Events for 05/13/2022 from all calendars

Noncommutative Geometry Seminar

Time: 08:00AM - 09:00AM

Location: ZOOM

Speaker: Bernd Ammann, University of Regensburg

Title: Yamabe constants, Yamabe invariants and Gromov-Lawson surgeries

Abstract: In this talk I want to study the (conformal) Yamabe constant of a closed Riemannian (resp. conformal) manifold and how it is affected by Gromov-Lawson type surgeries. This yields information about Yamabe invariants and their bordism invariance. So far the talk gives an overview over older results of mine in joint work with M. Dahl, N. Große, E. Humbert, and N. Otoba. A further consequence is that many results about the space of metrics with positive scalar curvature may be generalized to spaces of metrics with Yamabe constant above $t>0$. In particular we will present the following Chernysh-Walsh type result which is work in progress: if $N^n$ arises from $M^n$ by a surgery of dimension $k\in\{2,3,\ldots,n-3\}$, then a Gromov-Lawson type surgery construction defines a homotopy equivalence from the space of metrics on $M$ with Yamabe constant above $t\in (0,\Lambda_{n,k})$ to the corresponding space on $N$.

URL: Event link

Noncommutative Geometry Seminar

Time: 09:15AM - 10:15AM

Location: ZOOM

Speaker: Claude LeBrun, Stony Brook University

Title: Yamabe Invariants, Weyl Curvature, and the Differential Topology of 4-Manifolds

Abstract: The behavior of the Yamabe invariant, as defined in Bernd Ammann’s previous lecture, differs strangely in dimension 4 from what is seen in any other dimension. These peculiarities not only manifest themselves in the context of the usual scalar curvature, but also occur in connection with certain curvature quantities that are built out of the scalar and Weyl curvatures. In this lecture, I will explain how the Seiberg-Witten equations not only allow one compute the Yamabe invariant for many interesting 4-manifolds, but also give rise to other curvature inequalities. I will then point out applications of these results to the theory of Einstein manifolds, while also highlighting related open questions that have so far proved impervious to these techniques.

URL: Event link

Working Seminar on Banach and Metric Spaces

Time: 10:00AM - 11:30PM

Location: BLOC 306

Speaker: Chris Gartland, Texas A&M University

Title: Geometry of Lipschitz free spaces I

Geometry Seminar

Time: 4:00PM - 5:00PM

Location: Zoom

Speaker: Daniel Erman, University of Wisconsin Madison

Title: Matrix factorizations of generic polynomials

Abstract: Matrix factorizations provide a way to understand the complexity of a polynomial, and they arise in a wide array of mathematical areas. I’ll give an overview on matrix factorizations and the Buchweitz-Greuel-Schreyer Conjecture on the minimal rank of such a factorization. I’ll also discuss a recent proof of this conjecture for generic polynomials, which involves ultraproduct techniques.