Kommende Vorträge

Seminar webpage: https://wrreeves.github.io/Unterseminar/index.html

“In 90s Nakajima and Grojnowski identified the total cohomology of the Hilbert schemes of points on a smooth projective surface with the Fock space representation of the Heisenberg algebra associated to its cohomology lattice. Following a conjecture by Grojnowski, Segal and Wang extended this to any smooth projective variety by replacing Hilbert schemes with symmetric powers and cohomology with equivariant K-theory. Later, Krug lifted this to the level of derived categories.

We discuss asymptotic counting problems related to the orbit length and the decomposition of orbits into primitive ones, for the action of an endomorphism of an arbitrary algebraic group (such as an elliptic curves, torus, unipotent group,…) over the algebraic closure of a finite field. We present analogues of classical results from number theory related to Mertens’s second theorem and the Erdös-Kac theorem. By making some examples completely explicit, cute transcendental numbers akin the Kempner number make their appearance. (Joint work with Sun Woo Park.)