Symmetries and correspondences


June 2 2017, Mathematical Institute Oxford, L5

Informal meeting on interaction of arithmetic geometry and quantum field theory

12:00-13:30 Mikhail Kapranov Relations on Hall algebras and zeroes of zeta functions

Abstract. I will discuss how relations among natural generators of the Hall algebra of vector bundles on a curve over F_q are related to the zeroes of the zeta function of the curve.

14:30-16:00 Minhyong Kim Linking numbers and arithmetic duality

Abstract. Over the last few decades, a number of authors have discussed the analogy between linking numbers in 3d manifold topology and symbols in arithmetic. This talk will outline some results that make this precise in terms of natural complexes associated to arithmetic duality theorems. In particular, a ‘finite path integral’ formula for power residue symbols will be described.