O1) Obtaining p-adic deformations for the space of extended period polynomials and control
theorems for overconvergent modular symbols.
O2)A database for the mod N Galois representations attached to semistable elliptic curves of conductor N.
A database of the expansion of cusp forms attached to semistable elliptic curves in terms of products of two Eisenstein series of weight 1. Conjectural links between the two databases.
O3)Congruences between cusp forms and Eisenstein series of prime level.
- 5 submitted/ published articles in highly ranked internation journals
-databases regarding the Galois representations
of semistable elliptic curves and of the representations of cusp forms attached to them in terms of products of two Eisenstein series of weight 1.
-Organizing 3 international conferences in this area of research.