Description
I will focus on special values of zeta functions both in topology and in arithmetic and show that one can understand properties of arithmetic special values using topology. On the topological side I will consider the Reidemeister torsion of a 3-manifold with a symplectic representation and give a cohomological formula for it. I will then sketch an analogous picture in arithmetic concerning the central value of the L-function of a symplectic representation on a curve and will show how the topological theorem is crucially used in the proof of the arithmetic one. This is based on joint work with Akshay Venkatesh.