Organizing Committee
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 toy-models, 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
One of the main objectives of this semester will be to integrate researchers from different horizons, and therefore special attention will be devoted to foster interdisciplinary interactions. There will be an additional introductory workshop at the beginning of the semester, and various events held in preparation of each workshop as well as in-depth follow-up discussions.

Image for "Hamiltonian Methods in Dispersive and Wave Evolution Equations"

Confirmed Speakers & Participants

  • Speaker
  • Poster Presenter
  • Attendee
  • Virtual Attendee
  • Siddhant Agrawal
    University of Massachusetts Amherst
    Sep 7-Oct 15, 2021
  • Yvonne Alama Bronsard
    Sorbonne Université
    Sep 18-Nov 2, 2021
  • Patricia Alonso Ruiz
    Texas A&M University
    Oct 15-31, 2021; Nov 29-Dec 11, 2021
  • Ioakeim Ampatzoglou
    Courant Institute of Mathematical Sciences, New York University
    Oct 18-22, 2021
  • Xinliang An
    National University of Singapore
    Sep 8-Dec 10, 2021
  • Gerard Awanou
    University of Illinois, Chicago
    Sep 20-24, 2021
  • Aidan Backus
    Brown University
    Sep 9-Dec 10, 2021
  • Byeong-Ho Bahn
    University of Massachusetts Amherst
    Sep 8-Dec 10, 2021
  • Hajer Bahouri
    Université Paris-Est - Créteil
    Sep 8-Dec 10, 2021
  • Valeria Banica
    Sorbonne Université
    Sep 19-Oct 4, 2021
  • Weizhu Bao
    National University of Singapore
    Sep 8-Dec 10, 2021
  • Marius Beceanu
    University at Albany SUNY
    Sep 13-Dec 10, 2021
  • Jacob Bedrossian
    University of Maryland
    Oct 18-22, 2021
  • Massimiliano Berti
    SISSA
    Oct 14-Dec 10, 2021
  • Roberta Bianchini
    Italian National Research Council, CNR
    Oct 18-Nov 5, 2021
  • Anxo Biasi
    Jagiellonian University
    Oct 1-Dec 10, 2021
  • Lydia Bieri
    University of Michigan
    Sep 8-Dec 10, 2021
  • Piotr Bizon
    Jagiellonian University
    Dec 6-10, 2021
  • Bjoern Bringmann
    Institute for Advanced Study
    Oct 17-Dec 10, 2021
  • Nicolas Burq
    University Paris-Sud
    Oct 18-22, 2021
  • Nicolas Camps
    Université Paris Saclay
    Sep 7-Dec 10, 2021
  • Esteban Cardenas
    University of Texas at Austin
    Oct 18-22, 2021
  • Amin Chabchoub
    University of Sydney
    Sep 20-24, 2021
  • Andreia Chapouto
    University of Edinburgh
    Dec 6-10, 2021
  • Jehanzeb Chaudhary
    University of New Mexico
    Sep 7-Dec 11, 2021
  • Gong Chen
    Fields institute
    Sep 8-Dec 8, 2021
  • Brian Choi
    Southern Methodist University
    Dec 6-10, 2021
  • Charles Collot
    Cergy-Paris Université
    Oct 18-22, 2021
  • Diego Cordoba
    ICMAT
    Sep 8-Dec 10, 2021
  • Stefan Czimek
    Brown University (ICERM)
    Sep 8-Dec 10, 2021
  • Magdalena Czubak
    University of Colorado at Boulder
    Sep 13-Dec 10, 2021
  • Joel Dahne
    Uppsala University
    Sep 8-Dec 10, 2021
  • David Damanik
    RICE University
    Dec 6-10, 2021
  • Anne-Sophie de Suzzoni
    Ecole Polytechnique
    Oct 18-22, 2021
  • Yu Deng
    University of Southern California
    Sep 15-Dec 15, 2021
  • Yu Deng
    University of Southern California
    Oct 18-22, 2021
  • Giuseppe Di Fazio
    University of Catania
    Sep 9-Dec 10, 2021
  • Benjamin Dodson
    John Hopkins University
    Dec 6-10, 2021
  • Michele Dolce
    Imperial College London
    Sep 13-Dec 10, 2021
  • Hongjie Dong
    Brown University
    Oct 18-22, 2021
  • Emmanuel Dormy
    ENS
    Sep 20-24, 2021; Nov 12-25, 2021
  • Jinqiao Duan
    Illinois Institute of Technology
    Sep 13-Dec 10, 2021
  • Sergey Dyachenko
    University at Buffalo
    Sep 20-24, 2021
  • Daniel Eceizabarrena
    University of Massachusetts Amherst
    Sep 8-Dec 10, 2021
  • Debbie Eeltink
    MIT
    Sep 20-24, 2021
  • Chenjie Fan
    Academy of Mathematics and Systems Science, CAS
    Sep 8-Dec 10, 2021
  • Allen Fang
    Sorbonne University
    Dec 6-10, 2021
  • Erwan Faou
    INRIA Rennes
    Sep 19-Dec 10, 2021
  • Serena Federico
    Ghent University
    Oct 16-Nov 6, 2021
  • Patrick Flynn
    Brown
    Sep 8-Dec 10, 2021
  • Luigi Forcella
    Heriot-Watt University
    Oct 18-22, 2021
  • Gilles Francfort
    Universite Paris 13
    Oct 4-7, 2021
  • Rupert Frank
    LMU Munich
    Dec 6-10, 2021
  • Irene Gamba
