Geodesics on SO(n) and an Infinite Class of Equilibria of a Weighted Dirichlet Energy

Topic: 
Geodesics on SO(n) and an Infinite Class of Equilibria of a Weighted Dirichlet Energy
Date & Time: 
Thursday, March 28, 2019 - 11:00 to 12:00
Speaker: 
George Morrison, NYU Shanghai
Location: 
Room 264, Geography Building, Zhongbei Campus, East China Normal University

Abstract:
The goal here is to classify an infinite class of rotationally-invariant equilibria of a weighted Dirichlet energy, subject to an incompressibility constraint on the solution. Specifically we consider as candidate solutions “whirl” maps, which are uniquely characterised by a oneparameter family of curves over the compact Lie group SO(n). A study of irrotational vector fields leads to a striking difference in the solution of this problem depending on whether the underlying spatial dimension is odd or even.

Biography:
George Morrison is a Postdoctoral Fellow at NYU Shanghai. Prior to joining NYU Shanghai in January 2019, George studied at the University of Sussex as an undergraduate and postgraduate, culminating in the award of a Ph.D. in the fall of 2018. His main research interests are calculus of variations and partial differential equations.

 

Seminar by the NYU-ECNU Institute of Mathematical Sciences at NYU Shanghai