Euler Classes, Pairings, and Duality

Explore a 45-minute conference talk by Kate Ponto from the University of Kentucky, delving into the concept of Euler classes, pairings, and duality. Discover how classical Morita equivalence defines an Euler class for modules, generalizing the Euler characteristic for spaces. Gain insights into the fundamental structure of the Euler class and its compatibility with a familiar pairing on Hochschild homology. Examine different forms of duality and their implications in homotopy theory. This talk was part of the Conference on Homotopy Theory with Applications to Arithmetic and Geometry held at the Fields Institute from June 27-30, 2022.