Organizing Committee
 Diego Cordoba
ICMAT  Erwan Faou
INRIA Rennes  Patrick Gerard
ParisSud University, Orsay  Pierre Germain
NYU  Courant Institute  Alexandru Ionescu
Princeton University  Alex Kiselev
Duke University  Andrea Nahmod
University of Massachusetts Amherst  Kenji Nakanishi
Research Institute for Mathematical Sciences, Kyoto University  Benoit Pausader
Brown University  Themistoklis Sapsis
MIT  Gigliola Staffilani
Massachusetts Institute of Technology
Abstract
Dispersive equations are ubiquitous in nature. They govern the motion of waves in plasmas, ferromagnets, and elastic bodies, the propagation of light in optical fibers and of water in canals. They are relevant from the ocean scale down to atom condensates. There has been much recent progress in different directions, in particular in the exploration of the phase space of solutions of semilinear equations, advances towards a soliton resolution conjecture, the study of asymptotic stability of physical systems, the theoretical and numerical study of weak turbulence and transfer of energy in systems out of equilibrium, the introduction of tools from probability and the recent incorporation of computer assisted proofs. This semester aims to bring together these new developments and to explore their possible interconnection.
Dispersive phenomena appear in physical situations, where some energy is conserved, and are naturally related to Hamiltonian systems. This semester proposes to explore this link further by bringing together experimentalists, scientists, computational scientists and mathematicians with a common interest in exploring the various aspects of dispersive equations, from their analysis to their applications, and developing tools to facilitate experimentation. One key focus will be on global approaches, either in the sense of analyzing the overall landscape of the phase space, or in the study of generic solutions (e.g. of properties “almost surely true” in an appropriate sense). Another key focus will be experimental, in the sense of developing and analyzing instructive toymodels, implementing numerical experiments, and in some cases, simply of looking at interesting special cases.
The main events will be centered around three workshops
 one workshop on numerics, modeling and experiments in wave phenomena
 one workshop on generic behavior of dispersive solutions and wave turbulence
 one workshop on Hamiltonian methods and asymptotic dynamics
Confirmed Speakers & Participants
 Speaker
 Poster Presenter
 Attendee
 Virtual Attendee

Siddhant Agrawal
University of Massachusetts AmherstSep 7Oct 15, 2021

Yvonne Alama Bronsard
Sorbonne UniversitéSep 18Nov 2, 2021

Patricia Alonso Ruiz
Texas A&M UniversityOct 1531, 2021; Nov 29Dec 11, 2021

Ioakeim Ampatzoglou
Courant Institute of Mathematical Sciences, New York UniversityOct 1822, 2021

Xinliang An
National University of SingaporeSep 8Dec 10, 2021

Gerard Awanou
University of Illinois, ChicagoSep 2024, 2021

Aidan Backus
Brown UniversitySep 9Dec 10, 2021

ByeongHo Bahn
University of Massachusetts AmherstSep 8Dec 10, 2021

Hajer Bahouri
Université ParisEst  CréteilSep 8Dec 10, 2021

Valeria Banica
Sorbonne UniversitéSep 19Oct 4, 2021

Weizhu Bao
National University of SingaporeSep 8Dec 10, 2021

Marius Beceanu
University at Albany SUNYSep 13Dec 10, 2021

Jacob Bedrossian
University of MarylandOct 1822, 2021

Massimiliano Berti
SISSAOct 14Dec 10, 2021

Roberta Bianchini
Italian National Research Council, CNROct 18Nov 5, 2021

Anxo Biasi
Jagiellonian UniversityOct 1Dec 10, 2021

Lydia Bieri
University of MichiganSep 8Dec 10, 2021

Piotr Bizon
Jagiellonian UniversityDec 610, 2021

Bjoern Bringmann
Institute for Advanced StudyOct 17Dec 10, 2021

Nicolas Burq
University ParisSudOct 1822, 2021

Nicolas Camps
Université Paris SaclaySep 7Dec 10, 2021

Esteban Cardenas
University of Texas at AustinOct 1822, 2021

Amin Chabchoub
University of SydneySep 2024, 2021

Andreia Chapouto
University of EdinburghDec 610, 2021

Jehanzeb Chaudhary
University of New MexicoSep 7Dec 11, 2021

Gong Chen
Fields instituteSep 8Dec 8, 2021

Brian Choi
Southern Methodist UniversityDec 610, 2021

Charles Collot
CergyParis UniversitéOct 1822, 2021

Diego Cordoba
ICMATSep 8Dec 10, 2021

Stefan Czimek
Brown University (ICERM)Sep 8Dec 10, 2021

Magdalena Czubak
University of Colorado at BoulderSep 13Dec 10, 2021

Joel Dahne
Uppsala UniversitySep 8Dec 10, 2021

David Damanik
RICE UniversityDec 610, 2021

AnneSophie de Suzzoni
Ecole PolytechniqueOct 1822, 2021

Yu Deng
University of Southern CaliforniaSep 15Dec 15, 2021

Yu Deng
University of Southern CaliforniaOct 1822, 2021

Giuseppe Di Fazio
University of CataniaSep 9Dec 10, 2021

Benjamin Dodson
John Hopkins UniversityDec 610, 2021

Michele Dolce
Imperial College LondonSep 13Dec 10, 2021

Hongjie Dong
Brown UniversityOct 1822, 2021

Emmanuel Dormy
ENSSep 2024, 2021; Nov 1225, 2021

Jinqiao Duan
Illinois Institute of TechnologySep 13Dec 10, 2021

Sergey Dyachenko
University at BuffaloSep 2024, 2021

Daniel Eceizabarrena
University of Massachusetts AmherstSep 8Dec 10, 2021

Debbie Eeltink
MITSep 2024, 2021

Chenjie Fan
Academy of Mathematics and Systems Science, CASSep 8Dec 10, 2021

Allen Fang
Sorbonne UniversityDec 610, 2021

Erwan Faou
INRIA RennesSep 19Dec 10, 2021

Serena Federico
Ghent UniversityOct 16Nov 6, 2021

Patrick Flynn
BrownSep 8Dec 10, 2021

Luigi Forcella
HeriotWatt UniversityOct 1822, 2021

Gilles Francfort
Universite Paris 13Oct 47, 2021

Rupert Frank
LMU MunichDec 610, 2021

Irene Gamba
University of Texas at AustinSep 2024, 2021

Claudia García
Universitat de BarcelonaSep 8Dec 11, 2021

Eduardo GarciaJuarez
Universitat de BarcelonaSep 8Dec 11, 2021

Louise Gassot
Laboratoire de Mathématiques d'Orsay  Université ParisSaclaySep 1, 2021Mar 14, 2022

Patrick Gerard
ParisSud University, OrsaySep 15Nov 15, 2021

Pierre Germain
NYU  Courant InstituteSep 8Dec 10, 2021

Elena Giorgi
Princeton UniversityDec 610, 2021

Tainara Gobetti Borges
Brown UniversitySep 10Dec 10, 2021

Javier Gomez Serrano
Princeton UniversitySep 13Dec 10, 2021

Sigal Gottlieb
University of Massachusetts DartmouthSep 2024, 2021

Ricardo Grande Izquierdo
University of MichiganSep 8Dec 10, 2021

Benoît Grébert
University of NantesSep 8Dec 11, 2021

Sandrine Grellier
Université d'OrléansSep 13Dec 10, 2021

Marcel Guardia
Universitat Politècnica de CatalunyaOct 1822, 2021

Yan Guo
Brown UniversityDec 610, 2021

Zaher Hani
University of MichiganSep 18Dec 11, 2021

Amirali Hannani
CEREMADE, Université Paris Dauphine, PSLSep 8Dec 10, 2021

Benjamin HarropGriffiths
University of California, Los AngelesOct 1822, 2021

Susanna Haziot
Brown University MathematicsSep 8Dec 10, 2021

Siming He
Duke UniversityOct 1822, 2021

Sebastian Herr
Bielefeld UniversityDec 610, 2021

Justin Holmer
Brown UniversitySep 15Dec 10, 2021

Slim IBRAHIM
University of VictoriaSep 8Dec 10, 2021

Alexandru Ionescu
Princeton UniversitySep 8Dec 10, 2021

Sameer Iyer
Princeton UniversityDec 610, 2021

Olaniyi Iyiola
Clarkson UniversitySep 2024, 2021

Jonathan Jaquette
Boston UniversitySep 2024, 2021

Pranava Jayanti
University Of Maryland College ParkSep 2024, 2021; Oct 1822, 2021

