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.