DubTop Seminar: Motivic classifying spaces

The integral Hodge conjecture was famously disproved by Atiyah and Hirzebruch, who found a counterexample in the cohomology of the classifying space of a certain finite group. Following a question proposed by Totaro in his 2014 book, it is natural to ask whether analogous phenomena occur in the motivic setting. In this talk, I will study motivic classifying spaces in richer motivic cohomology theories, including algebraic K-theory and hermitian K-theory. This is joint work with Prerna Dhankhar, Rebecca Field, Arjun Nigam, and J.D. Quigley.