distinguished lecture series presents

###### Jean-Pierre Wintenberger

### University of Strasbourg

###### Research Area

Number theory

###### Visit

Wednesday, April 3, 2013 to Saturday, April 20, 2013

###### Location

MS 6627

distinguished lecture series presents

Number theory

Wednesday, April 3, 2013 to Saturday, April 20, 2013

MS 6627

Jean-Pierre Wintenberger was born in Neuilly-sur-Seine, near Paris, in 1954. He got his first thesis in 1978 and his Thèse d’Etat (Habilitation) in 1984 in Grenoble, under the supervision of Jean-Marc Fontaine. He held the position of researcher in CNRS from 1978 to 1991, first in Grenoble then in Orsay. He has been a professor in Université de Strasbourg since 1991. He is member of the Institut Universitaire de France since 2007, received in 2008 the Prix Thérèse Gautier from French Academy of Science, and was an invited speaker in the Number Theory Section at the International Congress of Mathematicians held in Hyderabad, India, in August 2010. In 2011, Wintenberger was awarded the Frank Nelson Cole Prize in Number Theory along with Chandrashekhar Khare for their proof of Serre’s modularity conjecture.

Notes and recordings are not available for these lectures.

On Serre’s modularity conjecture: Let Gǫ be the absolute Galois group of the field of rational numbers. Serre conjectured that an irreducible odd representation of Gǫ with values in GL₂(F), F a finite field, arises from a modular form. We will state the conjecture, describe some of its consequences and, if time allows, show how the conjecture fits in a general framework.

About the proof of Serre’s modularity conjecture: We will give some hints on the proofs of Serre’s modularity conjecture (jw C. Khare).

Ramification in Iwasawa theory: Let F be a totally real number field and let p be a prime number. Let L be the cyclotomic field generated over F by roots of unity of order a power of p. Following Wiles proof of Iwasawa main conjecture, we construct a Z extension of Z whose ramification at an auxiliary prime is equivalent to Leopoldt conjecture (jw C. Khare).

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