Departement Mathematik

Number theory seminar

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Herbstsemester 2009

Datum / Zeit Referent:in Titel Ort
25. September 2009
15:15-16:15 		Dr. Sergey Gorchinskiy
Steklov Mathematical Institute
Details

Number Theory Seminar

Titel Biextension of Chow groups
Referent:in, Affiliation Dr. Sergey Gorchinskiy, Steklov Mathematical Institute
Datum, Zeit 25. September 2009, 15:15-16:15
Ort 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. Oktober 2009
14:15-15:15 		Prof. Dr. Manfred Einsiedler
ETH Zurich, Switzerland
Details

Number Theory Seminar

Titel Badly approximable numbers and unique ergodicity on adelic quotients
Referent:in, Affiliation Prof. Dr. Manfred Einsiedler, ETH Zurich, Switzerland
Datum, Zeit 2. Oktober 2009, 14:15-15:15
Ort
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. Oktober 2009
14:15-15:15 		Prof. Dr. Umberto Zannier
SNS Pisa
Details

Number Theory Seminar

Titel On the gcd(u-1,v-1) for S-units u,v and applications
Referent:in, Affiliation Prof. Dr. Umberto Zannier, SNS Pisa
Datum, Zeit 16. Oktober 2009, 14:15-15:15
Ort 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. Oktober 2009
14:15-15:15 		Prof. Dr. Florian Breuer
Stellenbosch
Details

Number Theory Seminar

Titel Kronecker congruence relations for Drinfeld modular polynomials
Referent:in, Affiliation Prof. Dr. Florian Breuer, Stellenbosch
Datum, Zeit 30. Oktober 2009, 14:15-15:15
Ort 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
Details

Number Theory Seminar

Titel Arithmetic geometric topology: sum motiv(e)ation
Referent:in, Affiliation Prof. Dr. Brent Doran, ETH Zurich, Switzerland
Datum, Zeit 6. November 2009, 14:15-15:15
Ort 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
Details

Number Theory Seminar

Titel Hilbert modular forms of weight 1/2 and theta functions
Referent:in, Affiliation Dr. Abhishek Saha, ETH Zurich, Switzerland
Datum, Zeit 20. November 2009, 14:15-15:15
Ort 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
Details

Number Theory Seminar

Titel Counting rational matrices of a given characteristic polynomial
Referent:in, Affiliation Dr. Thomas Zamojski, EPFL, Switzerland
Datum, Zeit 27. November 2009, 14:15-15:15
Ort 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. Dezember 2009
14:15-15:15 		Dr. Cyril Demarche
Université Paris-Sud
Details

Number Theory Seminar

Titel Integral points and strong approximation on homogeneous spaces
Referent:in, Affiliation Dr. Cyril Demarche, Université Paris-Sud
Datum, Zeit 4. Dezember 2009, 14:15-15:15
Ort 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. Dezember 2009
14:15-15:15 		Prof. Dr. Jonathan Pila
Bristol
Details

Number Theory Seminar

Titel A model-theoretic approach to certain diophantine problems
Referent:in, Affiliation Prof. Dr. Jonathan Pila, Bristol
Datum, Zeit 11. Dezember 2009, 14:15-15:15
Ort 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. Dezember 2009
14:15-15:15
Details

Number Theory Seminar

Titel No seminar.
Referent:in, Affiliation
Datum, Zeit 18. Dezember 2009, 14:15-15:15
Ort HG G 43
No seminar.
HG G 43

Organisatoren:innen: Clemens Fuchs, Özlem Imamoglu, Emmanuel Kowalski, Richard Pink, Gisbert Wüstholz

Archiv: FS 24 HS 23 FS 23 HS 22 FS 22 HS 21 FS 21 HS 20 FS 20 HS 19 FS 19 HS 18 FS 18 HS 17 FS 17 HS 16 FS 16 HS 15 FS 15 HS 14 FS 14 HS 13 FS 13 HS 12 FS 12 HS 11 FS 11 HS 10 FS 10 HS 09

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