# Events for 09/23/2020 from all calendars

## Geometry Seminar

Time: 11:00AM - 12:00PM

Location: zoom

Speaker: Filip Rupniewski, IMPAN

Title: Cactus rank and identification of secant inside cactus varieties

Abstract: Every secant variety is contained in the corresponding cactus variety. However, according to our knowledge, there is no explicit equation of the secant variety which does not vanish on the cactus variety. I will present an algorithm for deciding if a given point in the cactus variety belongs to the secant variety in some special cases. I will also show the theorem for calculating the cactus rank of forms divisible by a large power of a linear form which allowed us to design the mentioned algorithm. Based on a joint work with M. Gałązka and T. Mańdziuk.

## Noncommutative Geometry Seminar

Time: 1:00PM - 2:00PM

Location: Zoom 942810031

Speaker: Rudolf Zeidler, University of Göttingen

Title: Scalar curvature comparison via the Dirac operator

Abstract: In recent years, Gromov proposed studying the geometry of positive scalar curvature (abbreviated by "psc") via various metric inequalities. In particular, he proposed the following conjecture: Let $M$ be a closed manifold which does not admit a metric of psc. Then for any Riemannian metric on $V = M \times [-1,1]$ of scalar curvature $\geq n(n-1)$ the estimate $d(\partial_- V, \partial_+ V) \leq 2\pi/n$ holds, where $\partial_\pm V = M \times \{\pm 1\}$ and $n = \dim V$. Previously, Rosenberg and Stolz conjectured similarly that if $M$ does not admit psc, then $M \times \mathbb{R}$ does not admit a complete metric of psc and $M \times \mathbb{R}^2$ does not admit a complete metric of uniformly psc. In this talk, we will discuss a new geometric phenomenon consisting of a precise quantitative interplay between distance estimates and scalar curvature bounds which underlies these three conjectures. We will explain that this phenomenon arises if $M$ admits an obstruction to psc using the index theory of Dirac operators.

## Topology Seminar

Time: 4:00PM - 5:00PM

Location: Zoom

Speaker: Tianqi Wu, Harvard CMSA

Title: Koebe circle domain conjecture and the Weyl problem in hyperbolic 3-space

Abstract: In 1908, Paul Koebe conjectured that every open connected set in the plane is conformally diffeomorphic to an open connected set whose boundary components are either round circles or points. The Weyl problem, in the hyperbolic setting, asks for isometric embedding of surfaces of curvature at least -1 into the hyperbolic 3-space. We show that there are close relationships among the Koebe conjecture, the Weyl problem and the work of Alexandrov and Thurston on convex surfaces. This is a joint work with Feng Luo.