Ramesh Sreekantan: Algebraic cycles on Abelian and K3 surfaces

There are several conjectures in the theory of algebraic cycles relating groups of algebraic cycles, on the one hand, with values of certain zeta functions, on the other. One well known example is the Dirichlet Class number formula relating the units group and class group with the value at 0 of the Dedekind zeta function. \zeta_K^*(0)=-R_Kh_K/w_k Several people have formulated general conjectures generalizing this formula. In this talk we will describe some work on algebraic cycles on Abelian surfaces and K3 surfaces which is motivated by trying to prove these conjectures in some special cases.