Expected results

Objectives:

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.

Dissemination:

- 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.

Rezultate Asteptate

Obiective:

O1) Obtinerea deformarilor p-adice ale spatiului de polinoame de perioade extinse si demonstrarea
teoremei de control pentru simboluri modulare supraconvergente.
O2) Calcularea unei baze de date pentru reprezentari Galois mod N asociate curbelor eliptice
semistabile de conductor N. Calcularea unei baze de date a coeficientilor expansiunii formelor
cuspidale asociate curbelor elliptice rationale semistabile in functie de produse de doua serii Eisenstein de pondere 1. Exprimarea unor conjecturi experimentale care leaga cele doua baze de date.
O3) Demonstrarea existentei congruentelor dintre forme cuspidale si serii Eisenstein pentru nivel prim.

Diseminare:

-5 articole submise/publicate in reviste bine cotate international
-baza de date privind reprezentarile Galois atasate curbelor eliptice rationale semistabile precum si a reprezentarii formelor modulare atasate in functie de produse de doua serii Eisenstein de pondere 1.
-Organizarea a 3 conferinte internationale