Colloquia Patavina: p-Adic Families of Modular Forms

Martedi' 12 Giugno 2012 - Adrian Iovita


Martedi' 12 Giugno 2012 alle ore 16:00 in aula 1A150 della Torre Archimede il Professor Adrian Iovita (Univ. Padova) terra' una conferenza della serie Colloquia Patavina.

La Commissione Colloquia
P. Ciatti, M.A. Garuti, M. Pavon, F. Rossi

p-Adic Families of Modular Forms

Adrian Iovita (Univ. Padova)

An elliptic modular form (of some weight and level) is a complex valued holomorphic function on the upper half plane which satisfies a certain transformation property with respect to the action of a subgroup of SL(2, Z) and which is also holomorphic at the boundary of the upper half plane. To some of these modular forms (more precisely to the eigenforms for the Hecke operators) one can attach a complex L-function and a family of representations of the absolute Galois group of the rationals.
If E is an elliptic curve over the rationals, we say that E is modular if the L-function of E (or, equivalently, the family of Galois representations attached to E) equals the L-function (respectively, the Galois representations) of a weight 2 modular eigenform of a precisely defined level.
In 1996 Andrew Wiles and his collaborators proved that every elliptic curve over the rationals is modular and this implied the famous Fermat's Last Theorem.
In this talk we will be particularly interested in congruences modulo integers between various modular forms. R. Coleman noticed in 1996 that the congruences modulo powers of a fixed prime p between elliptic modular forms are explained by the existence of certain p-adic analytic families of such objects. Recently, together with F. Andreatta, V. Pilloni and G. Stevens we have been able to give geometric interpretations of Coleman's constructions and to generalize them to Hilbert and Siegel automorphic forms.

-Breve curriculum
Bucharest University, Bucharest, Romania, B.S. in Mathematics, 1978.
Boston University, Boston Massachusetts, Ph.D. in Mathematics, May 1996
Adviser: Professor Glenn Stevens
Dissertation: p-Adic Cohomology of Abelian Varieties

-- Professor Straordinario, Universita' degli Studi di Padova, Padova, Italy, January 2007
-- Professor, Canada Research Chair Tier II, Concordia University, Montreal, January 2003
-- Assistant Professor, University of Washington, September 1998 - August 2003
-- Postdoctoral Fellow, CICMA (McGill University and Concordia University) Montreal, 1996-1998

-- The Ribemboin Prize for excellence in research in Number Theory, the Canadian Number Theory Association, Waterloo, 2008.
-- Canada Research Chair Tier II, 2008-2013.
-- Canada Research Chair Tier II, 2003-2008.
-- NSERC research grant; p-adic families of Galois representations, 2011-2016.
-- NSERC research grant; p-adic continuity of the Main Conjecture, 2003-2011.
-- NSF grant: Galois Representations, June 2000 - June 2003.
-- Junior Faculty Development Award, University ofWashington Award, 2001.

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