Dissertation Defense: "Noncommutative Borsuk-Ulam Theorems"

Abstract: I will present the highlights of my work on extending the Borsuk-Ulam theorem of algebraic topology into the world of C*-algebras, motivated by related theorems and conjectures of previous researchers. The classical Borsuk-Ulam theorem maintains that any odd, continuous map on a topological sphere must behave nontrivially with respect to certain invariants, and this statement may be rephrased (in multiple ways) in terms of function algebras on spheres. Certain of these translations remain true when the function algebra undergoes deformation processes.  Moreover, one version applies to any unital C*-algebra with a saturated action of a finite group, and the C*-algebraic point of view sheds light on improvements of classical results in the topological setting.

Hosts: John McCarthy, Spencer T. Olin Professor of Arts & Sciences and Xiang Tang, Professor of Mathematics.