Time: Wednesday, October 9th, 2024 , 13:30-14:30
Speaker: Xiaolong Han, Shanghai Institute for Mathematics and Interdisciplinary
Abstract: For closed hyperbolic 3-manifolds, Brock and Dunfield made a conjecture about the upper bound on the ratio of L2-norm to Thurston norm. We first talk about its proof assuming manifolds have bounded volume and describe some generic behavior. We then talk about the connection between the Thurston norm, best Lipschitz circle-valued maps, and maximal stretch laminations, building on the recent work of Daskalopoulos and Uhlenbeck, and Farre, Landesberg, and Minsky. We show that the distance between a level set and its translation is the reciprocal of the Lipschitz constant, bounded by the topological entropy of the pseudo-Anosov monodromy if M fibers.