Differential Geometry Seminar Series : Feng & Jiang -- Liquid Crystal Flows & Cheeger-Colding Theory

Venue: Carslaw AGR (829) 

Time: 11:30AM--1:30PM, 15/10/2019 

------------------------------------ 

Lecturer: Joe Feng (UQ) 

Title: Convergence of the Ginburg-Laudau approximation for nematic liquid crystal flows 

Abstract: The Ericksen-Leslie system models the hydrodynamic flow of the nematic type of
liquid crystal.  Under the so-called one-constant approximation with the vanishing
Leslie tensor, the Ericksen-Leslie system reduces to the Navier-Stokes equations coupled
with the harmonic map flow into spheres.  The classical approach is the Ginzburg-Landau
approximation of which the convergence is known as the Lin-Liu problem.  We will review
some developments, especially on the simplified system and discuss some recent progress
on the Lin-Liu problem for the general system.  

------------------------------------ 

Lecturer: Wenshuai Jiang (USyd) 

Title: Introduction to Cheeger-Colding theory about Ricci curvature and recent progress 

Abstract: in these serial seminars, we will focus on manifolds with lower Ricci
curvature bounds.  By studying the structure of Gromov-Hausdorff limit of a sequence of
manifolds with lower Ricci curvature, Cheeger-Colding obtained several important and
fundamental results about Ricci curvature.  It turns out that such theory has
significant applications to the existence of Kaehler-Einstein metrics, Ricci flow,
geometric groups and other related topics.  

The aim of theses seminars is systematically introducing Cheeger-Colding theory and
discussing its related applications.  At the end we will discuss recent progress by
Cheeger-Naber and a joint work with Cheeger-Naber.  

This is the sixth lecture for Jiang’s series.