    University of Texas at Austin
    Sep 20-24, 2021
  • Claudia García
    Universitat de Barcelona
    Sep 8-Dec 11, 2021
  • Eduardo Garcia-Juarez
    Universitat de Barcelona
    Sep 8-Dec 11, 2021
  • Louise Gassot
    Laboratoire de Mathématiques d'Orsay - Université Paris-Saclay
    Sep 1, 2021-Mar 14, 2022
  • Patrick Gerard
    Paris-Sud University, Orsay
    Sep 15-Nov 15, 2021
  • Pierre Germain
    NYU - Courant Institute
    Sep 8-Dec 10, 2021
  • Elena Giorgi
    Princeton University
    Dec 6-10, 2021
  • Tainara Gobetti Borges
    Brown University
    Sep 10-Dec 10, 2021
  • Javier Gomez Serrano
    Princeton University
    Sep 13-Dec 10, 2021
  • Sigal Gottlieb
    University of Massachusetts Dartmouth
    Sep 20-24, 2021
  • Ricardo Grande Izquierdo
    University of Michigan
    Sep 8-Dec 10, 2021
  • Benoît Grébert
    University of Nantes
    Sep 8-Dec 11, 2021
  • Sandrine Grellier
    Université d'Orléans
    Sep 13-Dec 10, 2021
  • Marcel Guardia
    Universitat Politècnica de Catalunya
    Oct 18-22, 2021
  • Yan Guo
    Brown University
    Dec 6-10, 2021
  • Zaher Hani
    University of Michigan
    Sep 18-Dec 11, 2021
  • Amirali Hannani
    CEREMADE, Université Paris Dauphine, PSL
    Sep 8-Dec 10, 2021
  • Benjamin Harrop-Griffiths
    University of California, Los Angeles
    Oct 18-22, 2021
  • Susanna Haziot
    Brown University Mathematics
    Sep 8-Dec 10, 2021
  • Siming He
    Duke University
    Oct 18-22, 2021
  • Sebastian Herr
    Bielefeld University
    Dec 6-10, 2021
  • Justin Holmer
    Brown University
    Sep 15-Dec 10, 2021
  • Slim IBRAHIM
    University of Victoria
    Sep 8-Dec 10, 2021
  • Alexandru Ionescu
    Princeton University
    Sep 8-Dec 10, 2021
  • Sameer Iyer
    Princeton University
    Dec 6-10, 2021
  • Olaniyi Iyiola
    Clarkson University
    Sep 20-24, 2021
  • Jonathan Jaquette
    Boston University
    Sep 20-24, 2021
  • Pranava Jayanti
    University Of Maryland College Park
    Sep 20-24, 2021; Oct 18-22, 2021
  • Hao Jia
    University of Minnesota
    Nov 14-Dec 10, 2021
  • Istvan Kadar
    University of Cambridge
    Oct 18-22, 2021
  • Adilbek Kairzhan
    University of Toronto
    Sep 8-Dec 11, 2021
  • Thomas Kappeler
    Universität Zürich
    Sep 10-Dec 10, 2021
  • George Karniadakis
    Brown University
    Sep 20-24, 2021
  • Dean Katsaros
    UMass amherst
    Sep 8-Dec 10, 2021
  • Panayotis Kevrekidis
    University of Massachusetts Amherst
    Sep 8-Dec 10, 2021
  • Alex Kiselev
    Duke University
    Sep 8-Dec 10, 2021
  • Friedrich Klaus
    Karlsruhe Institute of Technology
    Oct 18-22, 2021
  • Haram Ko
    Brown University
    Sep 10-Dec 10, 2021
  • Herbert Koch
    University of Bonn
    Sep 8-Dec 10, 2021
  • Sudipta Kolay
    ICERM
    Sep 1, 2021-May 31, 2022
  • Kristin Kurianski
    California State University, Fullerton
    Sep 19-25, 2021
  • Christophe Lacave
    Universite Grenoble Alpes
    Sep 20-24, 2021
  • Thierry Laurens
    University of California, Los Angeles
    Dec 6-10, 2021
  • Gyu Eun Lee
    University of Edinburgh
    Sep 20-24, 2021; Oct 18-22, 2021; Dec 6-10, 2021
  • Tristan Leger
    Princeton University
    Oct 17-Nov 13, 2021
  • Yao Li
    University of Massachusetts Amherst
    Sep 8-Dec 10, 2021
  • Jichun Li
    University of Nevada Las Vegas
    Sep 20-24, 2021
  • Guopeng Li
    University of Edinburgh
    Oct 18-22, 2021
  • Felipe Linares
    IMPA
    Oct 18-22, 2021
  • Kyle Liss
    University of Maryland, College Park
    Sep 8-Dec 15, 2021
  • Ruoyuan Liu
    University of Edinburgh
    Oct 18-22, 2021
  • Jonas Luhrmann
    Texas A&M University
    Oct 15-31, 2021; Nov 28-Dec 11, 2021
  • Jani Lukkarinen
    University of Helsinki
    Dec 4-11, 2021
  • Brad Marston
    Brown University
    Sep 20-24, 2021
  • Yvan Martel
    École Polytechnique
    Dec 6-10, 2021
  • Jeremy Marzuola
    University of North Carolina
    Sep 9-Dec 10, 2021
  • Nader Masmoudi
    Courant Institute of Mathematical Sciences at NYU
    Sep 13-Dec 10, 2021
  • Alberto Maspero
    Scuola Internazionale Superiore di Studi Avanzati (SISSA)
    Oct 18-22, 2021
  • Jonathan Mattingly
    Duke University
    Oct 18-22, 2021
  • Joseph Miller
    University of Texas at Austin
    Oct 17-Dec 11, 2021
  • Peter Miller
    University of Michigan
    Dec 6-10, 2021
  • Jose Morales E.
