University of Victoria

Tue 28 Jan 2020, 3:30pm
Diff. Geom, Math. Phys., PDE Seminar
PIMS Lounge, ESB

Selfsimilar blowup profiles for slightly supercritical nonlinear Schrödinger equations

PIMS Lounge, ESB
Tue 28 Jan 2020, 3:30pm4:30pm
Abstract
We construct radially symmetric selfsimilar blowup 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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Johns Hopkins University

Thu 20 Feb 2020, 3:30pm
Diff. Geom, Math. Phys., PDE Seminar
PIMS Lounge

Minimizers for the thin onephase free boundary problem

PIMS Lounge
Thu 20 Feb 2020, 3:30pm4:30am
Abstract
e consider the thin onephase free boundary problem, associated to minimizing a weighted Dirichlet energy of thefunction in the halfspace 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, 3:30pm4:30pm
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, 3:30pm4:30pm
Abstract
We will discuss Gradient flow structures in parabolic type PDEs and interface motions. Such structure introduces physical interpretations to timedependent PDEs in terms of energy dissipation, and allows a weak notion of globaltime solutions to nonlinear PDE problems. In broader terms, we will discuss minimizing movements, which approximates dissipative PDE systems with a discretetime 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.
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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, 3:30pm4:30pm
Abstract
We will discuss Gradient flow structures in parabolic type PDEs and interface motions. Such structure introduces physical interpretations to timedependent PDEs in terms of energy dissipation, and allows a weak notion of globaltime solutions to nonlinear PDE problems. In broader terms, we will discuss minimizing movements, which approximates dissipative PDE systems with a discretetime 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.
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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, 3:30pm4:30pm
Abstract
We will discuss Gradient flow structures in parabolic type PDEs and interface motions. Such structure introduces physical interpretations to timedependent PDEs in terms of energy dissipation, and allows a weak notion of globaltime solutions to nonlinear PDE problems. In broader terms, we will discuss minimizing movements, which approximates dissipative PDE systems with a discretetime 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.
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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, 3:30pm4:30pm
Abstract
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University of IndianaBloomington

Tue 7 Apr 2020, 3:30pm
Diff. Geom, Math. Phys., PDE Seminar
PIMS Lounge

TBA

PIMS Lounge
Tue 7 Apr 2020, 3:30pm4:30pm
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, 3:30pm4:30pm
Abstract
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Note for Attendees
The first lecture in the series of 3 lectures.