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Spring Semester 2013

Date / Time Speaker Title Location
1 March 2013
14:15-15:15 		Rodolphe Richard
EPFL Lausanne
Event Details

Number Theory Seminar

Title On pi-exponentials : Radius of Convergence and Witt vectors
Speaker, Affiliation Rodolphe Richard, EPFL Lausanne
Date, Time 1 March 2013, 14:15-15:15
Location HG G 43
Abstract What is the convergence radius of exp(T) (on the p-adic line)? of exp(T+T^2) ? of exp(T+T^p) ? We will give, in elementary terms, a new and original approach to Pulita's theory of pi-exponentials, and to one of its applications: an algorithm to compute the p-adic radius of convergence of series which are the exponential of a polynomial. Our approach simplifies an algorithm described by Christol from Pulita's work, and leads to explicit formulas. If time allow, we will present the complete proof, based entirely on the theory of Witt vectors.
On pi-exponentials : Radius of Convergence and Witt vectorsread_more
HG G 43
8 March 2013
14:15-15:15 		Prof. Dr. Árpád Tóth
Eötvös Loránd Universität, Budapest
Event Details

Number Theory Seminar

Title Weakly harmonic forms in weight 2
Speaker, Affiliation Prof. Dr. Árpád Tóth, Eötvös Loránd Universität, Budapest
Date, Time 8 March 2013, 14:15-15:15
Location HG G 43
Weakly harmonic forms in weight 2
HG G 43
12 April 2013
14:15-15:15 		Prof. Dr. Emmanuel Kowalski
ETH Zurich
Event Details

Number Theory Seminar

Title Gowers norms of trace functions over finite fields
Speaker, Affiliation Prof. Dr. Emmanuel Kowalski, ETH Zurich
Date, Time 12 April 2013, 14:15-15:15
Location HG G 43
Abstract The Gowers norms of a function defined on an abelian group measure the distribution of the values of the function over certain linear "patterns", and play important roles in additive combinatorics and in what is called higher-order Fourier analysis. The talk will recall this context and will then consider functions of algebraic origin on a prime field, in a precise sense, showing that except in well-understood cases, their Gowers norms are essentially as small as possible. (Joint work with É. Fouvry and Ph. Michel.)
Gowers norms of trace functions over finite fieldsread_more
HG G 43
17 May 2013
14:15-15:15 		Dr. Rafael von Känel
Institut des Hautes Études Scientifiques, France
Event Details

Number Theory Seminar

Title Modularity and integral points on moduli schemes
Speaker, Affiliation Dr. Rafael von Känel, Institut des Hautes Études Scientifiques, France
Date, Time 17 May 2013, 14:15-15:15
Location HG G 43
Abstract On combining modularity with Arakelov theory, we obtain finiteness results for integral points on moduli schemes of elliptic curves. The method is fully effective. For example, on applying the method to the projective line minus three points and to once punctured Mordell elliptic curves, we improve the actual best explicit height upper bounds for the solutions of S-unit and Mordell equations. In addition, the method gives an effective Shafarevich conjecture for abelian varieties of GL(2)-type.
Modularity and integral points on moduli schemesread_more
HG G 43
24 May 2013
14:15-15:15 		Dr. Marc Levine
Universität Duisburg-Essen
Event Details

Number Theory Seminar

Title Motives underlying classical homotopy theory
Speaker, Affiliation Dr. Marc Levine, Universität Duisburg-Essen
Date, Time 24 May 2013, 14:15-15:15
Location HG G 43
Abstract A basic invariant of classical homotopy theory are the stable homotopy groups of spheres. Up to now, no complete computation of these groups is available, but one of the main tools for their computation, the Adams-Novikov spectral sequence, reveals a deep connection with arithmetic aspects of (rank 1 commutative) formal groups. Voevodsky conjectured that the start of this spectral sequence is closely related to another spectral sequence that converges to the motivic analog of the stable homotopy groups of spheres. this second spectral sequence, known as the slice spectral sequence, is a close analog of Grothendieck's filtration by codimension on the cohomology of an algebraic variety. Recently, I uncovered a closer relation between these two constructions, establishing that the motivic slice spectral sequence and the Adams-Novikov spectral sequence agree in all their terms, not just the initial ones. This gives a new, algebro-geometric structure to the Adams-Novikov spectral sequence and conversely, the arithmetic of formal groups is surprisingly present in the slice spectral sequence. We will explain some of the ingredients that go into this connection, interesting in their own right.
Motives underlying classical homotopy theoryread_more
HG G 43
31 May 2013
14:15-15:15 		Prof. Dr. Ngaiming Mok
The University of Hong Kong
Event Details

Number Theory Seminar

Title Germs of measure-preserving holomorphic maps from bounded symmetric domains to their Cartesian products
Speaker, Affiliation Prof. Dr. Ngaiming Mok, The University of Hong Kong
Date, Time 31 May 2013, 14:15-15:15
Location HG G 43
Abstract Let X be the quotient of an irreducible bounded symmetric domain Ω by a lattice. In order to characterize algebraic correspondences on X commuting with exterior Hecke correspondences, Clozel-Ullmo reduced the problem to a rigidity statement about certain germs of holomorphic measure-preserving maps from (Ω; 0) into its Cartesian products. They proved that such maps are totally geodesic when dim(X) = 1. In a joint work with Sui-Chung Ng, we proved total geodesy when dim(Ω)  2 by means of methods of analytic continuation in Several Complex Variables. For the n-dimensional complex unit ball Bn, n  2, total geodesy follows then from Alexander’s theorem. According to the latter theorem, whenever n  2 a nonconstant germ of holomorphic map defined on a connected neighborhood U of a boundary point b 2 @Bn and mapping @Bn \U into @Bn \U must necessarily extend to an automorphism of Bn . When rank(Ω)  2 and denoting by Ω  S the Borel embedding of Ω as an open subset of its dual compact Hermitian manifold S, we deduce total geodesy from a new Alexander-type theorem for the nonsingular part Reg(@Ω) of the boundary by means of a reduction to a theorem due to Ochiai on analytic continuation of holomorphic maps which preserve S-structures. The latter theorem belongs to the theory of G-structures and the original proof was based on the cohomology theory of Lie algebras. A self-contained geometric proof of Ochiai’s theorem in the framework of a geometric theory of minimal rational tangents will also be given.
Germs of measure-preserving holomorphic maps from bounded symmetric domains to their Cartesian productsread_more
HG G 43

Organizers: Özlem Imamoglu, Emmanuel Kowalski, Richard Pink, Gisbert Wüstholz

Archive: SS 24 AS 23 SS 23 AS 22 SS 22 AS 21 SS 21 AS 20 SS 20 AS 19 SS 19 AS 18 SS 18 AS 17 SS 17 AS 16 SS 16 AS 15 SS 15 AS 14 SS 14 AS 13 SS 13 AS 12 SS 12 AS 11 SS 11 AS 10 SS 10 AS 09

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