    UTSA
    Sep 20-24, 2021
  • Adam Morgan
    University of Toronto
    Dec 6-10, 2021
  • Lin Mu
    University of Georgia
    Sep 8-Dec 10, 2021
  • Jason Murphy
    Missouri University of Science and Technology
    Sep 21-Dec 10, 2021
  • Andrea Nahmod
    University of Massachusetts Amherst
    Sep 8-Dec 10, 2021
  • Kenji Nakanishi
    Research Institute for Mathematical Sciences, Kyoto University
    Sep 8-Dec 10, 2021
  • Maria Ntekoume
    Rice University
    Dec 6-10, 2021
  • Tadahiro Oh
    The University of Edinburgh
    Dec 6-10, 2021
  • Miguel Onorato
    Università di Torino
    Sep 20-24, 2021
  • Ludivine Oruba
    Sorbonne Universite
    Sep 8-Dec 10, 2021
  • José Palacios
    Institut Denis Poisson, Université de Tours
    Sep 8-Dec 10, 2021
  • Yulin Pan
    University of Michigan, Ann Arbor
    Sep 20-24, 2021; Oct 18-22, 2021
  • Jaemin Park
    Universitat de Barcelona
    Sep 8-Dec 10, 2021
  • Benoit Pausader
    Brown University
    Sep 8-Dec 10, 2021
  • Nataša Pavlovic
    University of Texas at Austin
    Oct 18-22, 2021; Dec 6-10, 2021
  • Dmitry Pelinovsky
    McMaster University
    Dec 6-10, 2021
  • Galina Perelman
    LAMA
    Sep 8-Dec 10, 2021
  • Thi- Thao Phuong- Hoang
    Auburn University
    Sep 20-24, 2021
  • Samuel Punshon-Smith
    Institute for Advanced Study
    Oct 18-22, 2021
  • Fabio Pusateri
    University of Toronto
    Sep 8-Dec 10, 2021
  • Raaghav Ramani
    University of California, Davis
    Sep 20-24, 2021
  • Oscar Riano
    Florida International University
    Sep 20-24, 2021; Oct 18-22, 2021
  • Tristan Robert
    Université de Lorraine
    Oct 18-22, 2021
  • Igor Rodnianski
    Princeton University
    Dec 6-10, 2021
  • Casey Rodriguez
    MIT
    Dec 6-10, 2021
  • Matthew Rosenzweig
    Massachusetts Institute of Technology
    Sep 8-Dec 10, 2021
  • Svetlana Roudenko
    Florida International University
    Oct 18-22, 2021; Dec 6-10, 2021
  • Frédéric Rousset
    Département de Mathématiques d’Orsay
    Oct 15-Nov 15, 2021
  • Themistoklis Sapsis
    MIT
    Sep 8-Dec 10, 2021
  • Nancy Scherich
    University of Toronto
    Sep 1, 2021-May 31, 2022
  • Wilhelm Schlag
    Yale University
    Dec 6-10, 2021
  • Birgit Schoerkhuber
    University of Innsbruck, Austria
    Dec 6-10, 2021
  • Katharina Schratz
    Heriot-Watt University
    Sep 20-24, 2021
  • Diaraf Seck
    University Cheikh Anta Diop of Dakar
    Sep 8-Dec 10, 2021
  • Anastassiya Semenova
    ICERM, Brown University
    Sep 1, 2021-May 31, 2022
  • Chengyang Shao
    Massachusetts Institute of Technology
    Sep 13-Dec 10, 2021
  • Jalal Shatah
    New York University
    Oct 18-22, 2021
  • Jie Shen
    Purdue University
    Sep 20-24, 2021
  • Gigliola Staffilani
    Massachusetts Institute of Technology
    Sep 8-Dec 10, 2021
  • Annalaura Stingo
    University of California Davis
    Sep 8-Dec 10, 2021
  • Walter Strauss
    Brown University
    Sep 8-Dec 10, 2021
  • Catherine Sulem
    University of Toronto
    Sep 8-Dec 10, 2021
  • Chenmin Sun
    CY Cergy-Paris Université
    Sep 8-Dec 10, 2021
  • changzhen Sun
    University of Paris-Saclay
    Sep 9-Dec 10, 2021
  • Ruoci Sun
    Karlsruhe Institute of Technology
    Oct 18-22, 2021
  • Mouhamadou Sy
    Imperial College London
    Oct 18-22, 2021
  • Tomoyuki Tanaka
    Nagoya University
    Oct 18-22, 2021
  • Maja Taskovic
    Emory University
    Sep 9-Dec 10, 2021
  • Daniel Tataru
    University of California, Berkeley
    Dec 6-10, 2021
  • Minh-Binh Tran
    Southern Methodist University
    Oct 18-22, 2021
  • Nikolay Tzvetkov
    University of Cergy-Pontoise
    Sep 8-Dec 10, 2021
  • Tim Van Hoose
    Missouri University of Science and Technology
    Oct 17-23, 2021
  • Luis Vega
    Basque Center for Applied Mathematics (BCAM)
    Sep 17-Dec 10, 2021
  • Paolo Ventura
    SISSA
    Oct 18-22, 2021
  • Monica Visan
    University of California, Los Angeles
    Sep 20-24, 2021; Oct 18-22, 2021
  • Weinan Wang
    University of Arizona
    Sep 8-Dec 10, 2021
  • Li Wang
    University of Minnesota
    Sep 20-24, 2021
  • Hong Wang
    Institute for Advanced Study (IAS)
    Dec 6-10, 2021
  • Xuecheng Wang
    Tsinghua University
    Sep 8-Dec 10, 2021
  • Billy Warner
    University of Texas at Austin
    Oct 18-22, 2021
  • Klaus Widmayer
    EPFL, Switzerland
    Oct 12-Nov 15, 2021
  • Jon Wilkening
    University of California, Berkeley
    Sep 20-24, 2021
  • Bobby Wilson
    University of Washington
    Sep 20-24, 2021
  • Bobby Wilson
    University of Washington
    Sep 8-Dec 10, 2021
  • Sijue Wu
    University of Michigan
    Dec 6-10, 2021
  • Lei Wu
    Lehigh University
    Oct 18-22, 2021
  • Kai Yang
    Florida International University
    Sep 20-24, 2021
  • Jiaqi Yang
    ICERM
    Sep 1, 2021-May 31, 2022
  • Zhuolun Yang
    Brown University
    Sep 8-Dec 10, 2021
  • Yao Yao
    Georgia Tech
    Sep 20-24, 2021
  • Lei Yu
    Tongji University
    Oct 18-22, 2021
  • Xueying Yu
    University of Washington
    Sep 8-Dec 10, 2021
  • Haitian Yue
    University of Southern California
    Sep 14-Dec 10, 2021
  • Zhiyuan Zhang
    New York University
    Sep 20-24, 2021; Oct 18-22, 2021; Dec 6-10, 2021
  • Chenyu Zhang
    Brown University
    Sep 20-24, 2021
  • Jiqiang Zheng
    Institute of Applied Physics and Computational Mathematics
    Dec 6-10, 2021
  • Guangqu Zheng
    University of Edinburgh
    Oct 18-22, 2021
  • SHIJUN ZHENG
    Georgia Southern University
    Sep 20-24, 2021; Oct 18-22, 2021; Dec 6-10, 2021
  • Hui Zhu
    University of Michigan
    Oct 18-22, 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 EDT
    Coffee Break
    11th Floor Collaborative Space
Thursday, September 9, 2021
Hamiltonian Methods in Dispersive and Wave Evolution Equations
  • 9:00 - 10:30 am EDT
    Local well-posedness for dispersive equations
    Tutorial - 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 well-posedness and study the asymptotics.
