I'm going to talk about an old question of van Douwen: Are the shift map and its inverse conjugate in the automorphism group of P($\omega$)/fin? By the late 1980's, van Douwen and Shelah proved that it is consistent they are not conjugate. Specifically, any automorphism witnessing their conjugacy would need to be nontrivial (van Douwen), but it is consistent that all automorphisms are trivial (Shelah). In this talk I'm going to discuss the recently-proven complementary result: it is consistent that the shift map and its inverse are conjugate and, in fact, it follows from CH.

Does P($\omega$)/fin know its right hand from its left?

Tue, Apr. 2 2:30pm (MATH 3…

Lie Theory

Carl Mautner (UC Riverside)

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The Schur algebra is a finite-dimensional algebra that relates the representation theory of symmetric and general linear groups. In joint work with Tom Braden we introduce a new algebra we call the Hilbert Schur algebra, which is also finite-dimensional and has the Schur algebra as a quotient. I will describe this algebra, our motivation for defining it, and some of its interesting algebraic and combinatorial properties.

Hilbert Schur algebras Sponsored by the Meyer Fund

Together we will watch and discuss some introductory and overview materials covering knot theory from a graduate topology level

An introduction to knot theory

Tue, Apr. 2 10:10pm (MATH …

Functional Analysis

Rufus Willett (University of Hawaii)

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The HK conjecture predicts an isomorphism between the homology of certain groupoids, and the K-theory of their C*-algebras. On the other hand, the Baum-Connes conjecture predicts a topological computation of the K-theory of groupoid C*-algebras. Both conjectures are wrong: there are counterexamples to the HK conjecture due to Scarparo, Deeley, Ortega-Scarparo, and Chaiser; and to the Baum-Connes conjecture due to Higson-Lafforgue-Skandalis.

I will explain some interactions between these two conjectures, in particular focusing on the precise sense in which Baum-Connes predicts that HK is wrong, and how one might try to fix these issues. I will not assume any prior knowledge of the HK or Baum-Connes conjecture, and will focus on the case of group actions rather than general groupoids (for simplicity).

Some of this is based on joint work with Christian Bönicke, Clément Dell'Aiera, and Jamie Gabe; some on joint work with Robin Deeley; and some on work of Valerio Proietti and Makoto Yamashita (that I had nothing to do with).

The HK and Baum-Connes conjectures Sponsored by the National Science Foundation