform Strichartz estimate for the Schr ̈odinger equation with potentials solving the wave equation. This is joint work with Timothy Candy and Kenji Nakanishi.

11:30 am  12:15 pm ESTTBD11th Floor Lecture Hall
 Svetlana Roudenko, Florida International University

12:30  2:30 pm ESTLunch/Free Time

2:30  3:15 pm ESTTBD11th Floor Lecture Hall
 Daniel Tataru, University of California, Berkeley

3:30  4:00 pm ESTCoffee Break11th Floor Collaborative Space

4:00  4:45 pm ESTSimple motion of stretchlimited elastic strings11th Floor Lecture Hall
 Virtual Speaker
 Casey Rodriguez, University of North Carolina
Abstract
Perfectly flexible strings are among the simplest onedimensional continuum bodies and have a rich mechanical and mathematical theory dating back to the derivation of their equations of motion by Euler and Lagrange. In classical treatments, the string is either completely extensible (force produces stretching) or completely inextensible (every segment has a fixed length, regardless of the motion). However, common experience is that a string can be stretched (is extensible), and after a certain amount of force is applied the stretch of the string is maximized (becoming inextensible). In this talk, we discuss a simple model for these stretchlimited elastic strings, in what way they model ``elastic" behavior, the wellposedness and asymptotic stability of certain simple motions, and (many) open questions.
Friday, December 10, 2021

9:00  9:45 am ESTTBD11th Floor Lecture Hall
 Pierre Germain, NYU  Courant Institute

10:00  10:30 am ESTCoffee Break11th Floor Collaborative Space

10:30  11:15 am ESTNontrivial selfsimilar blowup in energy supercritical wave equations11th Floor Lecture Hall
 Birgit Schoerkhuber, University of Innsbruck, Austria
Abstract
Selfsimilar solutions play an important role in the dynamics of nonlinear wave equations as they provide explicit examples for finitetime blowup. This talk will be concerned with the focusing cubic and the quadratic wave equation, respectively, in dimensions where the models are energy supercritical. For both equations, we present new selfsimilar solutions with nontrivial profiles, which are completely explicit in all supercritical dimensions. Furthermore, we analyse their stability locally in backward light cones without symmetry assumptions. This involves a delicate spectral problem that we are able to solve rigorously only in particular space dimensions. In these cases, we prove that the solutions are codimension one stable modulo translations in a backward light cone of the blowup point. This is joint work with Irfan Glogić (Vienna) and Elek Csobo (Innsbruck).

11:30 am  12:15 pm ESTThe stability of charged black holes11th Floor Lecture Hall
 Virtual Speaker
 Elena Giorgi, Columbia University
Abstract
Black hole solutions in General Relativity are parametrized by their mass, spin and charge. In this talk, I will motivate why the charge of black holes adds interesting dynamics to solutions of the Einstein equation thanks to the interaction between gravitational and electromagnetic radiation. Such radiations are solutions of a system of coupled wave equations with a symmetric structure which allows to define a combined energymomentum tensor for the system. Finally, I will show how this physicalspace approach is resolutive in the most general case of KerrNewman black hole, where the interaction between the radiations prevents the separability in modes.

12:30  2:00 pm ESTLunch/Free Time

2:00  2:45 pm ESTInvariance of the Gibbs measures for the periodic generalized KdV equations11th Floor Lecture Hall
 Virtual Speaker
 Andreia Chapouto, UCLA
Abstract
In this talk, we consider the periodic generalized Kortewegde Vries equations (gKdV). In particular, we study gKdV with the Gibbs measure initial data. The main difficulty lies in constructing localintime dynamics in the support of the measure. Since gKdV is analytically illposed in the L2based Sobolev support, we instead prove deterministic local wellposedness in some FourierLebesgue spaces containing the support of the Gibbs measure. New key ingredients are bilinear and trilinear Strichartz estimates adapted to the FourierLebesgue setting. Once we construct localintime dynamics, we apply Bourgain's invariant measure argument to prove almost sure global wellposedness of the defocusing gKdV and invariance of the Gibbs measure. Our result completes the program initiated by Bourgain (1994) on the invariance of the Gibbs measures for periodic gKdV equations. This talk is based on joint work with Nobu Kishimoto (RIMS, University of Kyoto).

3:00  3:45 pm ESTTBD11th Floor Lecture Hall
 Sameer Iyer, UC Davis

4:00  4:30 pm ESTCoffee Break11th Floor Collaborative Space
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