  • 11:00 am - 12:30 pm EDT
    Ergodicity of Markov processes: theory and computation
    Tutorial - 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 EDT
    ICERM Welcome
    Welcome - 11th Floor Lecture Hall
    • Brendan Hassett, ICERM/Brown University
  • 2:00 - 3:00 pm EDT
    Grad Student/ PostDoc Introductions
    Introductions - 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 Paris-Saclay
    • 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 EDT
    Coffee Break
    11th Floor Collaborative Space
Friday, September 10, 2021
Hamiltonian Methods in Dispersive and Wave Evolution Equations
  • 9:00 - 10:30 am EDT
    Local well-posedness for dispersive equations
    Tutorial - 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 well-posedness and study the asymptotics.
  • 11:00 am - 12:30 pm EDT
    Ergodicity of Markov processes: theory and computation
    Tutorial - 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 EDT
    Grad Student/ PostDoc Introductions
    Introductions - 11th Floor Lecture Hall
    • Bjoern Bringmann, Institute for Advanced Study
    • Stefan Czimek, Brown University (ICERM)
    • Daniel Eceizabarrena, University of Massachusetts Amherst
    • Eduardo Garcia-Juarez, 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 EDT
    Coffee Break
    11th Floor Collaborative Space
Monday, September 13, 2021
Hamiltonian Methods in Dispersive and Wave Evolution Equations
  • 9:00 - 10:30 am EDT
    Computer-assisted proofs in PDEs
    Tutorial - 11th Floor Lecture Hall
    • Javier Gomez Serrano, Princeton University
    Abstract
    In this minicourse we will present some recent results concerning computer-assisted 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 EDT
    Ergodicity of Markov processes: theory and computation
    Tutorial - 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 EDT
    Welcoming Reception
    Reception - Hemenway's patio
Tuesday, September 14, 2021
Hamiltonian Methods in Dispersive and Wave Evolution Equations
  • 9:00 - 10:30 am EDT
    Local well-posedness for dispersive equations
    Tutorial - 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 well-posedness and study the asymptotics.
  • 11:00 am - 12:30 pm EDT
    Computer-assisted proofs in PDEs
    Tutorial - 11th Floor Lecture Hall
    • Javier Gomez Serrano, Princeton University
    Abstract
    In this minicourse we will present some recent results concerning computer-assisted 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 EDT
    Coffee Break
    11th Floor Collaborative Space
Wednesday, September 15, 2021
Hamiltonian Methods in Dispersive and Wave Evolution Equations
  • 9:00 - 10:30 am EDT
    Local well-posedness for dispersive equations
    Tutorial - 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 well-posedness and study the asymptotics.
  • 11:00 am - 12:30 pm EDT
    Computer-assisted proofs in PDEs
    Tutorial - 11th Floor Lecture Hall
    • Javier Gomez Serrano, Princeton University
    Abstract
    In this minicourse we will present some recent results concerning computer-assisted 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 EDT
    Coffee Break
    11th Floor Collaborative Space
  • 3:15 - 4:15 pm EDT
    Grads/Postdocs Meet with ICERM Directorate
    11th 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 EDT
    Coffee Break
    11th Floor Collaborative Space
Friday, September 17, 2021
Hamiltonian Methods in Dispersive and Wave Evolution Equations
  • 9:00 - 10:30 am EDT
    Local well-posedness for dispersive equations
    Tutorial - 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 well-posedness and study the asymptotics.
  • 11:00 am - 12:30 pm EDT
    Computer-assisted proofs in PDEs
    Tutorial - 11th Floor Lecture Hall
    • Javier Gomez Serrano, Princeton University
    Abstract
    In this minicourse we will present some recent results concerning computer-assisted 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 EDT
    Coffee Break
    11th Floor Collaborative Space
Monday, September 20, 2021
  • 9:50 - 10:00 am EDT
    Welcome
    11th Floor Lecture Hall
    • Brendan Hassett, ICERM/Brown University
  • 10:00 - 10:40 am EDT
    Quasilinear Diffusion of magnetized fast electrons in a mean field of quasi-particle waves packets
    11th Floor Lecture Hall
    • Speaker
    • Irene Gamba, University of Texas at Austin
    • Session Chair
    • Luis Vega, Basque Center for Applied Mathematics (BCAM)
    Abstract
    Quasi-linear diffusion of magnetized fast electrons in momentum space results from stimulated emission and absorption of waves packets via wave-particle 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 (quasi-particles) 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 quasi-particle 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 EDT
    Coffee Break
    11th Floor Collaborative Space
  • 11:15 am - 12:00 pm EDT
    Modeling inviscid water waves
    11th 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 two-dimensional water waves in a fully non-linear regime. The free-surface 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 EDT
    Lunch/Free Time
  • 1:15 - 1:55 pm EDT
    Anomalous 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 size-dependent. 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 EDT
    On the asymptotic stability of shear flows and vortices
    11th 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 EDT
    Reception
    Hemenway's Patio (weather permitting)
Tuesday, September 21, 2021
  • 10:00 - 10:40 am EDT
    Small scale formations in the incompressible porous media equation
    11th 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 finite-time blow-up 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 infinite-in-time 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 EDT
    Coffee Break
    11th Floor Collaborative Space
  • 11:15 am - 12:00 pm EDT
    PINNs and DeepOnets for Wave Systems
    11th Floor Lecture Hall
    • Virtual Speaker
    • George Karniadakis, Brown University
  • 12:15 - 1:45 pm EDT
    Lunch/Free Time
  • 1:45 - 2:25 pm EDT
    The second boundary value problem for a discrete Monge-Ampere equation
    11th 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 Monge-Ampere equation of geometric optics and optimal transport. It is the natural generalization of the popular Oliker-Prussner 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 EDT
    Lightning Talks
    11th Floor Lecture Hall
  • 3:45 - 4:15 pm EDT
    Coffee Break
    11th Floor Collaborative Space
Wednesday, September 22, 2021
  • 10:00 - 10:40 am EDT
    Efficient and accurate structure preserving schemes for complex nonlinear systems
    11th 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 higher-order accuracy.
