**Mahesh Kakde** (Princeton)

*Congruences in non-commutative Iwasawa theory*

In this talk I will discuss the results on computation of K_{1}
groups of certain Iwasawa algebras. I will sketch a strategy for
deducing the non-commutative main conjecture of Iwasawa theory from
results obtained from these computation and certain number theoretic
input i.e. abelian main conjectures and certain congruences between
abelian p-adic L-functions. I will discuss a case in which these
congruences can be proven (for example Katz's p-adic L-function under
certain assumptions).