Hao Jia
University of MinnesotaNov 14Dec 10, 2021

Istvan Kadar
University of CambridgeOct 1822, 2021

Adilbek Kairzhan
University of TorontoSep 8Dec 11, 2021

Thomas Kappeler
Universität ZürichSep 10Dec 10, 2021

George Karniadakis
Brown UniversitySep 2024, 2021

Dean Katsaros
UMass amherstSep 8Dec 10, 2021

Panayotis Kevrekidis
University of Massachusetts AmherstSep 8Dec 10, 2021

Alex Kiselev
Duke UniversitySep 8Dec 10, 2021

Friedrich Klaus
Karlsruhe Institute of TechnologyOct 1822, 2021

Haram Ko
Brown UniversitySep 10Dec 10, 2021

Herbert Koch
University of BonnSep 8Dec 10, 2021

Sudipta Kolay
ICERMSep 1, 2021May 31, 2022

Kristin Kurianski
California State University, FullertonSep 1925, 2021

Christophe Lacave
Universite Grenoble AlpesSep 2024, 2021

Thierry Laurens
University of California, Los AngelesDec 610, 2021

Gyu Eun Lee
University of EdinburghSep 2024, 2021; Oct 1822, 2021; Dec 610, 2021

Tristan Leger
Princeton UniversityOct 17Nov 13, 2021

Yao Li
University of Massachusetts AmherstSep 8Dec 10, 2021

Jichun Li
University of Nevada Las VegasSep 2024, 2021

Guopeng Li
University of EdinburghOct 1822, 2021

Felipe Linares
IMPAOct 1822, 2021

Kyle Liss
University of Maryland, College ParkSep 8Dec 15, 2021

Ruoyuan Liu
University of EdinburghOct 1822, 2021

Jonas Luhrmann
Texas A&M UniversityOct 1531, 2021; Nov 28Dec 11, 2021

Jani Lukkarinen
University of HelsinkiDec 411, 2021

Brad Marston
Brown UniversitySep 2024, 2021

Yvan Martel
École PolytechniqueDec 610, 2021

Jeremy Marzuola
University of North CarolinaSep 9Dec 10, 2021

Nader Masmoudi
Courant Institute of Mathematical Sciences at NYUSep 13Dec 10, 2021

Alberto Maspero
Scuola Internazionale Superiore di Studi Avanzati (SISSA)Oct 1822, 2021

Jonathan Mattingly
Duke UniversityOct 1822, 2021

Joseph Miller
University of Texas at AustinOct 17Dec 11, 2021

Peter Miller
University of MichiganDec 610, 2021

Jose Morales E.
UTSASep 2024, 2021

Adam Morgan
University of TorontoDec 610, 2021

Lin Mu
University of GeorgiaSep 8Dec 10, 2021

Jason Murphy
Missouri University of Science and TechnologySep 21Dec 10, 2021

Andrea Nahmod
University of Massachusetts AmherstSep 8Dec 10, 2021

Kenji Nakanishi
Research Institute for Mathematical Sciences, Kyoto UniversitySep 8Dec 10, 2021

Maria Ntekoume
Rice UniversityDec 610, 2021

Tadahiro Oh
The University of EdinburghDec 610, 2021

Miguel Onorato
Università di TorinoSep 2024, 2021

Ludivine Oruba
Sorbonne UniversiteSep 8Dec 10, 2021

José Palacios
Institut Denis Poisson, Université de ToursSep 8Dec 10, 2021

Yulin Pan
University of Michigan, Ann ArborSep 2024, 2021; Oct 1822, 2021

Jaemin Park
Universitat de BarcelonaSep 8Dec 10, 2021

Benoit Pausader
Brown UniversitySep 8Dec 10, 2021

Nataša Pavlovic
University of Texas at AustinOct 1822, 2021; Dec 610, 2021

Dmitry Pelinovsky
McMaster UniversityDec 610, 2021

Galina Perelman
LAMASep 8Dec 10, 2021

Thi Thao Phuong Hoang
Auburn UniversitySep 2024, 2021

Samuel PunshonSmith
Institute for Advanced StudyOct 1822, 2021

Fabio Pusateri
University of TorontoSep 8Dec 10, 2021

Raaghav Ramani
University of California, DavisSep 2024, 2021

Oscar Riano
Florida International UniversitySep 2024, 2021; Oct 1822, 2021

Tristan Robert
Université de LorraineOct 1822, 2021

Igor Rodnianski
Princeton UniversityDec 610, 2021

Casey Rodriguez
MITDec 610, 2021

Matthew Rosenzweig
Massachusetts Institute of TechnologySep 8Dec 10, 2021

Svetlana Roudenko
Florida International UniversityOct 1822, 2021; Dec 610, 2021

Frédéric Rousset
Département de Mathématiques d’OrsayOct 15Nov 15, 2021

Themistoklis Sapsis
MITSep 8Dec 10, 2021

Nancy Scherich
University of TorontoSep 1, 2021May 31, 2022

Wilhelm Schlag
Yale UniversityDec 610, 2021

Birgit Schoerkhuber
University of Innsbruck, AustriaDec 610, 2021

Katharina Schratz
HeriotWatt UniversitySep 2024, 2021

Diaraf Seck
University Cheikh Anta Diop of DakarSep 8Dec 10, 2021

Anastassiya Semenova
ICERM, Brown UniversitySep 1, 2021May 31, 2022

Chengyang Shao
Massachusetts Institute of TechnologySep 13Dec 10, 2021

Jalal Shatah
New York UniversityOct 1822, 2021

Jie Shen
Purdue UniversitySep 2024, 2021

Gigliola Staffilani
Massachusetts Institute of TechnologySep 8Dec 10, 2021

Annalaura Stingo
University of California DavisSep 8Dec 10, 2021

Walter Strauss
Brown UniversitySep 8Dec 10, 2021

Catherine Sulem
University of TorontoSep 8Dec 10, 2021

Chenmin Sun
CY CergyParis UniversitéSep 8Dec 10, 2021

changzhen Sun
University of ParisSaclaySep 9Dec 10, 2021

Ruoci Sun
Karlsruhe Institute of TechnologyOct 1822, 2021

Mouhamadou Sy
Imperial College LondonOct 1822, 2021

Tomoyuki Tanaka
Nagoya UniversityOct 1822, 2021

Maja Taskovic
Emory UniversitySep 9Dec 10, 2021

Daniel Tataru
University of California, BerkeleyDec 610, 2021

MinhBinh Tran
Southern Methodist UniversityOct 1822, 2021

Nikolay Tzvetkov
University of CergyPontoiseSep 8Dec 10, 2021

Tim Van Hoose
Missouri University of Science and TechnologyOct 1723, 2021

Luis Vega
Basque Center for Applied Mathematics (BCAM)Sep 17Dec 10, 2021

Paolo Ventura
SISSAOct 1822, 2021

Monica Visan
University of California, Los AngelesSep 2024, 2021; Oct 1822, 2021

Weinan Wang
University of ArizonaSep 8Dec 10, 2021

Li Wang
University of MinnesotaSep 2024, 2021

Hong Wang
Institute for Advanced Study (IAS)Dec 610, 2021

Xuecheng Wang
Tsinghua UniversitySep 8Dec 10, 2021

Billy Warner
University of Texas at AustinOct 1822, 2021

Klaus Widmayer
EPFL, SwitzerlandOct 12Nov 15, 2021

Jon Wilkening
University of California, BerkeleySep 2024, 2021

Bobby Wilson
University of WashingtonSep 2024, 2021

Bobby Wilson
University of WashingtonSep 8Dec 10, 2021

Sijue Wu
University of MichiganDec 610, 2021

Lei Wu
Lehigh UniversityOct 1822, 2021

Kai Yang
Florida International UniversitySep 2024, 2021

Jiaqi Yang
ICERMSep 1, 2021May 31, 2022

Zhuolun Yang
Brown UniversitySep 8Dec 10, 2021

Yao Yao
Georgia TechSep 2024, 2021

Lei Yu
Tongji UniversityOct 1822, 2021

Xueying Yu
University of WashingtonSep 8Dec 10, 2021

Haitian Yue
University of Southern CaliforniaSep 14Dec 10, 2021

Zhiyuan Zhang
New York UniversitySep 2024, 2021; Oct 1822, 2021; Dec 610, 2021

Chenyu Zhang
Brown UniversitySep 2024, 2021

Jiqiang Zheng
Institute of Applied Physics and Computational MathematicsDec 610, 2021

Guangqu Zheng
University of EdinburghOct 1822, 2021

SHIJUN ZHENG
Georgia Southern UniversitySep 2024, 2021; Oct 1822, 2021; Dec 610, 2021

Hui Zhu
University of MichiganOct 1822, 2021
Visit dates listed on the participant list may be tentative and subject to change without notice.
Semester Schedule
Wednesday, September 8, 2021
Hamiltonian Methods in Dispersive and Wave Evolution Equations

3:00  3:30 pm EDTCoffee Break11th Floor Collaborative Space
Thursday, September 9, 2021
Hamiltonian Methods in Dispersive and Wave Evolution Equations

9:00  10:30 am EDTLocal wellposedness for dispersive equationsTutorial  11th Floor Lecture Hall
 Alexandru Ionescu, Princeton University
 Benoit Pausader, Brown University
Abstract
This is a short introduction to the classical techniques for dispersive equations. We will present various equations and some methods to obtain local and global wellposedness and study the asymptotics.

11:00 am  12:30 pm EDTErgodicity of Markov processes: theory and computationTutorial  11th Floor Lecture Hall
 Yao Li, University of Massachusetts Amherst
Abstract
In this short course, I’ll cover the ergodicity of Markov processes on measurable state spaces. Both theoretical results and computational methods are based on the coupling technique. The following topics will be covered. 1, Markov process, transition kernel, and coupling. 2, Renewal theory with focusing on simultaneous renewal time. 3, Lyapunov criterion for geometric/polynomial ergodicity. 4, How to construct a Lyapunov function? 5, Numerical estimation of geometric/polynomial ergodicity. 6, Numerical estimation of invariant probability measure (if time permits).