  • 10:55 - 11:15 am EDT
    Coffee Break
    11th Floor Collaborative Space
  • 11:15 am - 12:00 pm EDT
    Energy growth for the Schrödinger map and the binormal flow
    11th 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 EDT
    Lunch/Free Time
  • 1:45 - 2:25 pm EDT
    Water Waves with Background Flow over Obstacles and Topography
    11th 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, multiply-connected 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 EDT
    Coffee Break
    11th Floor Collaborative Space
  • 3:15 - 3:55 pm EDT
    Topological Origin of Certain Fluid and Plasma Waves
    11th 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 non-trivial 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 EDT
    Resonances as a Computational Tool
    11th Floor Lecture Hall
    • Katharina Schratz, Heriot-Watt University
  • 10:55 - 11:15 am EDT
    Coffee Break
    11th Floor Collaborative Space
  • 11:15 am - 12:00 pm EDT
    Efficient time-stepping methods for the rotating shallow water equations
    11th 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 time-stepping 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 time-stepping algorithm based on the strong stability preserving Runge-Kutta 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 EDT
    Lunch/Free Time
  • 1:45 - 2:25 pm EDT
    Dynamics in particle suspension flow
    11th 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 Hele-Shaw 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 particle-rich 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 self-similar accumulation of particles at the interface between suspension and air. Our results demonstrate that the combination of the shear- induced migration, the advancing fluid-fluid interface, and Taylor dispersion yield the self-similar and gradual accumulation of particles.
  • 2:45 - 3:15 pm EDT
    Coffee Break
    11th Floor Collaborative Space
  • 3:15 - 3:55 pm EDT
    Separatrix crossing and symmetry breaking in NLSE-like systems due to forcing and damping
    11th Floor Conference Room
    • Debbie Eeltink, MIT
    Abstract
    The nonlinear Schrödinger equation (NLSE) is a workhorse for many different fields (e.g. optical fibers, Bose-Einstein 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 well-studied 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 phase-space for the NLSE, spanned by the relative phase of the sidebands, and the energy fraction in the sidebands. Using wave-tank measurements, we show that forcing and damping the NLSE induces separatrix crossing: switching from one solution-type to the other in the phase-space. Our experiments are performed on deep water waves, which are better described by the higher-order NLSE, the Dysthe equation. We, therefore, extend our three-wave 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 water-wave 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 EDT
    Coffee Break
    11th Floor Collaborative Space
  • 10:00 - 10:40 am EDT
    Extreme Wave Events in Reflective Environments
    11th 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 uni-directional 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 EDT
    Coffee Break
    11th Floor Collaborative Space
  • 11:15 - 11:55 am EDT
    Symmetry in stationary and uniformly rotating solutions of the Euler equations
    11th Floor Lecture Hall
    • Javier Gomez Serrano, Princeton University
  • 12:10 - 12:50 pm EDT
    High order strong stability preserving multi-derivative implicit and IMEX Runge--Kutta methods with asymptotic preserving properties
    11th 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 two-derivative Runge--Kutta schemes, and SSP implicit-explicit (IMEX) multi-derivative Runge--Kutta schemes where the time-step 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 backward-in-time 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 Runge--Kutta schemes of order up to $p=4$, and IMEX Runge--Kutta schemes of order up to $p=3$. For the multi-derivative 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 Bhatnagar-Gross-Krook (BGK) kinetic equation.
