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 Events
Yakine Bahri
University of Victoria
Tue 28 Jan 2020, 3:30pm
Diff. Geom, Math. Phys., PDE Seminar
PIMS Lounge, ESB
Self-similar blow-up profiles for slightly supercritical nonlinear Schrödinger equations
PIMS Lounge, ESB
Tue 28 Jan 2020, 3:30pm-4:30pm

Abstract

We construct radially symmetric self-similar blow-up profiles for the mass supercritical nonlinear Schrödinger equation with nonlinear exponent close to the mass critical case and for any space dimension. These profiles bifurcate from the ground state solitary wave. In this talk, we present the argument which relies on the matched asymptotics method and we derive an exponentially smallness condition on the Sobolev critical exponent as conjectured by Sulem and Sulem in 1997.

This is a joint work with Yvan Martel and Pierre Raphaël.
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Yannick Sire
Johns Hopkins University
Thu 20 Feb 2020, 3:30pm
Diff. Geom, Math. Phys., PDE Seminar
PIMS Lounge
Minimizers for the thin one-phase free boundary problem
PIMS Lounge
Thu 20 Feb 2020, 3:30pm-4:30am

Abstract

 e consider the thin one-phase free boundary problem, associated to minimizing a weighted Dirichlet energy of thefunction in the half-space plus the area of the positivity set of that function restricted to the boundary. I will provide a rather complete picture of the (partial ) regularity of the free boundary, providing content and structure estimates on the singular set of the free boundary when it exists. All of these results hold for the full range of the relevant weight related to an anomalous diffusion on the boundary. The approach does not follow the standard one introduced in the seminal work of Alt and Caffarelli. Instead, the nonlocal nature of the distributional measure associated to a minimizer necessitates arguments which are less reliant on the underlying PDE. This opens several directions of research that I will ltry to describe. 
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University of California, Davis
Tue 25 Feb 2020, 3:30pm
Diff. Geom, Math. Phys., PDE Seminar
PIMS Lounge, ESB
TBA
PIMS Lounge, ESB
Tue 25 Feb 2020, 3:30pm-4:30pm

Abstract

TBA
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UCLA
Tue 3 Mar 2020, 3:30pm SPECIAL
Diff. Geom, Math. Phys., PDE Seminar / PIMS Seminars and PDF Colloquiums
PIMS lounge
PIMS distinguished visitor minicourse: Gradient flows and minimizing movements. Lecture 1
PIMS lounge
Tue 3 Mar 2020, 3:30pm-4:30pm

Abstract

We will discuss Gradient flow structures in parabolic type PDEs and interface motions. Such structure introduces physical interpretations to time-dependent PDEs in terms of energy dissipation, and allows a weak notion of global-time solutions to nonlinear PDE problems. In broader terms, we will discuss minimizing movements, which approximates dissipative PDE systems with a discrete-time optimization problem. Lecture 1 will be a general introduction. Lecture 2 and 3 will discuss specific examples of minimizing movements: the mean curvature flow and nonlinear diffusions with Darcy's law.

Note for Attendees

 The first lecture in the series of 3 lectures. 
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UCLA
Thu 5 Mar 2020, 3:30pm SPECIAL
Diff. Geom, Math. Phys., PDE Seminar / PIMS Seminars and PDF Colloquiums
PIMS lounge
PIMS distinguished visitor minicourse: Gradient flows and minimizing movements. Lecture 2.
PIMS lounge
Thu 5 Mar 2020, 3:30pm-4:30pm

Abstract

We will discuss Gradient flow structures in parabolic type PDEs and interface motions. Such structure introduces physical interpretations to time-dependent PDEs in terms of energy dissipation, and allows a weak notion of global-time solutions to nonlinear PDE problems. In broader terms, we will discuss minimizing movements, which approximates dissipative PDE systems with a discrete-time optimization problem. Lecture 1 will be a general introduction. Lecture 2 and 3 will discuss specific examples of minimizing movements: the mean curvature flow and nonlinear diffusions with Darcy's law.

Note for Attendees

  The second lecture in the series of 3 lectures. 
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UCLA
Tue 10 Mar 2020, 3:30pm SPECIAL
Diff. Geom, Math. Phys., PDE Seminar / PIMS Seminars and PDF Colloquiums
PIMS lounge
PIMS distinguished visitor minicourse: Gradient flows and minimizing movements. Lecture 3.
PIMS lounge
Tue 10 Mar 2020, 3:30pm-4:30pm

Abstract

We will discuss Gradient flow structures in parabolic type PDEs and interface motions. Such structure introduces physical interpretations to time-dependent PDEs in terms of energy dissipation, and allows a weak notion of global-time solutions to nonlinear PDE problems. In broader terms, we will discuss minimizing movements, which approximates dissipative PDE systems with a discrete-time optimization problem. Lecture 1 will be a general introduction. Lecture 2 and 3 will discuss specific examples of minimizing movements: the mean curvature flow and nonlinear diffusions with Darcy's law.

Note for Attendees

  The third lecture in the series of 3 lectures. 
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Kanazawa University, Japan
Tue 17 Mar 2020, 3:30pm
Diff. Geom, Math. Phys., PDE Seminar
PIMS lounge
TBA
PIMS lounge
Tue 17 Mar 2020, 3:30pm-4:30pm

Abstract

 
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Peter Sternberg
University of Indiana-Bloomington
Tue 7 Apr 2020, 3:30pm
Diff. Geom, Math. Phys., PDE Seminar
PIMS Lounge
TBA
PIMS Lounge
Tue 7 Apr 2020, 3:30pm-4:30pm

Abstract

 
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UC Irvine
Thu 18 Mar 2021, 3:30pm SPECIAL
Diff. Geom, Math. Phys., PDE Seminar
TBA
TBA
TBA
Thu 18 Mar 2021, 3:30pm-4:30pm

Abstract

 
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