1:30  2:00 pm EDTICERM WelcomeWelcome  11th Floor Lecture Hall
 Brendan Hassett, ICERM/Brown University

2:00  3:00 pm EDTGrad Student/ PostDoc IntroductionsIntroductions  11th Floor Lecture Hall
 Yvonne Alama Bronsard, Sorbonne Université
 Nicolas Camps, Université Paris Saclay
 Patrick Flynn, Brown
 Louise Gassot, Laboratoire de Mathématiques d'Orsay  Université ParisSaclay
 Dean Katsaros, UMass amherst
 Sudipta Kolay, ICERM
 Kyle Liss, University of Maryland, College Park
 Jaemin Park, Universitat de Barcelona
 Nancy Scherich, University of Toronto

3:00  3:30 pm EDTCoffee Break11th Floor Collaborative Space
Friday, September 10, 2021
Hamiltonian Methods in Dispersive and Wave Evolution Equations

9:00  10:30 am EDTLocal wellposedness for dispersive equationsTutorial  11th Floor Lecture Hall
 Alexandru Ionescu, Princeton University
 Benoit Pausader, Brown University
Abstract
This is a short introduction to the classical techniques for dispersive equations. We will present various equations and some methods to obtain local and global wellposedness and study the asymptotics.

11:00 am  12:30 pm EDTErgodicity of Markov processes: theory and computationTutorial  11th Floor Lecture Hall
 Yao Li, University of Massachusetts Amherst
Abstract
In this short course, I’ll cover the ergodicity of Markov processes on measurable state spaces. Both theoretical results and computational methods are based on the coupling technique. The following topics will be covered. 1, Markov process, transition kernel, and coupling. 2, Renewal theory with focusing on simultaneous renewal time. 3, Lyapunov criterion for geometric/polynomial ergodicity. 4, How to construct a Lyapunov function? 5, Numerical estimation of geometric/polynomial ergodicity. 6, Numerical estimation of invariant probability measure (if time permits).

2:00  3:30 pm EDTGrad Student/ PostDoc IntroductionsIntroductions  11th Floor Lecture Hall
 Bjoern Bringmann, Institute for Advanced Study
 Stefan Czimek, Brown University (ICERM)
 Daniel Eceizabarrena, University of Massachusetts Amherst
 Eduardo GarciaJuarez, Universitat de Barcelona
 Claudia García, Universitat de Barcelona
 Susanna Haziot, Brown University Mathematics
 Anastassiya Semenova, ICERM, Brown University
 Annalaura Stingo, University of California Davis
 Jiaqi Yang, ICERM
 Xueying Yu, University of Washington
 Haitian Yue, University of Southern California

3:00  3:30 pm EDTCoffee Break11th Floor Collaborative Space
Monday, September 13, 2021
Hamiltonian Methods in Dispersive and Wave Evolution Equations

9:00  10:30 am EDTComputerassisted proofs in PDEsTutorial  11th Floor Lecture Hall
 Javier Gomez Serrano, Princeton University
Abstract
In this minicourse we will present some recent results concerning computerassisted proofs in partial differential equations, starting from the basics of interval arithmetics. Particular emphasis will be put on the techniques, as opposed to the results themselves. There will be focus both on theory (lectures) and implementation (tutorial by Joel Dahne).

11:00 am  12:30 pm EDTErgodicity of Markov processes: theory and computationTutorial  11th Floor Lecture Hall
 Yao Li, University of Massachusetts Amherst
Abstract
In this short course, I’ll cover the ergodicity of Markov processes on measurable state spaces. Both theoretical results and computational methods are based on the coupling technique. The following topics will be covered. 1, Markov process, transition kernel, and coupling. 2, Renewal theory with focusing on simultaneous renewal time. 3, Lyapunov criterion for geometric/polynomial ergodicity. 4, How to construct a Lyapunov function? 5, Numerical estimation of geometric/polynomial ergodicity. 6, Numerical estimation of invariant probability measure (if time permits).

3:00  4:30 pm EDTWelcoming ReceptionReception  Hemenway's patio
Tuesday, September 14, 2021
Hamiltonian Methods in Dispersive and Wave Evolution Equations

9:00  10:30 am EDTLocal wellposedness for dispersive equationsTutorial  11th Floor Lecture Hall
 Alexandru Ionescu, Princeton University
 Benoit Pausader, Brown University
Abstract
This is a short introduction to the classical techniques for dispersive equations. We will present various equations and some methods to obtain local and global wellposedness and study the asymptotics.

11:00 am  12:30 pm EDTComputerassisted proofs in PDEsTutorial  11th Floor Lecture Hall
 Javier Gomez Serrano, Princeton University
Abstract
In this minicourse we will present some recent results concerning computerassisted proofs in partial differential equations, starting from the basics of interval arithmetics. Particular emphasis will be put on the techniques, as opposed to the results themselves. There will be focus both on theory (lectures) and implementation (tutorial by Joel Dahne).

3:00  3:30 pm EDTCoffee Break11th Floor Collaborative Space
Wednesday, September 15, 2021
Hamiltonian Methods in Dispersive and Wave Evolution Equations

9:00  10:30 am EDTLocal wellposedness for dispersive equationsTutorial  11th Floor Lecture Hall
 Alexandru Ionescu, Princeton University
 Benoit Pausader, Brown University
Abstract
This is a short introduction to the classical techniques for dispersive equations. We will present various equations and some methods to obtain local and global wellposedness and study the asymptotics.

11:00 am  12:30 pm EDTComputerassisted proofs in PDEsTutorial  11th Floor Lecture Hall
 Javier Gomez Serrano, Princeton University
Abstract
In this minicourse we will present some recent results concerning computerassisted proofs in partial differential equations, starting from the basics of interval arithmetics. Particular emphasis will be put on the techniques, as opposed to the results themselves. There will be focus both on theory (lectures) and implementation (tutorial by Joel Dahne).

3:00  3:30 pm EDTCoffee Break11th Floor Collaborative Space

3:15  4:15 pm EDTGrads/Postdocs Meet with ICERM Directorate11th Floor Lecture Hall
 Brendan Hassett, ICERM/Brown University
 Misha Kilmer, Tufts University
Thursday, September 16, 2021
Hamiltonian Methods in Dispersive and Wave Evolution Equations

3:00  3:30 pm EDTCoffee Break11th Floor Collaborative Space
Friday, September 17, 2021
Hamiltonian Methods in Dispersive and Wave Evolution Equations

9:00  10:30 am EDTLocal wellposedness for dispersive equationsTutorial  11th Floor Lecture Hall
 Alexandru Ionescu, Princeton University
 Benoit Pausader, Brown University
Abstract
This is a short introduction to the classical techniques for dispersive equations. We will present various equations and some methods to obtain local and global wellposedness and study the asymptotics.

11:00 am  12:30 pm EDTComputerassisted proofs in PDEsTutorial  11th Floor Lecture Hall
 Javier Gomez Serrano, Princeton University
Abstract
In this minicourse we will present some recent results concerning computerassisted proofs in partial differential equations, starting from the basics of interval arithmetics. Particular emphasis will be put on the techniques, as opposed to the results themselves. There will be focus both on theory (lectures) and implementation (tutorial by Joel Dahne).

3:00  3:30 pm EDTCoffee Break11th Floor Collaborative Space
Monday, September 20, 2021

9:50  10:00 am EDTWelcome11th Floor Lecture Hall
 Brendan Hassett, ICERM/Brown University

10:00  10:40 am EDTQuasilinear Diffusion of magnetized fast electrons in a mean field of quasiparticle waves packets11th Floor Lecture Hall
 Speaker
 Irene Gamba, University of Texas at Austin
 Session Chair
 Luis Vega, Basque Center for Applied Mathematics (BCAM)
Abstract
Quasilinear diffusion of magnetized fast electrons in momentum space results from stimulated emission and absorption of waves packets via waveparticle resonances. Such model consists in solving the dynamics of a system of classical kinetic diffusion processes described by the balance equations for electron probability density functions (electron pdf) coupled to the time dynamics waves (quasiparticles) in a quantum process of their resonant interaction. Such description results in a Mean Field model where diffusion coefficients are determined by the local spectral energy density of excited waves whose perturbations depend on flux averages of the electron pdf.
We will discuss the model and a mean field iteration scheme that simulates the dynamics of the space average model, where the energy spectrum of the excited wave time dynamics is calculated with a coefficient that depends on the electron pdf flux at a previous time step; while the time dynamics of the quasilinear model for the electron pdf is calculated by the spectral average of the quasiparticle wave under a classical resonant condition where the plasma wave frequencies couples the spectral energy to the momentum variable of the electron pdf. Recent numerical simulations will be presented showing a strong hot tail anisotropy formation and stabilization for the iteration in a 3 dimensional cylindrical model.
This is work in collaboration with Kun Huang, Michael Abdelmalik at UT Austin. 
10:55  11:15 am EDTCoffee Break11th Floor Collaborative Space

11:15 am  12:00 pm EDTModeling inviscid water waves11th Floor Lecture Hall
 Virtual Speaker
 Christophe Lacave, Universite Grenoble Alpes
 Session Chair
 Luis Vega, Basque Center for Applied Mathematics (BCAM)
Abstract
We consider numerical strategies to handle twodimensional water waves in a fully nonlinear regime. The freesurface is discretized via lagrangian tracers and the numerical strategy is constructed carefully to include desingularizations, but no artificial regularizations. We approach the formation of singularities in the wave breaking problem and also model solitary waves and the effect of an abruptly changing bottom. We present a rigorous analysis of the singular kernel operators involved in these methods.

