School of Mathematics

Asymptotic spectra and their applications I

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.

Singularity and comparison theorems for metrics with positive scalar curvature

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.

Construction of hypersurfaces of prescribed mean curvature

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.

Semitoric families

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.