Kyle Ormsby, Reed College

Abstract: After giving a historical overview of classical and topological Hochschild homology, I will introduce a motivic variant valued in the stable A^1-homotopy category. Over the field of complex numbers, computations reveal that motivic Hochschild homology of F_p exhibits a rich pattern of ``\tau-torsion'' elements. I will describe these computations and their significance, concluding with a no-go theorem regarding three potential motivic analogues of classical theorems. The talk will be accessible to those without prior experience in A^1-homotopy theory. This is joint work with Bjorn Dundas, Mike Hill, and Paul Arne Ostvaer.