Number Theory Seminar: Romyar Sharifi

I will discuss a conjecture which provides a relationship between Manin symbols in the homology of modular curves and cup products of cyclotomic units in Galois cohomology with restricted ramification. I hope to be able to give something of an idea of its meaning, with an eye towards generalization. I will also relate recent progress by Fukaya and Kato that essentially proves the conjecture under a mild but difficult to remove hypothesis.