School of Mathematics

Morse-Theoretic Aspects of the Willmore Energy

Alexis Michelat
ETH Zurich
November 13, 2018
We will present the project of using the Willmore elastic energy as a quasi-Morse function to explore
the topology of immersions of the 2-sphere into Euclidean spaces and explain how this relates to the
classical theory of complete minimal surfaces with finite total curvature.

This is partially a joint work in collaboration with Tristan Rivière.

Translators for Mean Curvature Flow

David Hoffman
Stanford University
November 13, 2018
A translator for mean curvature flow is a hypersurface $M$ with the property that translation is a mean curvature flow. That is, if the translation is
$t\rightarrow M+t\vec{v}$, then the normal component of the velocity vector $\vec{v}$ is equal to the mean curvature $\vec{ H}$. I will discuss recent joint work with Tom Ilmanen, Francisco Martin and Brian White, specifically our classification of the the complete translators in $R^3$ that are graphical, and the construction of new families of complete translators that are not graphical.

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.

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.

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.

Recent gluing constructions in Geometry and the gluing methodology

Nicos Kapouleas
Brown University; Member, School of Mathematics
November 7, 2018

Abstract: I will first concentrate on doubling gluing constructions for minimal surfaces, including a recent construction for free boundary minimal surfaces in the unit ball (with D. Wiygul: arXiv:1711.00818).


I will then discuss the Linearized Doubling methodology and its applications so far (J.  Differential Geom. 106:393-449, 2017; and with P. McGrath: arXiv:1707.08526),

and some further ongoing work expanding the scope of these methods to new cases.