Monday, September 27, 2021
Hamiltonian Methods in Dispersive and Wave Evolution Equations
  • 3:00 - 3:30 pm EDT
    Coffee Break
    11th Floor Collaborative Space
Tuesday, September 28, 2021
Hamiltonian Methods in Dispersive and Wave Evolution Equations
  • 10:00 - 11:00 am EDT
    RIEMANN’S NON-DIFFERENTIABLE 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 non-obvious 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 EDT
    ALMOST-GLOBAL WELL-POSEDNESS FOR 2D STRONGLY-COUPLED WAVE-KLEIN-GORDON SYSTEMS
    11th Floor Lecture Hall
    • Annalaura Stingo, University of California Davis
    Abstract
    (Joint with Mihaela Ifrim) In this talk we discuss the almost-global well-posedness of a wide class of coupled Wave-Klein-Gordon equations in 2+1 space-time dimensions, when initial data are small and localized. The Wave-Klein-Gordon systems arise from several physical models especially related to General Relativity but few results are known at present in lower space-time dimensions. Compared with prior related results, we here consider a strong quadratic quasilinear coupling between the wave and the Klein-Gordon 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 EDT
    Coffee Break
    11th Floor Collaborative Space
  • 3:00 - 4:00 pm EDT
    Semilinear Dispersive Equations
    11th 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 EDT
    Gender Diversity and the Mathematical Community
    11th Floor Lecture Hall
    • Andrea Nahmod, University of Massachusetts Amherst
    • Gigliola Staffilani, Massachusetts Institute of Technology
    Abstract
    Followed by a “brown-bag 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 EDT
    Coffee Break
    11th Floor Collaborative Space
Thursday, September 30, 2021
Hamiltonian Methods in Dispersive and Wave Evolution Equations
  • 11:00 am - 12:30 pm EDT
    Post Doc/Graduate Student Seminar
    Post 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 EDT
    Coffee Break
    11th Floor Collaborative Space
Friday, October 1, 2021
Hamiltonian Methods in Dispersive and Wave Evolution Equations
  • 3:00 - 3:30 pm EDT
    Coffee Break
    11th Floor Collaborative Space
Monday, October 4, 2021
Hamiltonian Methods in Dispersive and Wave Evolution Equations
  • 3:00 - 3:30 pm EDT
    Coffee Break
    11th Floor Collaborative Space
Tuesday, October 5, 2021
Hamiltonian Methods in Dispersive and Wave Evolution Equations
  • 10:00 - 11:00 am EDT
    The characteristic gluing problem of general relativity
    11th 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 infinite-dimensional space of conservation laws along null hypersurfaces for the linearized equations at Minkowski. We prove that this space splits into an infinite-dimensional space of gauge-dependent charges and a 10-dimensional space of gauge-invariant charges. We identify the 10 gauge-invariant charges to be related to the energy, linear momentum, angular momentum and center-of-mass 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 Corvino-Schoen 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 Carlotto-Schoen 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 EDT
    The role of hyperbolicity in deciding uniqueness for minimizers of an energy with linear growth
    11th Floor Lecture Hall
    • Gilles Francfort, Universite Paris 13
  • 3:00 - 3:30 pm EDT
    Coffee Break
    11th Floor Collaborative Space
Wednesday, October 6, 2021
Hamiltonian Methods in Dispersive and Wave Evolution Equations
  • 9:00 - 10:00 am EDT
    Professional Development: Ethics I
    Professional Development - 11th Floor Lecture Hall
  • 3:00 - 3:30 pm EDT
    Coffee Break
    11th Floor Collaborative Space
Thursday, October 7, 2021
Hamiltonian Methods in Dispersive and Wave Evolution Equations
  • 11:00 am - 12:30 pm EDT
    Post Doc/Graduate Student Seminar
    Post Doc/Graduate Student Seminar - 11th Floor Lecture Hall
  • 2:00 - 4:00 pm EDT
    Probabilistic well-posedness for nonlinear Schrödinger equation (I)
    11th Floor Lecture Hall
    • Haitian Yue, University of Southern California
    Abstract
    In this mini-course, we will introduce the probabilistic well-posedness 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 re-centering method; 3) the random averaging operator method.
  • 3:00 - 3:30 pm EDT
    Coffee Break
    11th Floor Collaborative Space
Friday, October 8, 2021
Hamiltonian Methods in Dispersive and Wave Evolution Equations
  • 1:30 - 3:00 pm EDT
    Probabilistic well-posedness for nonlinear Schrödinger equation (I)
    11th Floor Lecture Hall
    • Haitian Yue, University of Southern California
    Abstract
    In this mini-course, we will introduce the probabilistic well-posedness 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 re-centering method; 3) the random averaging operator method.
  • 3:00 - 3:30 pm EDT
    Coffee Break
    11th Floor Collaborative Space
Tuesday, October 12, 2021
Hamiltonian Methods in Dispersive and Wave Evolution Equations
  • 10:00 - 11:00 am EDT
    Superharmonic Instability of Stokes Waves
    11th 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 EDT
    Revisit singularity formation for the inviscid primitive equation
    11th 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 EDT
    Probabilistic well-posedness for nonlinear Schrödinger equation (II)
    11th Floor Lecture Hall
    • Yu Deng, University of Southern California
  • 3:00 - 3:30 pm EDT
    Coffee Break
    11th Floor Collaborative Space
Wednesday, October 13, 2021
Hamiltonian Methods in Dispersive and Wave Evolution Equations
  • 9:00 - 10:00 am EDT
    Professional Development: Ethics II
    Professional Development - 11th Floor Lecture Hall
  • 2:00 - 4:30 pm EDT
    Probabilistic well-posedness for nonlinear Schrödinger equation (II)
    11th Floor Lecture Hall
    • Yu Deng, University of Southern California
  • 3:00 - 3:30 pm EDT
    Coffee Break
    11th Floor Collaborative Space
Thursday, October 14, 2021
Hamiltonian Methods in Dispersive and Wave Evolution Equations
  • 11:00 am - 12:30 pm EDT
    Post Doc/Graduate Student Seminar
    Post Doc/Graduate Student Seminar - 11th Floor Lecture Hall
  • 3:00 - 3:30 pm EDT
    Coffee Break
    11th Floor Collaborative Space
Friday, October 15, 2021
Hamiltonian Methods in Dispersive and Wave Evolution Equations
  • 3:00 - 3:30 pm EDT
    Coffee Break
    11th Floor Collaborative Space
Monday, October 18, 2021
  • 8:45 - 9:00 am EDT
    Welcome
    11th Floor Lecture Hall
    • Brendan Hassett, ICERM/Brown University
  • 9:00 - 9:50 am EDT
    Microlocal analysis of singular measures
    11th Floor Lecture Hall
    • Virtual Speaker
    • Nicolas Burq, University Paris-Sud
  • 10:00 - 10:30 am EDT
    Coffee Break
    11th Floor Collaborative Space
  • 10:30 - 11:20 am EDT
    Full description of Benjamin-Feir instability of Stokes waves in deep water
    11th Floor Lecture Hall
    • Virtual Speaker
    • Alberto Maspero, Scuola Internazionale Superiore di Studi Avanzati (SISSA)
    Abstract
    Small-amplitude, traveling, space periodic solutions -- called Stokes waves -- of the 2 dimensional gravity water waves equations in deep water are linearly unstable with respect to long-wave 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 non-purely 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 EDT
    Lunch/Free Time
  • 1:00 - 1:50 pm EDT
    Breakdown of small amplitude breathers for the nonlinear Klein-Gordon equation
    11th 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 sine-Gordon 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 so-called 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 Klein-Gordon 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 EDT
    Fluctuations of \delta-moments for the free Schrödinger Equation
    11th Floor Lecture Hall
    • Luis Vega, Basque Center for Applied Mathematics (BCAM)
    Abstract
    I will present recent work done with S. Kumar and F.Ponce-Vanegas.
