BIMSA > SIMIS String Math Seminar SIMIS String Math Seminar Geometry of the Thurston norm
Geometry of the Thurston norm
Organizer
Veronica Pasquarella
Speaker
Xiaolong Han
Time
Wednesday, December 25, 2024 4:00 PM - 5:00 PM
Venue
SIMIS-1610
Abstract
We start by giving some definitions, examples and motivations for Thurston norms. We then talk about the connection between Thurston norms, L2-norms and minimal surfaces. We use the Thurston norm and the geometry of the level sets of a circle-valued maps to give a lower bound of the Thurston norm in terms of the length of the closed geodesic. We then explore the transverse geometry of circle-valued maps, which relate the Thurston norm with geodesic laminations of best Lipschitz maps. As an application, we relate the geometry of a fibered hyperbolic 3-manifold and the pseudo-Anosov entropy.
Speaker Intro
Xiaolong Han is an Assistant professor at Shanghai Institute of Mathematics and Interdisciplinary Sciences. Before joining SIMIS, he was a postdoc at Yau Mathematica Sciences Center at Tsinghua University. In 2021, he obtained his PhD degree from University of Illinois Urbana-Champaign. His research interest is low-dimensional manifolds and hyperbolic geometry.