## Applying History in Real Time: A Tale of Two Crises

Niall Ferguson

Milbank Family Senior Fellow, Hoover Institution, Stanford University

October 10, 2018

Niall Ferguson

Milbank Family Senior Fellow, Hoover Institution, Stanford University

October 10, 2018

Brian Freidin

Brown University; Visitor, School of Mathematics

October 10, 2018

Olga Turanova

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

October 10, 2018

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.

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.

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.