12:15  1:15 pm EDTLunch/Free Time

1:15  1:55 pm EDTAnomalous conduction in one dimensional chains: a wave turbulence approach.11th Floor Lecture Hall
 Miguel Onorato, Università di Torino
Abstract
Heat conduction in 3D macroscopic solids is in general well described by the Fourier's law. However, low dimensional systems, like for example nanotubes, may be characterized by a conductivity that is sizedependent. This phenomena, known as anomalous conduction, has been widely studied in one dimensional chains like FPUT, mostly using deterministic simulations of the microscopic model. Here, I will present a mesoscopic approach based on the wave turbulence theory and give the evidence, through extensive numerical simulations and theoretical arguments, that the anomalous conduction is the result of the presence of long waves that rapidly propagate from one thermostat to the other without interacting with other modes. I will also show that the scaling of the conductivity with the length of the chain obtained from the mesoscopic approach is consistent with the one obtained from microscopic simulations.

2:10  2:50 pm EDTOn the asymptotic stability of shear flows and vortices11th Floor Lecture Hall
 Alexandru Ionescu, Princeton University
Abstract
I will talk about some recent work on the global linear and nonlinear asymptotic stability of two families of solutions of the 2D Euler equations: shear flows on bounded channels and vortices in the plane. This is joint work with Hao Jia.

3:00  4:30 pm EDTReceptionHemenway's Patio (weather permitting)
Tuesday, September 21, 2021

10:00  10:40 am EDTSmall scale formations in the incompressible porous media equation11th Floor Conference Room
 Virtual Speaker
 Yao Yao, Georgia Tech
Abstract
The incompressible porous media (IPM) equation describes the evolution of density transported by an incompressible velocity field given by Darcy’s law. Here the velocity field is related to the density via a singular integral operator, which is analogous to the 2D SQG equation. The question of global regularity vs finitetime blowup remains open for smooth initial data, although numerical evidence suggests that small scale formation can happen as time goes to infinity. In this talk, I will discuss rigorous examples of small scale formations in the IPM equation: we construct solutions to IPM that exhibit infiniteintime growth of Sobolev norms, provided that they remain globally smooth in time. As an application, this allows us to obtain nonlinear instability of certain stratified steady states of IPM. This is a joint work with Alexander Kiselev.

10:55  11:15 am EDTCoffee Break11th Floor Collaborative Space

11:15 am  12:00 pm EDTPINNs and DeepOnets for Wave Systems11th Floor Lecture Hall
 Virtual Speaker
 George Karniadakis, Brown University

12:15  1:45 pm EDTLunch/Free Time

1:45  2:25 pm EDTThe second boundary value problem for a discrete MongeAmpere equation11th Floor Conference Room
 Gerard Awanou, University of Illinois, Chicago
Abstract
In this work we propose a natural discretization of the second boundary condition for the MongeAmpere equation of geometric optics and optimal transport. It is the natural generalization of the popular OlikerPrussner method proposed in 1988. For the discretization of the differential operator, we use a discrete analogue of the subdifferential. Existence, unicity and stability of the solutions to the discrete problem are established. Convergence results to the continuous problem are given.

2:40  3:45 pm EDTLightning Talks11th Floor Lecture Hall

3:45  4:15 pm EDTCoffee Break11th Floor Collaborative Space
Wednesday, September 22, 2021

10:00  10:40 am EDTEfficient and accurate structure preserving schemes for complex nonlinear systems11th Floor Conference Room
 Jie Shen, Purdue University
Abstract
Many complex nonlinear systems have intrinsic structures such as energy dissipation or conservation, and/or positivity/maximum principle preserving. It is desirable, sometimes necessary, to preserve these structures in a numerical scheme. I will present some recent advances on using the scalar auxiliary variable (SAV) approach to develop highly efficient and accurate structure preserving schemes for a large class of complex nonlinear systems. These schemes can preserve energy dissipation/conservation as well as other global constraints and/or are positivity/bound preserving, only require solving decoupled linear equations with constant coefficients at each time step, and can achieve higherorder accuracy.

10:55  11:15 am EDTCoffee Break11th Floor Collaborative Space

11:15 am  12:00 pm EDTEnergy growth for the Schrödinger map and the binormal flow11th Floor Lecture Hall
 Valeria Banica, Sorbonne Université
Abstract
In this talk I shall present a result of blow up of a density energy associated to the Schrödinger map and the binormal flow, a classical model for the dynamics of vortex filaments in Euler equations. This is a joint work with Luis Vega.

12:15  1:45 pm EDTLunch/Free Time

1:45  2:25 pm EDTWater Waves with Background Flow over Obstacles and Topography11th Floor Lecture Hall
 Virtual Speaker
 Jon Wilkening, University of California, Berkeley
Abstract
We present two accurate and efficient algorithms for solving the incompressible, irrotational Euler equations with a free surface in two dimensions with background flow over a periodic, multiplyconnected fluid domain that includes stationary obstacles and variable bottom topography. One approach is formulated in terms of the surface velocity potential while the other evolves the vortex sheet strength. Both methods employ layer potentials in the form of periodized Cauchy integrals to compute the normal velocity of the free surface. We also propose a new algorithm to dynamically vary the spacing of gridpoints on the free surface to efficiently resolve regions of high curvature as they develop. We study singularity formation and capillary effects and compare our numerical results with lab experiments.

2:45  3:15 pm EDTCoffee Break11th Floor Collaborative Space

3:15  3:55 pm EDTTopological Origin of Certain Fluid and Plasma Waves11th Floor Lecture Hall
 Brad Marston, Brown University
Abstract
Symmetries and topology play central roles in our understanding of physical systems. Topology, for instance, explains the precise quantization of the Hall effect and the protection of surface states in topological insulators against scattering from disorder or bumps. However discrete symmetries and topology have so far played little role in thinking about the fluid dynamics of oceans and atmospheres. In this talk I show that, as a consequence of the rotation of the Earth that breaks time reversal symmetry, equatorially trapped Kelvin and Yanai waves emerge as topologically protected edge modes. The nontrivial structure of the bulk Poincare ́ waves encoded through the first Chern number of value 2 guarantees the existence of these waves. Thus the oceans and atmosphere of Earth naturally share basic physics with topological insulators. As equatorially trapped Kelvin waves in the Pacific ocean are an important component of El Niño Southern Oscillation and other climate oscillations, these new results demonstrate that topology plays a surprising role in Earth’s climate system. We also predict that waves of topological origin will arise in magnetized plasmas. A planned experiment at UCLA’s Basic Plasma Science Facility to look for the waves is described.
Thursday, September 23, 2021

10:00  10:40 am EDTResonances as a Computational Tool11th Floor Lecture Hall
 Katharina Schratz, HeriotWatt University

10:55  11:15 am EDTCoffee Break11th Floor Collaborative Space

11:15 am  12:00 pm EDTEfficient timestepping methods for the rotating shallow water equations11th Floor Lecture Hall
 Virtual Speaker
 Thi Thao Phuong Hoang, Auburn University
Abstract
Numerical modeling of geophysical flows is challenging due to the presence of various coupled processes that occur at different spatial and temporal scales. It is critical for the numerical schemes to capture such a wide range of scales in both space and time to produce accurate and robust simulations over long time horizons.
In this talk, we will discuss efficient timestepping methods for the rotating shallow water equations discretized on spatial meshes with variable resolutions. Two different approaches will be considered: the first approach is a fully explicit local timestepping algorithm based on the strong stability preserving RungeKutta schemes, which allows different time step sizes in different regions of the computational domain. The second approach, namely the localized exponential time differencing method, is based on spatial domain decomposition and exponential time integrators, which makes possible the use of much larger time step sizes compared to explicit schemes and avoids solving nonlinear systems. Numerical results on various test cases will be presented to demonstrate the performance of the proposed methods. 
12:15  1:45 pm EDTLunch/Free Time

1:45  2:25 pm EDTDynamics in particle suspension flow11th Floor Conference Room
 Li Wang, University of Minnesota
Abstract
In this talk, I will consider two set up of particle suspension flow. One is a gravity driven flow down an incline, and the other is a pressure driven flow in a HeleShaw cell. In the former case, the interesting phenomena is the formation of singular shock that appears in the high particle concentration case that relates to the particlerich ridge observed in the experiments. We analyze the formation of the singular shock as well as its local structure. In the latter case, we rationalize a selfsimilar accumulation of particles at the interface between suspension and air. Our results demonstrate that the combination of the shear induced migration, the advancing fluidfluid interface, and Taylor dispersion yield the selfsimilar and gradual accumulation of particles.

