The inertia space of a compact Lie group action or, more generally, of a proper Lie groupoid, has an interesting singularity structure. Unlike the quotient space of the group action, respectively the groupoid, the inertia space cannot be stratified by orbit types, in general. In this talk, we explain this phenomenon. We also indicate a connection between the inertia space and the non-commutative geometry of the underlying groupoid in terms of basic relative Grauert-Grothendieck forms on the inertia space. We finally pose a conjecture about the Hochschild homology of the convolution algebra of the transformation groupoid of a compact Lie group action. The talk is based on joint work with with C. Farsi and Ch. Seaton (singularity theory of inertia groupoids) and with H. Posthuma and X. Tang (Grauert-Grothendieck forms and Hochschild homology of convolution algebras).
Inertia groupoids and a conjecture on the Hochschild homology of the convolution algebra of a compact Lie group action
Nov. 13, 2018 1pm (MATH 220)
Peter Mayr (CU)
X
We discuss Rosenberg's classification of maximal clones on finite sets and its consequences for the structure of finite algebras with WNU.
CSP maximal clones
Nov. 13, 2018 2pm (MATH 220)
Agnes Szendrei (CU Boulder) Cofinality Spectrum Problems, Part 1: A motivating example by Malliaris and Shelah
The theory of normal functions and the Hodge conjecture have their origin in the study of algebraic cycles by Lefschetz and Poincare. I will sketch the history of the subject and discuss some of my recent work on singularities of normal functions to the Hodge conjecture and the zero locus of a normal function to a conjectural filtration of Bloch and Beilinson.
Normal Functions and the Hodge Conjecture Sponsored by the Meyer Fund