Abstract:
I will provide some background on a conjecture of mine relating modular symbols in the homology of modular curves and cup products of cyclotomic units in the cohomology of integer rings.  I hope to describe some finer aspects of work on the conjecture and its direct refinements as well.

 

Title of 2nd talk : Reciprocity maps with restricted ramification

 

Abstract:

I will discuss work that I began long ago to compare various "reciprocity maps" in the cohomology of number fields with restricted ramification.  I will describe a couple of applications, in particular to the structure of Selmer groups of residual representations of families of cuspidal eigenforms congruent to Eisenstein series.