2:45  3:15 pm EDTCoffee Break11th Floor Collaborative Space

3:15  3:55 pm EDTSeparatrix crossing and symmetry breaking in NLSElike systems due to forcing and damping11th Floor Conference Room
 Debbie Eeltink, MIT
Abstract
The nonlinear Schrödinger equation (NLSE) is a workhorse for many different fields (e.g. optical fibers, BoseEinstein condensates, water waves). It describes the evolution of the envelope of a field in time or space, taking into account the nonlinear interaction of the components of the spectrum of the envelope. While the NLSE is wellstudied in its conservative form, a relevant question to ask is how does it respond to damping and forcing? Limiting the spectrum to only three components allows one to construct a phasespace for the NLSE, spanned by the relative phase of the sidebands, and the energy fraction in the sidebands. Using wavetank measurements, we show that forcing and damping the NLSE induces separatrix crossing: switching from one solutiontype to the other in the phasespace. Our experiments are performed on deep water waves, which are better described by the higherorder NLSE, the Dysthe equation. We, therefore, extend our threewave analysis to this system. However, our conclusions are general as the dynamics are driven by the leading order terms. To our knowledge, it is the first phase evolution extraction from waterwave measurements. Furthermore, we observe a growth and decay cycle for modulated plane waves that are conventionally considered stable. Finally, we give a theoretical demonstration that forcing the NLSE system can induce symmetry breaking during the evolution.
Friday, September 24, 2021
Hamiltonian Methods in Dispersive and Wave Evolution Equations

3:00  3:30 pm EDTCoffee Break11th Floor Collaborative Space

10:00  10:40 am EDTExtreme Wave Events in Reflective Environments11th Floor Lecture Hall
 Amin Chabchoub, University of Sydney
Abstract
Waves dynamics in coastal zones is known to comprise incident and reflective wave motion. We report an experimental study in which several incident JONSWAP wave trains have been generated in a unidirectional water wave tank while the artificial beach inclination and its permeability have been varied to allow a variety of reflective wave conditions. Key statistical features obtained from an adaptive coupled nonlinear Schrödinger model simulations show an excellent agreement with the laboratory data collected near the beach.

10:55  11:15 am EDTCoffee Break11th Floor Collaborative Space

11:15  11:55 am EDTSymmetry in stationary and uniformly rotating solutions of the Euler equations11th Floor Lecture Hall
 Javier Gomez Serrano, Princeton University

12:10  12:50 pm EDTHigh order strong stability preserving multiderivative implicit and IMEX RungeKutta methods with asymptotic preserving properties11th Floor Lecture Hall
 Sigal Gottlieb, University of Massachusetts Dartmouth
Abstract
In this talk we present a class of high order unconditionally strong stability preserving (SSP) implicit twoderivative RungeKutta schemes, and SSP implicitexplicit (IMEX) multiderivative RungeKutta schemes where the timestep restriction is independent of the stiff term. The unconditional SSP property for a method of order $p>2$ is unique among SSP methods, and depends on a backwardintime assumption on the derivative of the operator. We show that this backward derivative condition is satisfied in many relevant cases where SSP IMEX schemes are desired. We devise unconditionally SSP implicit RungeKutta schemes of order up to $p=4$, and IMEX RungeKutta schemes of order up to $p=3$. For the multiderivative IMEX schemes, we also derive and present the order conditions, which have not appeared previously. The unconditional SSP condition ensures that these methods are positivity preserving, and we present sufficient conditions under which such methods are also asymptotic preserving when applied to a range of problems, including a hyperbolic relaxation system, the Broadwell model, and the BhatnagarGrossKrook (BGK) kinetic equation.
Monday, September 27, 2021
Hamiltonian Methods in Dispersive and Wave Evolution Equations

3:00  3:30 pm EDTCoffee Break11th Floor Collaborative Space
Tuesday, September 28, 2021
Hamiltonian Methods in Dispersive and Wave Evolution Equations

10:00  11:00 am EDTRIEMANN’S NONDIFFERENTIABLE FUNCTION AND THE BINORMAL CURVATURE FLOW (Joint work with Valeria Banica)11th Floor Lecture Hall
 Luis Vega, Basque Center for Applied Mathematics (BCAM)
Abstract
We make a connection between a famous analytical object introduced in the 1860s by Riemann, as well as some variants of it, and a nonlinear geometric PDE, the binormal curvature flow. As a consequence this analytical object has a nonobvious non linear geometric interpretation. We recall that the binormal flow is a standard model for the evolution of vortex filaments. We prove the existence of solutions of the binormal flow with smooth trajectories that are as close as desired to curves with a multifractal behavior. Finally, we show that this behavior falls within the multifractal formalism of Frisch and Parisi, which is conjectured to govern turbulent fluids.

11:30 am  12:30 pm EDTALMOSTGLOBAL WELLPOSEDNESS FOR 2D STRONGLYCOUPLED WAVEKLEINGORDON SYSTEMS11th Floor Lecture Hall
 Annalaura Stingo, University of California Davis
Abstract
(Joint with Mihaela Ifrim) In this talk we discuss the almostglobal wellposedness of a wide class of coupled WaveKleinGordon equations in 2+1 spacetime dimensions, when initial data are small and localized. The WaveKleinGordon systems arise from several physical models especially related to General Relativity but few results are known at present in lower spacetime dimensions. Compared with prior related results, we here consider a strong quadratic quasilinear coupling between the wave and the KleinGordon equation and no restriction is made on the support of the initial data which only have a mild decay at infinity and very limited regularity.

2:30  3:00 pm EDTCoffee Break11th Floor Collaborative Space

3:00  4:00 pm EDTSemilinear Dispersive Equations11th Floor Lecture Hall
 Alexandru Ionescu, Princeton University
 Benoit Pausader, Brown University
Wednesday, September 29, 2021
Hamiltonian Methods in Dispersive and Wave Evolution Equations

11:30 am  12:15 pm EDTGender Diversity and the Mathematical Community11th Floor Lecture Hall
 Andrea Nahmod, University of Massachusetts Amherst
 Gigliola Staffilani, Massachusetts Institute of Technology
Abstract
Followed by a “brownbag lunch” (provided by ICERM) to be taken outside, where the discussion is expected to continue among smaller groups. RSVP required.

3:00  3:30 pm EDTCoffee Break11th Floor Collaborative Space
Thursday, September 30, 2021
Hamiltonian Methods in Dispersive and Wave Evolution Equations

11:00 am  12:30 pm EDTPost Doc/Graduate Student SeminarPost Doc/Graduate Student Seminar  11th Floor Lecture Hall
 Daniel Eceizabarrena, University of Massachusetts Amherst
 Claudia García, Universitat de Barcelona
 Haitian Yue, University of Southern California

3:00  3:30 pm EDTCoffee Break11th Floor Collaborative Space
Friday, October 1, 2021
Hamiltonian Methods in Dispersive and Wave Evolution Equations

3:00  3:30 pm EDTCoffee Break11th Floor Collaborative Space
Monday, October 4, 2021
Hamiltonian Methods in Dispersive and Wave Evolution Equations

3:00  3:30 pm EDTCoffee Break11th Floor Collaborative Space
Tuesday, October 5, 2021
Hamiltonian Methods in Dispersive and Wave Evolution Equations

10:00  11:00 am EDTThe characteristic gluing problem of general relativity11th Floor Lecture Hall
 Stefan Czimek, Brown University (ICERM)
Abstract
In this talk we introduce and solve the characteristic gluing problem for the Einstein vacuum equations. We show that obstructions to characteristic gluing come from an infinitedimensional space of conservation laws along null hypersurfaces for the linearized equations at Minkowski. We prove that this space splits into an infinitedimensional space of gaugedependent charges and a 10dimensional space of gaugeinvariant charges. We identify the 10 gaugeinvariant charges to be related to the energy, linear momentum, angular momentum and centerofmass of the spacetime. Based on this identification, we explain how to characteristically glue a given spacetime to a suitably chosen Kerr spacetime. As corollary we get an alternative proof of the CorvinoSchoen spacelike gluing to Kerr. Moreover, we apply our characteristic gluing method to localise characteristic initial data along null hypersurfaces. In particular, this yields a new proof of the CarlottoSchoen spacelike localization where our method yields no loss of decay, thus resolving an open problem. We also outline further applications. This is joint work with S. Aretakis (Toronto) and I. Rodnianski (Princeton).

11:30 am  12:30 pm EDTThe role of hyperbolicity in deciding uniqueness for minimizers of an energy with linear growth11th Floor Lecture Hall
 Gilles Francfort, Universite Paris 13

3:00  3:30 pm EDTCoffee Break11th Floor Collaborative Space
Wednesday, October 6, 2021
Hamiltonian Methods in Dispersive and Wave Evolution Equations

9:00  10:00 am EDTProfessional Development: Ethics IProfessional Development  11th Floor Lecture Hall

3:00  3:30 pm EDTCoffee Break11th Floor Collaborative Space
Thursday, October 7, 2021
Hamiltonian Methods in Dispersive and Wave Evolution Equations

11:00 am  12:30 pm EDTPost Doc/Graduate Student SeminarPost Doc/Graduate Student Seminar  11th Floor Lecture Hall

2:00  4:00 pm EDTProbabilistic wellposedness for nonlinear Schrödinger equation (I)11th Floor Lecture Hall
 Haitian Yue, University of Southern California
Abstract
In this minicourse, we will introduce the probabilistic wellposedness theory in the background of the nonlinear Schrödinger equation and in particular will focus on local (in time) dynamics with the random initial data. The following topics will be covered: 1) the basic settings of random data Cauchy theory; 2) Bourgain's recentering method; 3) the random averaging operator method.

3:00  3:30 pm EDTCoffee Break11th Floor Collaborative Space
Friday, October 8, 2021
Hamiltonian Methods in Dispersive and Wave Evolution Equations

1:30  3:00 pm EDTProbabilistic wellposedness for nonlinear Schrödinger equation (I)11th Floor Lecture Hall
 Haitian Yue, University of Southern California
Abstract
In this minicourse, we will introduce the probabilistic wellposedness theory in the background of the nonlinear Schrödinger equation and in particular will focus on local (in time) dynamics with the random initial data. The following topics will be covered: 1) the basic settings of random data Cauchy theory; 2) Bourgain's recentering method; 3) the random averaging operator method.

