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Autumn Semester 2009

Date / Time Speaker Title Location
25 September 2009
15:15-16:15 		Dr. Sergey Gorchinskiy
Steklov Mathematical Institute
Event Details

Number Theory Seminar

Title Biextension of Chow groups
Speaker, Affiliation Dr. Sergey Gorchinskiy, Steklov Mathematical Institute
Date, Time 25 September 2009, 15:15-16:15
Location HG G 43
Abstract The Poincare line bundle defines a biextension over the product of the Picard and Albenese varieties of a smooth projective algebraic variety. There will be discussed several ways to generalize this biextension for algebraic cycles of arbitrary codimension. One construction is explicit, while the others use, respectively, determinant of cohomology of coherent sheaves, the Poincare biextension over dual complex tori, and sheaves of K-groups.
Biextension of Chow groupsread_more
HG G 43
2 October 2009
14:15-15:15 		Prof. Dr. Manfred Einsiedler
ETH Zurich, Switzerland
Event Details

Number Theory Seminar

Title Badly approximable numbers and unique ergodicity on adelic quotients
Speaker, Affiliation Prof. Dr. Manfred Einsiedler, ETH Zurich, Switzerland
Date, Time 2 October 2009, 14:15-15:15
Location
Abstract Recall (which we will) that a real number a is called badly approximable if the digits c_n(a) in its continued fractions expansion are bounded. Boshernitzan asked whether there exists an irrational a for which sup_m limsup_n c_n(ma) is finite. We show how a measure classification result of Lindenstrauss on the adelic quotient SL_2(Q)\SL_2(A) shows that there is no such a. This and related work on the Diophantine properties of typical numbers in certain fractals is joint work with Fishman and Shapira.
Badly approximable numbers and unique ergodicity on adelic quotientsread_more
16 October 2009
14:15-15:15 		Prof. Dr. Umberto Zannier
SNS Pisa
Event Details

Number Theory Seminar

Title On the gcd(u-1,v-1) for S-units u,v and applications
Speaker, Affiliation Prof. Dr. Umberto Zannier, SNS Pisa
Date, Time 16 October 2009, 14:15-15:15
Location HG G 43
Abstract It is a joint result with P. Corvaja that if u,v are multiplicatively independent integers having all prime factors in a prescribed finite set S, then gcd(u-1,v-1) <<_{S,epsilon} max(|u|,|v|)^epsilon for all epsilon>0. We shall illustrate this statement and related ones, also in the context of function fields, together with some applications to a number of arithmetical and geometrical problems.
On the gcd(u-1,v-1) for S-units u,v and applicationsread_more
HG G 43
30 October 2009
14:15-15:15 		Prof. Dr. Florian Breuer
Stellenbosch
Event Details

Number Theory Seminar

Title Kronecker congruence relations for Drinfeld modular polynomials
Speaker, Affiliation Prof. Dr. Florian Breuer, Stellenbosch
Date, Time 30 October 2009, 14:15-15:15
Location HG G 43
Kronecker congruence relations for Drinfeld modular polynomials
HG G 43
6 November 2009
14:15-15:15 		Prof. Dr. Brent Doran
ETH Zurich, Switzerland
Event Details

Number Theory Seminar

Title Arithmetic geometric topology: sum motiv(e)ation
Speaker, Affiliation Prof. Dr. Brent Doran, ETH Zurich, Switzerland
Date, Time 6 November 2009, 14:15-15:15
Location HG G 43
Arithmetic geometric topology: sum motiv(e)ation
HG G 43
20 November 2009
14:15-15:15 		Dr. Abhishek Saha
ETH Zurich, Switzerland
Event Details

Number Theory Seminar

Title Hilbert modular forms of weight 1/2 and theta functions
Speaker, Affiliation Dr. Abhishek Saha, ETH Zurich, Switzerland
Date, Time 20 November 2009, 14:15-15:15
Location HG G 43
Abstract Hilbert modular forms of half integral weight are a natural generalization of the classical modular forms of half integral weight. An important example of such modular forms are provided by the theta functions. I will discuss my joint result with Sever Achimescu, which shows that the space of Hilbert modular forms of parallel weight 1/2 and fixed level and character has an explicit basis consisting of certain theta functions. This generalizes an old result of Serre and Stark.
Hilbert modular forms of weight 1/2 and theta functionsread_more
HG G 43
27 November 2009
14:15-15:15 		Dr. Thomas Zamojski
EPFL, Switzerland
Event Details

Number Theory Seminar

Title Counting rational matrices of a given characteristic polynomial
Speaker, Affiliation Dr. Thomas Zamojski, EPFL, Switzerland
Date, Time 27 November 2009, 14:15-15:15
Location HG G 43
Abstract We give an asymptotic formula for the number of rational matrices of given irreducible characteristic polynomial and of bounded height, solving a new case of Manin's conjecture. The proof strongly relies on measure rigidity for Cartan flows, and unlike previous methods, it does not make use of the theory of unipotent flows.
Counting rational matrices of a given characteristic polynomialread_more
HG G 43
4 December 2009
14:15-15:15 		Dr. Cyril Demarche
Université Paris-Sud
Event Details

Number Theory Seminar

Title Integral points and strong approximation on homogeneous spaces
Speaker, Affiliation Dr. Cyril Demarche, Université Paris-Sud
Date, Time 4 December 2009, 14:15-15:15
Location HG G 43
Abstract Let X be a homogeneous space of a connected linear algebraic group G, defined over a number field k. We consider some local-global principles concerning the existence of integral points on models of X over some open subsets of the spectrum of the ring of integers of k, and also the related problem of strong approximation on X. The main question is the following one : can we describe the closure of the set X(k) of rational points of X in a set of adelic points of X (endowed with the adelic topology) ? Assuming that the geometric stabilizers of X are connected or abelian, we prove formulae describing this closure either in terms of the integral Brauer-Manin obstruction on X, or in terms of the hypercohomology group of an explicit complex of k-tori. This work generalizes earlier results by Platonov, Kneser, Colliot-Thélène and Xu, Harari. In order to prove those results, we get some new arithmetic duality theorems for complexes of tori, which lead to some non-abelian arithmetic duality theorems for connected linear algebraic groups.
Integral points and strong approximation on homogeneous spacesread_more
HG G 43
11 December 2009
14:15-15:15 		Prof. Dr. Jonathan Pila
Bristol
Event Details

Number Theory Seminar

Title A model-theoretic approach to certain diophantine problems
Speaker, Affiliation Prof. Dr. Jonathan Pila, Bristol
Date, Time 11 December 2009, 14:15-15:15
Location HG G 43
Abstract I will describe some results about the distribution of rational points on certain non-algebraic sets in real space. They find their natural setting in the model-theoretic notion of an 'o-minimal structure over the real numbers'. I will describe a result joint with Alex Wilkie in this setting. Then I will describe some applications to diophantine problems in the Manin-Mumford-Andre-Oort circle of problems using a strategy proposed by Umberto Zannier.
A model-theoretic approach to certain diophantine problemsread_more
HG G 43
18 December 2009
14:15-15:15
Event Details

Number Theory Seminar

Title No seminar.
Speaker, Affiliation
Date, Time 18 December 2009, 14:15-15:15
Location HG G 43
No seminar.
HG G 43

Organizers: Clemens Fuchs, 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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