Events for 03/02/2023 from all calendars

Noncommutative Geometry Seminar

Time: 09:30AM - 10:30AM

Location: ZOOM

Speaker: Simon Brendle, Columbia

Title: Scalar curvature rigidity of polytopes

Abstract: We will discuss a scalar curvature rigidity theorem for convex polytopes. The proof uses the Fredholm theory for Dirac operators on manifolds with boundary, as well as an estimate due to Fefferman and Phong.

URL: Event link

Noncommutative Geometry Seminar

Time: 10:45AM - 11:45AM

Location: ZOOM

Speaker: Florian Johne, Columbia

Title: Intermediate curvature and a generalization of Geroch's conjecture

Abstract: In this talk we explain a non-existence result for metrics of positive m-intermediate curvature (a notion of curvature reducing to positive Ricci curvature for m=1, and positive scalar curvature for m=n−1) on closed orientable manifolds with topology Nn=Mn−m×Tm for n≤7. Our proof uses a slicing constructed by minimization of weighted areas, the associated stability inequality, and estimates on the gradients of the weights and the second fundamental form of the slices. This is joint work with Simon Brendle and Sven Hirsch.

Number Theory Seminar

Time: 2:30PM - 3:30PM

Location: BLOC 302

Speaker: Larry Rolen, Vanderbilt University

Title: Recent problems in partitions and other combinatorial functions

Abstract: In this talk, I will discuss recent work, joint with a number of collaborators, on analytic and combinatorial properties of the partition and related functions. This includes work on recent conjectures of Stanton, which aim to give a deeper understanding into the "rank" and "crank" functions which "explain" the famous partition congruences of Ramanujan. I will describe progress in producing such functions for other combinatorial functions using the theory of modular and Jacobi forms and recent connections with Lie-theoretic objects due to Gritsenko-Skoruppa-Zagier. I will also discuss how analytic questions about partitions can be used to study Stanton's conjectures, as well as recent conjectures on partition inequalities due to Chern-Fu-Tang and Heim-Neuhauser, which are related to the Nekrasov-Okounkov formula.