Friday, October 27, 2023
10/27/2023 - 10:00am
In this talk I will explain my recent solution of the Halpern-Weaver Conjecture. The result is that a strip of paper that is 1 unit wide must be more than sqrt(3) units long in order for it to be smoothly folded into a paper Moebius band, and this bound is sharp. The proof is elemetary enough that I can explain the whole thing during the talk. I’ll also talk about lots of related unsolved problems.
10/27/2023 - 2:00pm
Abstract: For a long time, there has been a folklore conjecture, often attributed to Thurston, which asserts that every almost Fuchsian manifold is foliated by closed incompressible constant mean curvature (CMC) surfaces. In this talk I will discuss our recent work using the modified mean curvature flow to prove the existence of closed incompressible surfaces of constant mean curvature in a certain class of almost Fuchsian manifolds. As an application, we confirm this CMC foliation conjecture for such a class of almost Fuchsian manifolds. This is joint work with Zheng Huang and Zhou Zhang.