• ICERM's lecture hall during an evening public lecture

    Welcome to ICERM

    The Institute for Computational and Experimental Research in Mathematics

  • ICERM's home (121 South Main Street) at night

    Welcome to ICERM

    The Institute for Computational and Experimental Research in Mathematics

  • ICERM's lecture hall

    Welcome to ICERM

    The Institute for Computational and Experimental Research in Mathematics

  • ICERM's conference room

    Welcome to ICERM

    The Institute for Computational and Experimental Research in Mathematics

This Week at ICERM

November 28, 2021

There are no events currently scheduled for November 28th.

November 29, 2021
  • 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
November 30, 2021
  • 9:30 - 10:20 am EST
    Asymptotic stability of the sine-Gordon kink under odd perturbations.
    11th Floor Lecture Hall
    • Jonas Luhrmann, Texas A&M University
    Abstract
    The sine-Gordon model is a classical nonlinear scalar field theory that was discovered in the 1860s in the context of the study of surfaces with constant negative curvature. Its equation of motion features soliton solutions called kinks and breathers, which play an important role for the long-time dynamics. I will begin the talk with an introduction to classical 1D scalar field theories and the asymptotic stability problem for kinks. After surveying recent progress on the problem, I will present a joint work with W. Schlag on the asymptotic stability of the sine-Gordon kink under odd perturbations. Our proof is perturbative and does not rely on the complete integrability of the sine-Gordon model. Key aspects are a super-symmetric factorization property of the linearized operator and a remarkable non-resonance property of a variable coefficient quadratic nonlinearity.
  • 10:30 - 11:20 am EST
    Gagliardo-Nirenberg-Sobolev inequality in Dirichlet spaces.
    11th Floor Lecture Hall
    • Patricia Alonso Ruiz, Texas A&M University
    Abstract
    The Gagliardo-Nirenberg-Sobolev inequality in R^n is a classical Sobolev embedding with many applications in the theory of PDEs and calculus of variations. In this talk, I will present the full scale of Gagliardo-Nirenberg-Sobolev inequalities in the more general framework of Dirichlet spaces with (sub-)Gaussian heat kernel estimates. In particular, we will discover that the optimal exponent in the embedding not only depends on the Hausdorff dimension of the underlying space, but also on other invariants. To this end, I will use a recent approach to (1,p)-Sobolev spaces via heat semigroups inspired by ideas going back to work of de Giorgi and Ledoux. If time permits, I will outline some results and conjectures concerning further Sobolev embeddings in this setting. The talk is based on joint work with F. Baudoin.
  • 11:30 am - 12:20 pm EST
    Birkhoff normal forms for Hamiltonian PDEs in their energy space
    11th Floor Lecture Hall
    • Benoît Grébert, University of Nantes
    Abstract
    We study the long time behavior of small solutions of semi-linear dispersive Hamiltonian partial differential equations on confined domains. Provided that the system enjoys a new non-resonance condition and a strong enough energy estimate, we prove that its low super-actions are almost preserved for very long times. Roughly speaking, it means that, only modes with the same linear frequency will be able to exchange energy in a reasonable time. Contrary to the previous existing results, we do not require the solutions to be especially smooth. They only have to live in the energy space. We apply our result to nonlinear Klein-Gordon equations in dimension $d=1$ and nonlinear Schrödinger equations in dimension $d\leq 2$.
  • 3:00 - 3:30 pm EST
    Coffee Break
    11th Floor Collaborative Space
December 1, 2021
  • 3:00 - 3:30 pm EST
    Coffee Break
    11th Floor Collaborative Space
December 2, 2021
  • 3:00 - 3:30 pm EST
    Coffee Break
    11th Floor Collaborative Space
December 3, 2021
  • 3:00 - 3:30 pm EST
    Coffee Break
    11th Floor Collaborative Space
December 4, 2021

There are no events currently scheduled for December 4th.

All event times are listed in ICERM local time in Providence, RI (Eastern Standard Time / UTC-5).

All event times are listed in .

Upcoming Programs

Hamiltonian Methods and Asymptotic Dynamics
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Braids
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Research Community in Algebraic Combinatorics
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Connect with ICERM

Brown University's Impact: Research at Brown magazine
Brown's ICERM reimagines what mathematics can be

May 28, 2021 - ICERM featured in Brown University's Impact: Research at Brown magazine

Kavita Ramanan
Kavita Ramanan named a newly elected member of The American Academy of Arts & Sciences

April 21, 2021 - The American Academy of Arts & Sciences announced today that Kavita Ramanan, Brown University's Roland George Dwight Richardson University Professor of Applied Mathematics and an ICERM co-PI, was elected as a new member.

New ICERM Deputy Director, Misha Kilmer

March 31, 2021 - ICERM is pleased to announce that Misha Kilmer is joining ICERM as a Deputy Director, effective July 1, 2021.