Algebraic Cycles and Hodge theory

By

Dr. Slava Archava

Abstract: The study of algebraic cycles begins with the classical theorem of Abel which answers the following question: given a collection of points p_i on a Riemann surface S and integers n_i when does there exist a meromorphic function on S with poles/zeroes of multiplicity n_i at p_i's? I would like to explain this theorem as well as more recent results. The subject is abound with beautiful results as well as many open questions (Hodge conjecture, one of the Clay Institute's Millennium problems, is a famous example) and brave conjectures. I will try to make the talk accessible and self-contained.