MS Seminar (Mathematics - String Theory)

Speaker: Mikhail Kapranov (Yale University)
Title: Cubic relations in Hall algebras and roots of zeta functions.
Date (JST): Wed, Aug 15, 2012, 15:30 - 17:00
Place: Seminar Room A
Abstract: The Hall algebra is an associative algebra that can be associated to any abelian or exact category with appropriate finiteness properties. The case of the category of vector bundles over a curve over a finite field and its analog for number fields has interesting arithmetic interpretation. It turns out that the space of cubic relations among a natural system of generators (i.e. a certain algebraic homology space of the Hall algebra) is identified with the space spanned by the zeroes of the zeta function of the curve (or of the number field). Joint work with O. Schiffmann, E. Vasserot.