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UBC Math
Wed 18 Jan 2017, 3:00pm SPECIAL
Department Colloquium
ESB 2012 (note special day)
Stability of elliptic Harnack inequality
ESB 2012 (note special day)
Wed 18 Jan 2017, 3:00pm-4:00pm

Abstract

Harnack inequalities have proved to be a powerful tool in PDE (regularity estimates), geometry (geometric flows) and probability (heat kernel estimates). In the early 1990s Grigor'yan and Saloff-Coste gave a characterisation of the parabolic Harnack inequality (PHI). This characterisation implies that PHI is stable under perturbations (quasi-isometries). In this talk, I will provide an introduction to Harnack inequalities and discuss the stability of elliptic Harnack inequality. 

This is joint work with Martin Barlow.

Note for Attendees

Tea and cookies will be served before this special colloquium.
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Hao Shen
Columbia University
Thu 19 Jan 2017, 3:30pm
Diff. Geom, Math. Phys., PDE Seminar
seminar has been cancelled.
CANCELLED: Scaling limits of open ASEP and ferromagnetic Glauber dynamics
seminar has been cancelled.
Thu 19 Jan 2017, 3:30pm-4:30pm

Abstract

 
We discuss two recent scaling limit results for discrete dynamics converging to stochastic PDEs. The first is the asymmetric simple exclusion process in contact with sources and sinks at boundaries, called Open ASEP.  We prove that under weakly asymmetric scaling the height function converges to the KPZ equation with Neumann boundary conditions. The second is the Glauber dynamics of the Blume-Capel model (a generalization of Ising model), in two dimensions with Kac potential. We prove that the averaged spin field converges to the stochastic quantization equations. The main purpose of this talk is to discuss the general issues one needs to address when passing from discrete to continuum, the common challenge in the proofs of such scaling limit theorems, and how we overcome these difficulties in the two specific models. (Based on joint works with Ivan Corwin and Hendrik Weber)
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Hao Shen
Columbia University
Fri 20 Jan 2017, 3:00pm
Department Colloquium
seminar has been cancelled.
CANCELLED: Singular Stochastic Partial Differential Equations - How do they arise and what do they mean?
seminar has been cancelled.
Fri 20 Jan 2017, 3:00pm-4:00pm

Abstract

 
Systems with random fluctuations are ubiquitous in the real world. Stochastic PDEs are default models for these random systems, just as PDEs are default models for deterministic systems. However, a large class of such stochastic PDEs were poorly understood until very recently: the presence of very singular random forcing as well as nonlinearities render it challenging to interpret what one even means by a ``solution". The recent breakthroughs by M. Hairer, M. Gubinelli and other researchers including the speaker not only established solution theories for these singular SPDEs, but also led to an explosion of new questions. These include scaling limits of random microscopic models, development of numerical schemes, ergodicity of random dynamical systems and a new approach to quantum field theory. In this talk we will discuss the main ideas of the recent solution theories of singular SPDEs, and how these SPDEs arise as limits of various important physical models.
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Toronto
Mon 23 Jan 2017, 3:00pm SPECIAL
Institute of Applied Mathematics
ESB 2012
TBA
ESB 2012
Mon 23 Jan 2017, 3:00pm-4:00pm

Abstract

 

Note for Attendees

Reception preceding the talk in ESB 4133 (the PIMS lounge). This is part of the IAM/PIMS distinguished colloquium series. 
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