Motivic Classes of Varieties and Stacks with Applications to Higgs Bundles and More

Explore the theory of motivic classes of varieties and stacks through this mathematical seminar lecture that begins with the fundamental motivations for motivic classes arising from point counting over finite fields. Learn the precise definitions of motivic classes of varieties, with particular attention to the additional relations required in finite characteristic settings. Discover symmetric powers and motivic zeta functions as universal versions of local zeta functions. Delve into the specialized topic of motivic classes of stacks, examining explicit formulas for the motivic classes of moduli of Higgs bundles, and gain insight into ongoing research on the motivic classes of moduli of bundles with connections.