    We study the process of dispersion of low-regularity 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 EDT
    Welcome Reception
    Reception - Hemenway's Patio
Tuesday, October 19, 2021
  • 9:00 - 9:50 am EDT
    Mathematical 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 EDT
    Coffee Break
    11th Floor Collaborative Space
  • 10:30 - 11:20 am EDT
    Mathematical 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 EDT
    Lunch/Free Time
  • 1:00 - 1:50 pm EDT
    Energy 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 quasi-resonant part of the NLS initial value problem we consider, in both the focusing and defocusing case, is globally well-posed for initial data of finite mass.
  • 2:00 - 2:50 pm EDT
    Determinants, commuting flows, and recent progress on completely integrable systems
    11th 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, well-posedness 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 EDT
    Lightning Talks
    11th Floor Lecture Hall
  • 4:00 - 4:30 pm EDT
    Coffee Break
    11th Floor Collaborative Space
Wednesday, October 20, 2021
  • 9:00 - 9:50 am EDT
    On the derivation of the Kinetic Wave Equation in the inhomogeneous setting
    11th Floor Lecture Hall
    • Virtual Speaker
    • Charles Collot, Cergy-Paris 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 space-inhomogeneous 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 EDT
    Coffee Break
    11th Floor Collaborative Space
  • 10:30 - 11:20 am EDT
    3 Problems in Wave Turbulence
    11th Floor Lecture Hall
    • Jalal Shatah, New York University
  • 11:30 - 11:40 am EDT
    Group Photo
    11th Floor Lecture Hall
  • 11:40 am - 1:00 pm EDT
    Lunch/Free Time
  • 1:00 - 1:50 pm EDT
    Constructing global solutions for energy supercritical NLS equations
    11th 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 well-known Gibbs measures based strategy and the standard fluctuation-dissipation 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 non-dispersive PDEs.
  • 2:00 - 2:30 pm EDT
    Coffee Break
    11th Floor Collaborative Space
  • 2:30 - 3:20 pm EDT
    Invariant Gibbs measures for NLS and Hartree equations
    11th 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 high-low 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 EDT
    Singularities in the weak turbulence regime
    11th Floor Lecture Hall
    • Virtual Speaker
    • Anne-Sophie 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 EDT
    Coffee Break
    11th Floor Collaborative Space
  • 10:30 - 11:20 am EDT
    A New model for the stochasticly perturbed 2d navier-stokes equations
    11th Floor Lecture Hall
    • Jonathan Mattingly, Duke University
    Abstract
    I will introduce a new model of the stochastically forced navier-stokes 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 EDT
    Lunch/Free Time
  • 1:00 - 1:50 pm EDT
    Global well-posedness for the fractional NLS on the unit disk
    11th 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 well-posedness 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 I-method in the fractional nonlinear Schr\"odinger equation setting.
  • 2:00 - 2:30 pm EDT
    Coffee Break
    11th Floor Collaborative Space
  • 2:30 - 3:20 pm EDT
    The wave maps equation and Brownian paths
    11th 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 well-posedness 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 EDT
    Positive Lyapunov exponents for the Galerkin-Navier-Stokes equations with stochastic forcing
    11th 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 high-dimensional, stochastic differential equations such as the weakly-damped Lorenz-96 (L96) model or Galerkin truncations of the 2d Navier-Stokes equations (joint with Alex Blumenthal and Sam Punshon-Smith). 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 so-called "projective process"); and (B) an L1-based 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 Punshon-Smith and I on verifying this condition for the 2d Galerkin-Navier-Stokes 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 EDT
    Coffee Break
    11th Floor Collaborative Space
  • 10:30 - 11:20 am EDT
    A tale of two generalizations of Boltzmann equation
    11th 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 binary-ternary 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 non-symmetric interaction of these gases.
  • 11:30 am - 12:20 pm EDT
    Some Recent Results On Wave Turbulence: Derivation, Analysis, Numerics and Physical Application
    11th Floor Lecture Hall
    • Minh-Binh Tran, Southern Methodist University
    Abstract
    Wave turbulence describes the dynamics of both classical and non-classical 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 Bose-Einstein Condensates.
