My research area is Algebraic Number Theory, more specifically, Iwasawa Theory.  I'm interested in main conjectures in Iwasawa Theory and their applications. I'm also interested in Iwasawa Theory of graphs. 

Here is my research statement.

3) Iwasawa Theory for the Branched $Z_p$- towers of Finite Graphs (with Daniel Vallieres)(arxiv )

We initiate the study of Iwasawa theory for branched  $Z_p$-towers of finite connected graphs. We prove an analogue of Iwasawa's asymptotic class number formula for the p-part of the number of spanning trees in this setting. Moreover, we find an explicit generator for the characteristic ideal of the torsion Iwasawa module governing the growth of the  p-part of the number of spanning trees in such towers. 

2)  Equivariant Iwasawa Theory for the Ritter-Weiss Module and Applications (with Cristian Popescu)  (in preparation)

We define a p- adic Ritter-Weiss module at the infinite level of the cyclotomic Iwasawa tower over a CM field and compute its Fitting ideal.  Using that we compute the Fitting ideal of a S,T - modified Iwasawa module which is the projective limit of certain S,T- ray class groups.

1)  An Unconditional Equivariant Main Conjecture in Iwasawa Theory (with Cristian  Popescu) ( pdf)(arxiv)

We use the recent work of Dasgupta and Kakde on the Brumer-Stark conjecture to prove a generalization of the equivariant main conjecture( of Greither and Popescu) unconditionally ( without the condition,  μ=0 ). As the main application we prove a refinement  of the Coates-Sinnott conjecture away from 2. We also generalize the keystone result of the Dasgupta- Kakde paper.