Invertible objects in stable homotopy theory

Irina Bobkova
Member; School of Mathematics
November 12, 2018
Computation of the stable homotopy groups of spheres is a long-standing open problem in algebraic topology. I will describe how chromatic homotopy theory uses localization of categories, analogous to localization for rings and modules, to split this problem into easier pieces, called chromatic levels. Each chromatic level can be understood using the theory of deformations of formal group laws. I will talk about recent results, and work in progress, at the second chromatic level.

Distinguishing fillings via dynamics of Fukaya categories

Yusuf Baris Kartal
Massachusetts Institute of Technology
November 12, 2018
Given a Weinstein domain $M$ and a compactly supported, exact symplectomorphism $\phi$, one can construct the open symplectic mapping torus $T_\phi$. Its contact boundary is independent of $\phi$ and thus $T_\phi$ gives a Weinstein filling of $T_0\times M$, where $T_0$ is the punctured 2-torus. In this talk, we will outline a method to distinguish $T_\phi$ from $T_0\times M$ using dynamics and deformation theory of their wrapped Fukaya categories.

Generic uniqueness of expanders with vanishing relative entropy

Felix Schulze
University College London
November 8, 2018

Abstract: We define a relative entropy for two expanding solutions to mean curvature flow of hypersurfaces, asymptotic to the same smooth cone at infinity. Adapting work of White and using recent results of Bernstein and Bernstein-Wang, we show that generically expanders with vanishing relative entropy are unique. This also implies that generically locally entropy minimizing expanders are unique. This is joint work with A. Deruelle.