School of Mathematics

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.