Monday, October 25, 2021
Hamiltonian Methods in Dispersive and Wave Evolution Equations
  • 3:00 - 3:30 pm EDT
    Coffee Break
    11th Floor Collaborative Space
Tuesday, October 26, 2021
Hamiltonian Methods in Dispersive and Wave Evolution Equations
  • 10:00 - 11:00 am EDT
    Weak universality for the fractional \Phi_2^4 under the wave dynamics
    11th Floor Lecture Hall
    • Chenmin Sun, CY Cergy-Paris 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 higher-order potentials with correct scalings. In this talk, we consider the weak universality of the two-dimensional fractional nonlinear wave equation. For a sequence of Hamiltonians of high-degree 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 Cauchy-theory 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 EDT
    Global axisymmetric Euler flows with rotation
    11th 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 non-vanishing 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 EDT
    Coffee Break
    11th Floor Collaborative Space
Wednesday, October 27, 2021
Hamiltonian Methods in Dispersive and Wave Evolution Equations
  • 9:00 - 10:00 am EDT
    Professional Development: Job Applications in Academia
    Professional Development - 11th Floor Lecture Hall
  • 3:00 - 3:30 pm EDT
    Coffee Break
    11th Floor Collaborative Space
Thursday, October 28, 2021
Hamiltonian Methods in Dispersive and Wave Evolution Equations
  • 11:00 am - 12:30 pm EDT
    Post Doc/Graduate Student Seminar
    Post Doc/Graduate Student Seminar - 11th Floor Lecture Hall
  • 3:00 - 3:30 pm EDT
    Coffee Break
    11th Floor Collaborative Space
Friday, October 29, 2021
Hamiltonian Methods in Dispersive and Wave Evolution Equations
  • 3:00 - 3:30 pm EDT
    Coffee Break
    11th Floor Collaborative Space
Monday, November 1, 2021
Hamiltonian Methods in Dispersive and Wave Evolution Equations
  • 3:00 - 3:30 pm EDT
    Coffee Break
    11th Floor Collaborative Space
Tuesday, November 2, 2021
Hamiltonian Methods in Dispersive and Wave Evolution Equations
  • 3:00 - 3:30 pm EDT
    Coffee Break
    11th Floor Collaborative Space
Wednesday, November 3, 2021
Hamiltonian Methods in Dispersive and Wave Evolution Equations
  • 9:00 - 10:00 am EDT
    Professional Development: Hiring Process
    Professional Development - 11th Floor Lecture Hall
  • 3:00 - 3:30 pm EDT
    Coffee Break
    11th Floor Collaborative Space
Thursday, November 4, 2021
Hamiltonian Methods in Dispersive and Wave Evolution Equations
  • 11:00 am - 12:30 pm EDT
    Post Doc/Graduate Student Seminar
    Post Doc/Graduate Student Seminar - 11th Floor Lecture Hall
  • 3:00 - 3:30 pm EDT
    Coffee Break
    11th Floor Collaborative Space
Friday, November 5, 2021
Hamiltonian Methods in Dispersive and Wave Evolution Equations
  • 3:00 - 3:30 pm EDT
    Coffee Break
    11th Floor Collaborative Space
Monday, November 8, 2021
Hamiltonian Methods in Dispersive and Wave Evolution Equations
  • 3:00 - 3:30 pm EST
    Coffee Break
    11th Floor Collaborative Space
Tuesday, November 9, 2021
Hamiltonian Methods in Dispersive and Wave Evolution Equations
  • 3:00 - 3:30 pm EST
    Coffee Break
    11th Floor Collaborative Space
Wednesday, November 10, 2021
Hamiltonian Methods in Dispersive and Wave Evolution Equations
  • 9:00 - 10:00 am EST
    Professional Development: Papers and Journals
    Professional Development - 11th Floor Lecture Hall
  • 3:00 - 3:30 pm EST
    Coffee Break
    11th Floor Collaborative Space
Thursday, November 11, 2021
Hamiltonian Methods in Dispersive and Wave Evolution Equations
  • 11:00 am - 12:30 pm EST
    Post Doc/Graduate Student Seminar
    Post Doc/Graduate Student Seminar - 11th Floor Lecture Hall
  • 3:00 - 3:30 pm EST
    Coffee Break
    11th Floor Collaborative Space
Friday, November 12, 2021
Hamiltonian Methods in Dispersive and Wave Evolution Equations
  • 3:00 - 3:30 pm EST
    Coffee Break
    11th Floor Collaborative Space
Monday, November 15, 2021
Hamiltonian Methods in Dispersive and Wave Evolution Equations
  • 3:00 - 3:30 pm EST
    Coffee Break
    11th Floor Collaborative Space
Tuesday, November 16, 2021
Hamiltonian Methods in Dispersive and Wave Evolution Equations
  • 3:00 - 3:30 pm EST
    Coffee Break
    11th Floor Collaborative Space
Wednesday, November 17, 2021
Hamiltonian Methods in Dispersive and Wave Evolution Equations
  • 9:00 - 10:00 am EST
    Professional Development: Grant Proposals
    Professional Development - 11th Floor Lecture Hall
  • 3:00 - 3:30 pm EST
    Coffee Break
    11th Floor Collaborative Space
Thursday, November 18, 2021
Hamiltonian Methods in Dispersive and Wave Evolution Equations
  • 11:00 am - 12:30 pm EST
    Post Doc/Graduate Student Seminar
    Post Doc/Graduate Student Seminar - 11th Floor Lecture Hall
  • 3:00 - 3:30 pm EST
    Coffee Break
    11th Floor Collaborative Space
Friday, November 19, 2021
Hamiltonian Methods in Dispersive and Wave Evolution Equations
  • 3:00 - 3:30 pm EST
    Coffee Break
    11th Floor Collaborative Space
Thursday, December 2, 2021
Hamiltonian Methods in Dispersive and Wave Evolution Equations
  • 11:00 am - 12:30 pm EST
    Post Doc/Graduate Student Seminar
    Post Doc/Graduate Student Seminar - 11th Floor Lecture Hall

All event times are listed in ICERM local time in Providence, RI (Eastern Daylight Time / UTC-4).

All event times are listed in .

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. In-depth directions and transportation information are available on our travel page.
Lodging/Housing
Visiting ICERM for longer than a week-long workshop? ICERM staff works with participants to locate accommodations that fit their needs. Since short-term 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 world-renowned 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?
J-1 visa requested via ICERM staff
Eligible to be reimbursed
B-1 or Visa Waiver Business (WB) –if you already have either visa – contact ICERM staff for a visa specific invitation letter.
Ineligible to be reimbursed
B-2 or Visa Waiver Tourist (WT)
Already in the US?

F-1 and J-1 not sponsored by ICERM: obtain a letter approving reimbursement from the International Office of your home institution PRIOR to travel.

H-1B 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 non-U.S. or non-E.U. airlines
  • Flights on U.K. airlines
  • Seats in economy plus, business class, or first class
  • Change ticket fees of any kind
  • Multi-use bus passes
  • Meals or incidentals
Advance Approval Required
  • Personal car travel to ICERM from outside New England
  • Multiple-destination 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 one-way 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.

Associated Semester Workshops

Hamiltonian Methods and Asymptotic Dynamics
Image for "Hamiltonian Methods and Asymptotic Dynamics"