3:00  3:30 pm EDTCoffee Break11th Floor Collaborative Space
Tuesday, October 12, 2021
Hamiltonian Methods in Dispersive and Wave Evolution Equations

10:00  11:00 am EDTSuperharmonic Instability of Stokes Waves11th Floor Lecture Hall
 Anastassiya Semenova, ICERM, Brown University
Abstract
We consider the classical problem of water waves on the surface of an ideal fluid in 2D. This work offers an investigation of dynamics and stability of nonlinear waves. We provide new insight into the stability of the Stokes waves by identifying previously inaccessible branches of instability in the equations of motion for fluid. The eigenvalues of the linearized problem that become unstable follow a selfsimilar law as they approach instability threshold, and a power law is suggested for unstable eigenvalues in the immediate vicinity of the limiting wave. Future direction of work is to study superharmonic instability of Stokes waves in finite depth.

11:30 am  12:30 pm EDTRevisit singularity formation for the inviscid primitive equation11th Floor Lecture Hall
 Slim IBRAHIM, University of Victoria
Abstract
The primitive equation is an important model for large scale fluid model including oceans and atmosphere. While solutions to the viscous model enjoy global regularity, inviscid solutions may develop singularities in finite time. In this talk, I will review the methods to show blowup, and share more recent progress on qualitative properties of the singularity formation.

2:00  4:30 pm EDTProbabilistic wellposedness for nonlinear Schrödinger equation (II)11th Floor Lecture Hall
 Yu Deng, University of Southern California

3:00  3:30 pm EDTCoffee Break11th Floor Collaborative Space
Wednesday, October 13, 2021
Hamiltonian Methods in Dispersive and Wave Evolution Equations

9:00  10:00 am EDTProfessional Development: Ethics IIProfessional Development  11th Floor Lecture Hall

2:00  4:30 pm EDTProbabilistic wellposedness for nonlinear Schrödinger equation (II)11th Floor Lecture Hall
 Yu Deng, University of Southern California

3:00  3:30 pm EDTCoffee Break11th Floor Collaborative Space
Thursday, October 14, 2021
Hamiltonian Methods in Dispersive and Wave Evolution Equations

11:00 am  12:30 pm EDTPost Doc/Graduate Student SeminarPost Doc/Graduate Student Seminar  11th Floor Lecture Hall

3:00  3:30 pm EDTCoffee Break11th Floor Collaborative Space
Friday, October 15, 2021
Hamiltonian Methods in Dispersive and Wave Evolution Equations

3:00  3:30 pm EDTCoffee Break11th Floor Collaborative Space
Monday, October 18, 2021

8:45  9:00 am EDTWelcome11th Floor Lecture Hall
 Brendan Hassett, ICERM/Brown University

9:00  9:50 am EDTMicrolocal analysis of singular measures11th Floor Lecture Hall
 Virtual Speaker
 Nicolas Burq, University ParisSud

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

10:30  11:20 am EDTFull description of BenjaminFeir instability of Stokes waves in deep water11th Floor Lecture Hall
 Virtual Speaker
 Alberto Maspero, Scuola Internazionale Superiore di Studi Avanzati (SISSA)
Abstract
Smallamplitude, traveling, space periodic solutions  called Stokes waves  of the 2 dimensional gravity water waves equations in deep water are linearly unstable with respect to longwave perturbations, as predicted by Benjamin and Feir in 1967. We completely describe the behavior of the four eigenvalues close to zero of the linearized equations at the Stokes wave, as the Floquet exponent is turned on. We prove in particular the conjecture that a pair of nonpurely imaginary eigenvalues depicts a closed figure eight, parameterized by the Floquet exponent, in full agreement with numerical simulations. This is a joint work with M. Berti and P. Ventura.

11:30 am  1:00 pm EDTLunch/Free Time

1:00  1:50 pm EDTBreakdown of small amplitude breathers for the nonlinear KleinGordon equation11th Floor Lecture Hall
 Virtual Speaker
 Marcel Guardia, Universitat Politècnica de Catalunya
Abstract
Breathers are temporally periodic and spatially localized solutions of evolutionary PDEs. They are known to exist for integrable PDEs such as the sineGordon equation, but are believed to be rare for general nonlinear PDEs. When the spatial dimension is equal to one, exchanging the roles of time and space variables (in the socalled spatial dynamics framework), breathers can be interpreted as homoclinic solutions to steady solutions and thus arise from the intersections of the stable and unstable manifolds of the steady states. In this talk, we shall study the nonlinear KleinGordon equation and show that small amplitude breathers cannot exist (under certain conditions). We also construct generalized breathers, these are solutions which are periodic in time and in space are localized up to exponentially small (with respect to the amplitude) tails. This is a joint work with O. Gomide, T. Seara and C. Zeng.

2:00  2:50 pm EDTFluctuations of \deltamoments for the free Schrödinger Equation11th Floor Lecture Hall
 Luis Vega, Basque Center for Applied Mathematics (BCAM)
Abstract
I will present recent work done with S. Kumar and F.PonceVanegas.
We study the process of dispersion of lowregularity solutions to the free Schrödinger equation using fractional weights. We give another proof of the uncertainty principle for fractional weights and use it to get a lower bound for the concentration of mass. We consider also the evolution when the initial datum is the Dirac comb in R. In this case we find fluctuations that concentrate at rational times and that resemble a realization of a Lévy process. Furthermore, the evolution exhibits multifractality. 
3:00  4:30 pm EDTWelcome ReceptionReception  Hemenway's Patio
Tuesday, October 19, 2021

9:00  9:50 am EDTMathematical wave turbulence and propagation of chaos (I)11th Floor Lecture Hall
 Yu Deng, University of Southern California
Abstract
The theory of wave turbulence can be traced back to the 1920s and has played significant roles in many different areas of physics. However, for a long time the mathematical foundation of the theory has not been established. The central topics here are the wave kinetic equation, which describes the thermodynamic limit of interacting wave systems, and the propagation of chaos, which is a fundamental physical assumption in this field that lacks mathematical justification. In this first talk, I will present recent results with Zaher Hani (University of Michigan), where we provide the first rigorous derivation of the wave kinetic equation, and also justify the propagation of chaos assumption in the same setting. In part (II), we will discuss some important ideas in the proof.

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

10:30  11:20 am EDTMathematical wave turbulence and propagation of chaos (II)11th Floor Lecture Hall
 Zaher Hani, University of Michigan
Abstract
The theory of wave turbulence can be traced back to the 1920s and has played significant roles in many different areas of physics. However, for a long time the mathematical foundation of the theory has not been established. The central topics here are the wave kinetic equation, which describes the thermodynamic limit of interacting wave systems, and the propagation of chaos, which is a fundamental physical assumption in this field that lacks mathematical justification. This talk is a continuation of that of Yu Deng (University of Southern California) who will present our recent joint results that provide the first rigorous derivation of the wave kinetic equation, and also justify the propagation of chaos assumption in the same setting. In this second part, we will discuss some important ideas in the proof.

11:30 am  1:00 pm EDTLunch/Free Time

1:00  1:50 pm EDTEnergy transfer for solutions to the nonlinear Schrodinger equation on irrational tori.11th Floor Lecture Hall
 Gigliola Staffilani, Massachusetts Institute of Technology
Abstract
We analyze the energy transfer for solutions to the defocusing cubic nonlinear Schr\"odinger (NLS) initial value problem on 2D irrational tori. Moreover we complement the analytic study with numerical experimentation. As a biproduct of our investigation we also prove that the quasiresonant part of the NLS initial value problem we consider, in both the focusing and defocusing case, is globally wellposed for initial data of finite mass.

2:00  2:50 pm EDTDeterminants, commuting flows, and recent progress on completely integrable systems11th Floor Lecture Hall
 Virtual Speaker
 Monica Visan, University of California, Los Angeles
Abstract
We will survey a number of recent developments in the theory of completely integrable nonlinear dispersive PDE. These include a priori bounds, the orbital stability of multisolitons, wellposedness at optimal regularity, and the existence of dynamics for Gibbs distributed initial data. I will describe the basic objects that tie together these disparate results, as well as the diverse ideas required for each problem.

3:10  4:00 pm EDTLightning Talks11th Floor Lecture Hall

4:00  4:30 pm EDTCoffee Break11th Floor Collaborative Space
Wednesday, October 20, 2021

9:00  9:50 am EDTOn the derivation of the Kinetic Wave Equation in the inhomogeneous setting11th Floor Lecture Hall
 Virtual Speaker
 Charles Collot, CergyParis Université
Abstract
The kinetic wave equation arises in weak wave turbulence theory. In this talk we are interested in its derivation as an effective equation from dispersive waves modelled with quadratic nonlinear Schrodinger equations. We focus on the spaceinhomogeneous case, which had not been treated earlier. More precisely, we will consider such a dispersive equations in a weakly nonlinear regime, and for highly oscillatory random Gaussian fields with localised enveloppes as initial data. A conjecture in statistical physics is that there exists a kinetic time scale on which, statistically, the Wigner transform of the solution (a space dependent local Fourier energy spectrum) evolve according to the kinetic wave equation.
I will present a joint work with Ioakeim Ampatzoglou and Pierre Germain (Courant Institute) in which we approach the problem of the validity of this kinetic wave equation through the convergence and stability of the corresponding Dyson series. We are able to identify certain nonlinearities, dispersion relations, and regimes, and for which the convergence indeed holds almost up to the kinetic time (arbitrarily small polynomial loss). 
10:00  10:30 am EDTCoffee Break11th Floor Collaborative Space

10:30  11:20 am EDT3 Problems in Wave Turbulence11th Floor Lecture Hall
 Jalal Shatah, New York University

11:30  11:40 am EDTGroup Photo11th Floor Lecture Hall

11:40 am  1:00 pm EDTLunch/Free Time

1:00  1:50 pm EDTConstructing global solutions for energy supercritical NLS equations11th Floor Lecture Hall
 Virtual Speaker
 Mouhamadou Sy, Imperial College London
Abstract
The last decades were very fruitful for the realm of dispersive PDEs. Besides several new deterministic developments in the study of the initial value problem and the behavior of solutions, probabilistic methods were introduced and made important progresses, particularly on bounded domain settings. Invariant measure are of considerable interest in these questions. However, in the context of energy supercritical equations, both the wellknown Gibbs measures based strategy and the standard fluctuationdissipation approach come across serious limitations. In this talk, we will present a new approach that combines the aforementioned ones to construct invariant measures, almost sure GWP, and strong controls on the time evolution of the solutions for the periodic NLS, with arbitrarily large power of nonlinearity and in any dimension. We will discuss the application to other contexts including nondispersive PDEs.

