Type: Seminar

Distribution: World

Expiry: 25 Nov 2019

CalTitle1: Liquid Crystal Flows & Cheeger-Colding Theory

Auth: zhangou@pzhangou3.pc (assumed)

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.