Coffee and bagels for participants start at 9:30.

We plan to start at 10am.

We plan to end at 4pm.

Higher-rank graphs (k-graphs) are a combinatorial model for C*-algebras; indeed, much of the structure of k-graph C*-algebras is encoded in the underlying combinatorial data of the k-graph.  However, different k-graphs can give rise to isomorphic or Morita equivalent C*-algebras.  In this talk, we present several ways to modify the structure of a k-graph which preserve the Morita equivalence class of the associated C*-algebra.  Our constructions are inspired by the analogous work for graph C*-algebras of Bates and Pask, as well as by the textile system approach to describing k-graphs.  This is joint work with C. Eckhardt, K. Fieldhouse, D. Gent, I. Gonzales, and D. Pask.

Given a Hilbert C*-correspondence over C(X), one can construct the associated Cuntz-Pimsner algebra. In the case that the correspondence is full, nonperiodic, and minimal, the resulting C*-algebra is simple and unital. An example of such a correspondence is obtained by taking the right Hilbert C(X)-module of continuous sections of a vector bundle over X and twisting the left multiplication by a minimal homeomorphism. As is the case of crossed products by minimal homeomorphisms, one can identify "orbit-breaking" C*-subalgebras. In this talk I will discuss these Cuntz--Pimsner C*-algebras and their orbit-breaking subalgebras, their relationship to one another, and when they can be classified by Elliott invariants. This is joint work with Adamo, Archey, Forough, Georgescu, Jeong and Viola.

In this talk I will explain how to define so-called “higher genera” for a proper cocompact action of a Lie group satisfying some additional assumptions. These higher genera are numbers, whose definition is inspired by index theory for Dirac type operators in Noncommutative Geometry, and generalize the signature and A-hat genus for compact manifolds. The main theorem states that the higher signatures are equivariant homotopy invariants and that vanishing of the higher A-hat numbers is a necessary condition for the existence of an invariant spin structure together with a metric of positive scalar curvature. This talk is based on joint work with P. Piazza.

In 1898 Ladislaus Bortkiewicz showed that the number of Prussian soldiers killed accidentally by horse kicks in a year follows a Poisson distribution. Since then the Poisson distribution and Poisson point processes have found numerous applications in engineering, physics, finance, biology, ecology, etc. We will ignore almost all of these and instead look at the Poisson process in random geometric graphs and random linear operators.

TBA

One of the most surprising discoveries in 4-manifold topology was the existence of smooth manifolds homeomorphic, but not diffeomorphic, to Euclidean 4-space. For fundamental reasons, this phenomenon can only occur in 4 dimensions. We will survey the subject, from its origin to recent developments regarding symmetries of such manifolds. This talk should be accessible to a broad audience.

The idea behind obstruction theory is that, given a fiber bundle, the existence of a section is determined by a particular cohomology class of the base space. This class is an obstruction in the sense that if it is zero in the cohomology ring, then a section exists. In this talk, we will consider the particular problem of finding linearly independent sections of vector bundles. This problem turns out to be equivalent to finding a single section of an associated bundle (Stiefel bundle). We will find that the corresponding obstruction to the existence of this section generally lies in a 'twisted' version of cohomology.