2:00  2:30 pm EDTCoffee Break11th Floor Collaborative Space

2:30  3:20 pm EDTInvariant Gibbs measures for NLS and Hartree equations11th Floor Lecture Hall
 Haitian Yue, University of Southern California
Abstract
In this talk, I'll present our results about invariant Gibbs measures for the periodic nonlinear Schrödinger equation (NLS) in 2D, for any (defocusing and renormalized) odd power nonlinearity and for the periodic Hartree equation in 3D. The results are achieved by introducing a new method (we call the random averaging operators method) which precisely captures the intrinsic randomness structure of the problematic highlow frequency interactions at the heart of this problem. This is work with Yu Deng (USC) and Andrea Nahmod (UMass Amherst).
Thursday, October 21, 2021

9:00  9:50 am EDTSingularities in the weak turbulence regime11th Floor Lecture Hall
 Virtual Speaker
 AnneSophie de Suzzoni, Ecole Polytechnique
Abstract
In this talk, we discuss the different regimes for the derivation of kinetic equations from the theory of weak turbulence for the quintic Schrödinger equation. In particular, we see that there exists a specific regime such that the correlations of the Fourier coefficients of the solution of the Schrödinger equation converge (in this regime) to a function that has an inifinite number of discontinuities.

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

10:30  11:20 am EDTA New model for the stochasticly perturbed 2d navierstokes equations11th Floor Lecture Hall
 Jonathan Mattingly, Duke University
Abstract
I will introduce a new model of the stochastically forced navierstokes equation. The model will be targeted at studying the Equations forced by a large scale forcing. I give a number of properties of the model.

11:30 am  1:00 pm EDTLunch/Free Time

1:00  1:50 pm EDTGlobal wellposedness for the fractional NLS on the unit disk11th Floor Lecture Hall
 Xueying Yu, University of Washington
Abstract
In this talk, we discuss the cubic nonlinear Schr\"odinger equation with the fractional Laplacian on the unit disk. We show the global wellposedness for certain radial initial data below the energy space and establish a polynomial bound of the global solution. The result is proved by extending the Imethod in the fractional nonlinear Schr\"odinger equation setting.

2:00  2:30 pm EDTCoffee Break11th Floor Collaborative Space

2:30  3:20 pm EDTThe wave maps equation and Brownian paths11th Floor Lecture Hall
 Bjoern Bringmann, Institute for Advanced Study
Abstract
We discuss the $(1+1)$dimensional wave maps equation with values in a compact Riemannian manifold $\mathcal{M}$. Motivated by the Gibbs measure problem, we consider Brownian paths on the manifold $\mathcal{M}$ as initial data. Our main theorem is the probabilistic local wellposedness of the associated initial value problem. The analysis in this setting involves analytic, geometric, and probabilistic aspects. This is joint work with J. Lührmann and G. Staffilani.
Friday, October 22, 2021

9:00  9:50 am EDTPositive Lyapunov exponents for the GalerkinNavierStokes equations with stochastic forcing11th Floor Lecture Hall
 Jacob Bedrossian, University of Maryland
Abstract
In this talk we discuss our recently introduced methods for obtaining strictly positive lower bounds on the top Lyapunov exponent of highdimensional, stochastic differential equations such as the weaklydamped Lorenz96 (L96) model or Galerkin truncations of the 2d NavierStokes equations (joint with Alex Blumenthal and Sam PunshonSmith). This hallmark of chaos has long been observed in these models, however, no mathematical proof had previously been made for any type of deterministic or stochastic forcing. The method we proposed combines (A) a new identity connecting the Lyapunov exponents to a Fisher information of the stationary measure of the Markov process tracking tangent directions (the socalled "projective process"); and (B) an L1based hypoelliptic regularity estimate to show that this (degenerate) Fisher information is an upper bound on some fractional regularity. For L96 and GNSE, we then further reduce the lower bound of the top Lyapunov exponent to proving that the projective process satisfies Hörmander's condition. I will also discuss the recent work of Sam PunshonSmith and I on verifying this condition for the 2d GalerkinNavierStokes equations in a rectangular, periodic box of any aspect ratio using some special structure of matrix Lie algebras and ideas from computational algebraic geometry.

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

10:30  11:20 am EDTA tale of two generalizations of Boltzmann equation11th Floor Lecture Hall
 Nataša Pavlovic, University of Texas at Austin
Abstract
In the first part of the talk we shall discuss dynamics of systems of particles that allow interactions beyond binary, and their behavior as the number of particles goes to infinity. This part of the talk is based on the joint work with Ampatzoglou on a derivation of a binaryternary Boltzmann equation describing the kinetic properties of a dense hard spheres gas, where particles undergo either binary or ternary instantaneous interactions, while preserving momentum and energy. An important challenge we overcome in deriving this equation is related to providing a mathematical framework that allows us to detect both binary and ternary interactions. In the second part of the talk we will discuss a rigorous derivation of a Boltzmann equation for mixtures of gases, which is a recent joint work with Ampatzoglou and Miller. We prove that the microscopic dynamics of two gases with different masses and diameters is well defined, and introduce the concept of a two parameter BBGKY hierarchy to handle the nonsymmetric interaction of these gases.

11:30 am  12:20 pm EDTSome Recent Results On Wave Turbulence: Derivation, Analysis, Numerics and Physical Application11th Floor Lecture Hall
 MinhBinh Tran, Southern Methodist University
Abstract
Wave turbulence describes the dynamics of both classical and nonclassical nonlinear waves out of thermal equilibrium. In this talk, we will discuss some of our recent results on some aspects of wave turbulence, concerning the derivation and analysis of wave kinetic equations, some numerical algorithms and physical applications in BoseEinstein Condensates.
Monday, October 25, 2021
Hamiltonian Methods in Dispersive and Wave Evolution Equations

3:00  3:30 pm EDTCoffee Break11th Floor Collaborative Space
Tuesday, October 26, 2021
Hamiltonian Methods in Dispersive and Wave Evolution Equations

10:00  11:00 am EDTWeak universality for the fractional \Phi_2^4 under the wave dynamics11th Floor Lecture Hall
 Chenmin Sun, CY CergyParis Université
Abstract
Parabolic \Phi^4 models, given by singular stochastic heat equation are believed to be the scaling limit for some physical relevant models. This motivated many recent results in the field of singular SPDE. In the context of dispersive equations, it is also of interest to investigate the limit of certain dispersive \Phi^4 models perturbed by higherorder potentials with correct scalings. In this talk, we consider the weak universality of the twodimensional fractional nonlinear wave equation. For a sequence of Hamiltonians of highdegree potentials scaling to the fractional \Phi_2^4, we first establish a sufficient and almost necessary criteria for the convergence of invariant measures to the fractional \Phi_2^4. Then we prove the convergence result for the sequence of associated wave dynamics to the (renormalized) cubic wave equation. The main difficulty is that we do not have a good local Cauchytheory for the highly supercritical nonlinearities. To prove the dynamical convergence, we rely on probabilistic ideas exploiting independence of different scales of frequencies. This is a joint work with Nikolay Tzvetkov and Weijun Xu.

11:30 am  12:30 pm EDTGlobal axisymmetric Euler flows with rotation11th Floor Lecture Hall
 Klaus Widmayer, EPFL, Switzerland
Abstract
We discuss the construction of a class of global, dynamical solutions to the 3d Euler equations near the stationary state given by uniform "rigid body" rotation. These solutions are axisymmetric, of Sobolev regularity and have nonvanishing swirl. At the heart of this result is the dispersive effect due to rotation, which is captured in our new "method of partial symmetries". This approach is adapted to maximally exploit the symmetries of this anisotropic problem, both for the linear and nonlinear analysis, and allows to globally propagate sharp decay estimates. This is joint work with Y. Guo and B. Pausader.

