Mathematics and Physics Seminar Series

AnnouncingAnnouncing

A Seminar Presentation

on Friday

February 16, 2018

from 3:00 pm - 3:45 pm in

North Hall 104

at The University of New Haven

Brownian motion on spaces with varying

dimension

— Dr. Shuwen Lou

Postdoctoral Fellow

Department of Statistical Sciences

University of Toronto

Abstract: The ﬁrst part of this talk will be an introduction to the relationship between

electrical networks in physics and Dirichlet forms. As a matter of fact, Dirichlet forms are

sometimes called “energy forms” because they characterize the energy consumed by electri-

cal networks when they are charged. In particular, we give the Dirichlet form characterization

for electrical networks with shorting. In the second part, we present a class of probabilistic

models of our interest: Brownian motion constructed on spaces with varying dimension, us-

ing the idea of “shorting”. Brownian motion on spaces with varying dimension has an intrinsic

interplay with the geometry of the underlying spaces, and therefore reveals many non-trivial

and interesting phenomena. We give an overview of their properties with an emphasis on the

two-sided heat kernel estimates. (This talk is based on my joint work with Zhen-Qing Chen.)

Fur ther Information

For further information, please contact Dr. Yasanthi Kottegoda at the Department of Mathematics and Physics,

Ofﬁce: Maxcy 315, 203-932-1206, YKottegoda@newhaven.edu.