Rok Gregorič: Representations, loop spaces, and Riemann-Roch

Datum objave: 19. 5. 2017
Seminar za geometrijo
Ponedeljek, 22.5.2017, ob 10.15, v predavalnici 3.06 na Jadranski 21
The projection formula is one of the most basic results of representation theory. In this lecture, we shall see how rephrasing it in the language of stacks and adding a sprinkle of derived algebraic geometry allows us to predict the form of the celebrated Riemann-Roch theorem. This gives a nice alternative and quite geometric point of view on this classical cornerstone of intersection theory. We will elaborate on the relationship to Hochschild homology, generalized notions of trace, and free loop spaces, indicating an approach to Riemann-Roch of Ben-Zvi and Nadler.

This lecture will be rather informal, and concentrated on pointing out some topology-inspired ideas which have become increasingly prominent in algebraic geometry in the last few decades.