3:00  3:30 pm EDTCoffee Break11th Floor Collaborative Space
Wednesday, October 27, 2021
Hamiltonian Methods in Dispersive and Wave Evolution Equations

9:00  10:00 am EDTProfessional Development: Job Applications in AcademiaProfessional Development  11th Floor Lecture Hall

3:00  3:30 pm EDTCoffee Break11th Floor Collaborative Space
Thursday, October 28, 2021
Hamiltonian Methods in Dispersive and Wave Evolution Equations

11:00 am  12:30 pm EDTPost Doc/Graduate Student SeminarPost Doc/Graduate Student Seminar  11th Floor Lecture Hall

3:00  3:30 pm EDTCoffee Break11th Floor Collaborative Space
Friday, October 29, 2021
Hamiltonian Methods in Dispersive and Wave Evolution Equations

3:00  3:30 pm EDTCoffee Break11th Floor Collaborative Space
Monday, November 1, 2021
Hamiltonian Methods in Dispersive and Wave Evolution Equations

3:00  3:30 pm EDTCoffee Break11th Floor Collaborative Space
Tuesday, November 2, 2021
Hamiltonian Methods in Dispersive and Wave Evolution Equations

3:00  3:30 pm EDTCoffee Break11th Floor Collaborative Space
Wednesday, November 3, 2021
Hamiltonian Methods in Dispersive and Wave Evolution Equations

9:00  10:00 am EDTProfessional Development: Hiring ProcessProfessional Development  11th Floor Lecture Hall

3:00  3:30 pm EDTCoffee Break11th Floor Collaborative Space
Thursday, November 4, 2021
Hamiltonian Methods in Dispersive and Wave Evolution Equations

11:00 am  12:30 pm EDTPost Doc/Graduate Student SeminarPost Doc/Graduate Student Seminar  11th Floor Lecture Hall

3:00  3:30 pm EDTCoffee Break11th Floor Collaborative Space
Friday, November 5, 2021
Hamiltonian Methods in Dispersive and Wave Evolution Equations

3:00  3:30 pm EDTCoffee Break11th Floor Collaborative Space
Monday, November 8, 2021
Hamiltonian Methods in Dispersive and Wave Evolution Equations

3:00  3:30 pm ESTCoffee Break11th Floor Collaborative Space
Tuesday, November 9, 2021
Hamiltonian Methods in Dispersive and Wave Evolution Equations

3:00  3:30 pm ESTCoffee Break11th Floor Collaborative Space
Wednesday, November 10, 2021
Hamiltonian Methods in Dispersive and Wave Evolution Equations

9:00  10:00 am ESTProfessional Development: Papers and JournalsProfessional Development  11th Floor Lecture Hall

3:00  3:30 pm ESTCoffee Break11th Floor Collaborative Space
Thursday, November 11, 2021
Hamiltonian Methods in Dispersive and Wave Evolution Equations

11:00 am  12:30 pm ESTPost Doc/Graduate Student SeminarPost Doc/Graduate Student Seminar  11th Floor Lecture Hall

3:00  3:30 pm ESTCoffee Break11th Floor Collaborative Space
Friday, November 12, 2021
Hamiltonian Methods in Dispersive and Wave Evolution Equations

3:00  3:30 pm ESTCoffee Break11th Floor Collaborative Space
Monday, November 15, 2021
Hamiltonian Methods in Dispersive and Wave Evolution Equations

3:00  3:30 pm ESTCoffee Break11th Floor Collaborative Space
Tuesday, November 16, 2021
Hamiltonian Methods in Dispersive and Wave Evolution Equations

3:00  3:30 pm ESTCoffee Break11th Floor Collaborative Space
Wednesday, November 17, 2021
Hamiltonian Methods in Dispersive and Wave Evolution Equations

9:00  10:00 am ESTProfessional Development: Grant ProposalsProfessional Development  11th Floor Lecture Hall

3:00  3:30 pm ESTCoffee Break11th Floor Collaborative Space
Thursday, November 18, 2021
Hamiltonian Methods in Dispersive and Wave Evolution Equations

11:00 am  12:30 pm ESTPost Doc/Graduate Student SeminarPost Doc/Graduate Student Seminar  11th Floor Lecture Hall

3:00  3:30 pm ESTCoffee Break11th Floor Collaborative Space
Friday, November 19, 2021
Hamiltonian Methods in Dispersive and Wave Evolution Equations

3:00  3:30 pm ESTCoffee Break11th Floor Collaborative Space
Thursday, December 2, 2021
Hamiltonian Methods in Dispersive and Wave Evolution Equations

11:00 am  12:30 pm ESTPost Doc/Graduate Student SeminarPost Doc/Graduate Student Seminar  11th Floor Lecture Hall
All event times are listed in ICERM local time in Providence, RI (Eastern Daylight Time / UTC4).
All event times are listed in .
ICERM local time in Providence, RI is Eastern Daylight Time (UTC4). Would you like to switch back to ICERM time or choose a different custom timezone?
Your Visit to ICERM
 ICERM Facilities
 ICERM is located on the 10th & 11th floors of 121 South Main Street in Providence, Rhode Island. ICERM's business hours are 8:30am  5:00pm during this event. See our facilities page for more info about ICERM and Brown's available facilities.
 Traveling to ICERM
 ICERM is located at Brown University in Providence, Rhode Island. Providence's T.F. Green Airport (15 minutes south) and Boston's Logan Airport (1 hour north) are the closest airports. Providence is also on Amtrak's Northeast Corridor. Indepth directions and transportation information are available on our travel page.
 Lodging/Housing
 Visiting ICERM for longer than a weeklong workshop? ICERM staff works with participants to locate accommodations that fit their needs. Since shortterm furnished housing is in very high demand, take advantage of the housing options ICERM may recommend. Contact housing@icerm.brown.edu for more details.
 Childcare/Schools
 Those traveling with family who are interested in information about childcare and/or schools should contact housing@icerm.brown.edu.
 Technology Resources
 Wireless internet access and wireless printing is available for all ICERM visitors. Eduroam is available for members of participating institutions. Thin clients in all offices and common areas provide open access to a web browser, SSH terminal, and printing capability. See our Technology Resources page for setup instructions and to learn about all available technology.
 Accessibility
 To request special services, accommodations, or assistance for this event, please contact accessibility@icerm.brown.edu as far in advance of the event as possible. Thank you.
 Discrimination and Harassment Policy
 ICERM is committed to creating a safe, professional, and welcoming environment that benefits from the diversity and experiences of all its participants. Both the Brown University "Code of Conduct", "Discrimination and Workplace Harassment Policy", and "Title IX Policy" apply to all ICERM participants and staff. Participants with concerns or requests for assistance on a discrimination or harassment issue should contact the ICERM Director or Assistant Director of Finance & Administration; they are the responsible employees at ICERM under this policy.
 Exploring Providence
 Providence's worldrenowned culinary scene provides ample options for lunch and dinner. Neighborhoods near campus, including College Hill Historic District, have many local attractions. Check out the map on our Explore Providence page to see what's near ICERM.
Visa Information
Contact visa@icerm.brown.edu for assistance.
 Need a US Visa?
 J1 visa requested via ICERM staff
 Eligible to be reimbursed
 B1 or Visa Waiver Business (WB) –if you already have either visa – contact ICERM staff for a visa specific invitation letter.
 Ineligible to be reimbursed
 B2 or Visa Waiver Tourist (WT)
 Already in the US?

F1 and J1 not sponsored by ICERM: obtain a letter approving reimbursement from the International Office of your home institution PRIOR to travel.
H1B holders do not need letter of approval.
All other visas: alert ICERM staff immediately about your situation.
ICERM does not reimburse visa fees. This chart is to inform visitors whether the visa they enter the US on allows them to receive reimbursement for the items outlined in their invitation letter.
Financial Support
 ORCID iD
 As this program is funded by the National Science Foundation (NSF), ICERM is required to collect your ORCID iD if you are receiving funding to attend this program. Be sure to add your ORCID iD to your Cube profile as soon as possible to avoid delaying your reimbursement.
 Acceptable Costs

 1 roundtrip between your home institute and ICERM
 Flights on U.S. or E.U. airlines – economy class to either Providence airport (PVD) or Boston airport (BOS)
 Ground Transportation to and from airports and ICERM.
 Unacceptable Costs

 Flights on nonU.S. or nonE.U. airlines
 Flights on U.K. airlines
 Seats in economy plus, business class, or first class
 Change ticket fees of any kind
 Multiuse bus passes
 Meals or incidentals
 Advance Approval Required

 Personal car travel to ICERM from outside New England
 Multipledestination plane ticket; does not include layovers to reach ICERM
 Arriving or departing from ICERM more than a day before or day after the program
 Multiple trips to ICERM
 Rental car to/from ICERM
 Flights on a Swiss, Japanese, or Australian airlines
 Arriving or departing from airport other than PVD/BOS or home institution's local airport
 2 oneway plane tickets to create a roundtrip (often purchased from Expedia, Orbitz, etc.)
 Reimbursement Requests

Request Reimbursement with Cube
Refer to the back of your ID badge for more information. Checklists are available at the front desk and in the Reimbursement section of Cube.
 Reimbursement Tips

 Scanned original receipts are required for all expenses
 Airfare receipt must show full itinerary and payment
 ICERM does not offer per diem or meal reimbursement
 Allowable mileage is reimbursed at prevailing IRS Business Rate and trip documented via pdf of Google Maps result
 Keep all documentation until you receive your reimbursement!
 Reimbursement Timing

6  8 weeks after all documentation is sent to ICERM. All reimbursement requests are reviewed by numerous central offices at Brown who may request additional documentation.
 Reimbursement Deadline

Submissions must be received within 30 days of ICERM departure to avoid applicable taxes. Submissions after thirty days will incur applicable taxes. No submissions are accepted more than six months after the program end.