MIT Combinatorics Seminar Counting covers of elliptic curves Dawei Chen  (Harvard University) Friday, April 20, 2007    4:15 pm    Room 2-136 ABSTRACT Many algebro-geometric problems about moduli spaces eventually boil down to deep combinatorial problems. In this talk I will show, by using symmetric groups, how combinatorics natually arises when we study the loci of certain branched covers of elliptic curves in the moduli space of genus g curves. Most of the results and open problems will be stated in a purely combinatorial setting. I will also mention a geometric interpretation that provides surprisingly neat proofs for some equalities from enumerative combinatorics.