Candace Bethea (University of South Carolina): The Compactly Supported A^1-Euler Characteristic and Hochschild Homology

In this talk I will discuss joint work with Niny Arcilla Maya, Morgan Opie, Kirsten Wickelgren, and Inna Zakharevich in which we define a compactly supported motivic Euler characteristic and show it agrees with previous definitions as well as defines a homomorphism from K_0(Var/k) to the Grothendieck-Witt group of k in characteristic 0. In the first half of the seminar I will talk about the A^1 Euler characteristic and results of Levine-Raskit and Bachmann-Wickelgren on how to compute it. In the second half of the seminar I will talk about our computation using the Hochschild Homology of a smooth scheme, the benefits of defining the Euler characteristic in this way, and if time allows an example of how one might try to go about proving the main theorem in a different way.