Events for 05/01/2023 from all calendars

Noncommutative Geometry Seminar

Time: 2:00PM - 3:00PM

Location: BLOC 302

Speaker: Jintao Deng, University of Waterloo

Title: The $K$-theory of Roe algebras and the coarse Baum-Connes conjecture

Abstract: The coarse Baum-Connes conjecture claims that a certain assembly is an isomorphism. It has important applications in the study of the existence of a metric with positive scalar curvature and the Novikov conjecture on the homotopy invariance of the higher signature on a manifold. In this talk, I will talk about the Roe algebras which encode the large-scale geometry of a metric space. The higher index of an elliptic operator is an element of the K-theory of this algebra. The coarse Baum-Connes conjecture provides an algorithm to compute its $K$-theory. I will talk about our recent result that the coarse Baum-Connes conjecture holds for the relative expanders constructed by Arzhantseva and Tessera which is not coarsely embeddable into Hilbert space. I will also talk about a recent result on the equivariant coarse Baum-Connes conjecture.

Colloquium

Time: 4:00PM - 5:00PM

Location: Bloc 117

Speaker: Galen Dorpalen-Barry

Description: Title: Cones of Hyperplane Arrangements

Abstract: Hyperplane arrangements dissect R^n into connected components called regions. A well-known theorem of Zaslavsky counts regions as a sum of nonnegative integers called Whitney numbers of the first kind. A generalization of this theorem counts regions within any cone defined as the intersection of a collection of halfspaces from the arrangement, leading to a notion of Whitney numbers for each cone. This talk concerns Whitney numbers for arrangements coming from reflection groups (the braid arrangement and Shi arrangements). In order to describe these Whitney numbers, we define the Varchenko-Gel’fand ring of a cone of an arbitrary arrangement and use techniques inspired by Gröbner bases to obtain a general presentation for this ring.