## Elliptic/Harmonic measures and the geometry of domains

Zihui Zhao

University of Washington; Member, School of Mathematics

October 5, 2018

Zihui Zhao

University of Washington; Member, School of Mathematics

October 5, 2018

Jeroen Zuiddam

Member, School of Mathematics

October 5, 2018

Fernando Marquez

Princeton University

October 8, 2018

In this talk I will survey recent advances on the existence theory of minimal hypersurfaces from the variational point of view. I will discuss what we know, what we do not know and point to future directions. This is based on joint works with Andre Neves.

Joseph Palmer

Rutgers University

October 8, 2018

Semitoric systems are a type of 4-dimensional integrable system which has been classified by Pelayo-Vu Ngoc in terms of five invariants, one of which is a family of polygons generalizing the Delzant polygons which classify 4-dimensional toric integrable systems. In this talk we present one-parameter families of integrable systems which are semitoric at all but finitely many values of the parameter, which we call semitoric families, with the goal of developing a strategy to find a semitoric system associated to a given partial list of semitoric invariants.

Jeroen Zuiddam

Member, School of Mathematics

October 9, 2018

These two talks will introduce the asymptotic rank and asymptotic subrank of tensors and graphs - notions that are key to understanding basic questions in several fields including algebraic complexity theory, information theory and combinatorics.

Matrix rank is well-known to be multiplicative under the Kronecker product, additive under the direct sum, normalized on identity matrices and non-increasing under multiplying from the left and from the right by any matrices. In fact, matrix rank is the only real matrix parameter with these four properties.

Chao Li

Stanford University; Visitor, School of Mathematics

October 9, 2018

Following a program proposed by Gromov, we study metric singularities of positive scalar curvature of codimension two and three. In addition, we describe a comparison theorem for positive scalar curvature that is captured by polyhedra. Part of this talk is based on joint work with C. Mantoulidis.

Jonathan Zhu

Harvard University; Visitor, School of Mathematics

October 9, 2018

We'll describe a joint project with X. Zhou in which we use min-max techniques to prove existence of closed hypersurfaces with prescribed mean curvature in closed Riemannian manifolds. Our min-max theory handles the case of nonzero constant mean curvature, and more recently a generic class of smooth prescription functions, without assuming a sign condition.

Gregg Hallinan

California Institute of Technology

October 9, 2018

Olga Turanova

University of California, Los Angeles; Visitor, School of Mathematics

October 10, 2018

Brian Freidin

Brown University; Visitor, School of Mathematics

October 10, 2018