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Spring Semester 2010

Date / Time Speaker Title Location
5 March 2010
14:15-15:15 		Dr. Florian Luca
UNAM Mexico
Event Details

Number Theory Seminar

Title Diophantine equations with combinatorial numbers
Speaker, Affiliation Dr. Florian Luca, UNAM Mexico
Date, Time 5 March 2010, 14:15-15:15
Location HG G 43
Abstract There are many Diophantine equations involving factorials, binomial coefficients and products of consecutive integers which have been studied in several papers. To give just two examples, a famous result of Erdös and Selfridge is that a product of two or more consecutive positive integers is never a a perfect power (of exponent larger than 1), while all nontrivial solutions of the Diophantine equation {n \choose k}={m \choose l} are still not known. In my talk, I will present several results of the above flavour when factorials and products of consecutive integers are replaced by their q-counterpart, or more generally, by products of consecutive members of a Lucas sequence. For example, the product of two or more consecutive Fibonacci numbers is never a perfect power (except for the trivial case F_1F_2=1), all Fibonomial coefficients {n \choose k}_F are distinct for 2<= k<= n/2 and in fact if we order them increasingly by size the difference between any two consecutive ones tends to infinity with their size in an effective way, and there are only finitely many Catalan numbers that are also q-Catalan for some integer q>1. The proofs use a combination between classical techniques in exponential Diophantine equations and distribution of primes with several arithmetic constraints and have been obtained in various joint works with E. Fouvry, D. Marques, T. N. Shorey, P. Stanica and P. Young.
Diophantine equations with combinatorial numbersread_more
HG G 43
12 March 2010
14:15-15:15 		Prof. Dr. Ralf Schmidt
University of Oklahoma
Event Details

Number Theory Seminar

Title Kohnen's plus space condition
Speaker, Affiliation Prof. Dr. Ralf Schmidt, University of Oklahoma
Date, Time 12 March 2010, 14:15-15:15
Location HG G 43
Abstract Kohnen has introduced a subspace of the space of half-integral weight modular forms called the plus space. Elements of this space correspond nicely to integral weight modular forms under the Shimura lifting. In the talk we will give a representation theoretic interpretation of the plus space condition and draw some conclusions for half-integral weight modular forms. This is joint work with Brooks Roberts.
Kohnen's plus space conditionread_more
HG G 43
19 March 2010
14:15-15:15 		Dr. Nicolas Billerey
Univ. Duisburg-Essen
Event Details

Number Theory Seminar

Title Isogenies of prime degree over number fields
Speaker, Affiliation Dr. Nicolas Billerey, Univ. Duisburg-Essen
Date, Time 19 March 2010, 14:15-15:15
Location HG G 43
Abstract Let K be a number field and E be an elliptic curve defined over K. The so-called exceptional set for (E,K) consisting of prime numbers p such that E has a p-isogeny defined over K is finite if and only if E does not have CM over K. In this talk, I will state a criterion which allows, in various situations, to explicitly determine the exceptional set when it is finite. I will also give some numerical examples.
Isogenies of prime degree over number fieldsread_more (CANCELLED)
HG G 43
26 March 2010
14:15-15:15 		Dr. Alexander Gorodnik
University of Bristol
Event Details

Number Theory Seminar

Title Diophantine approximation on homogeneous varieties
Speaker, Affiliation Dr. Alexander Gorodnik, University of Bristol
Date, Time 26 March 2010, 14:15-15:15
Location HG G 43
Abstract We discuss the problem of Diophantine approximation on algebraic varieties, which was considered by Waldschmidt in the setting of abelean varieties. We investigate this problem for varieties equipped with actions of semisimple groups. Using techniques from the theory of automorphic representations, we establish estimates on the exponents of Diophantine approximation that are optimal in a number of cases. This is a joint work with A. Ghosh and A. Nevo.
Diophantine approximation on homogeneous varietiesread_more
HG G 43
16 April 2010
14:15-15:15 		Prof. Dr. Brent Doran
ETH Zurich
Event Details

Number Theory Seminar

Title Arithmetic geometric topology: Hopf revisited
Speaker, Affiliation Prof. Dr. Brent Doran, ETH Zurich
Date, Time 16 April 2010, 14:15-15:15
Location HG G 43
Arithmetic geometric topology: Hopf revisited
HG G 43
23 April 2010
11:15-18:30
Event Details

Number Theory Seminar

Title ETH Number Theory Days 2010
Speaker, Affiliation
Date, Time 23 April 2010, 11:15-18:30
Location HG
Abstract This joint event of ETHZ and EPFL is organized by P. Michel and G. Wüstholz. For further information follow the link above.
ETH Number Theory Days 2010read_more
HG
24 April 2010
10:15-12:30
Event Details

Number Theory Seminar

Title ETH Number Theory Days 2010
Speaker, Affiliation
Date, Time 24 April 2010, 10:15-12:30
Location HG
Abstract This joint event of ETHZ and EPFL is organized by P. Michel and G. Wüstholz. For further information follow the link above.
ETH Number Theory Days 2010read_more
HG
7 May 2010
14:15-15:15 		Dr. Lenny Taelman
University of Leiden/EPFL
Event Details

Number Theory Seminar

Title A characteristic p analogue of the class number formula
Speaker, Affiliation Dr. Lenny Taelman, University of Leiden/EPFL
Date, Time 7 May 2010, 14:15-15:15
Location HG G 43
A characteristic p analogue of the class number formula
HG G 43
14 May 2010
14:15-15:15 		Prof. Dr. Laurent Berger
ENS Lyon
Event Details

Number Theory Seminar

Title The p-adic local Langlands correspondence for GL_2(Q_p)
Speaker, Affiliation Prof. Dr. Laurent Berger, ENS Lyon
Date, Time 14 May 2010, 14:15-15:15
Location HG G 43
Abstract In this talk, I will give a survey of the p-adic local Langlands correspondence for GL_2(Q_p). It is a bijection between some 2-dimensional representations of Gal(Q_p^bar/Q_p) and some representations of GL_2(Q_p). This bijection can in fact be constructed using the theory of (phi,Gamma)-modules and some results of p-adic analysis. One then deduces some interesting arithmetical applications.
The p-adic local Langlands correspondence for GL_2(Q_p)read_more
HG G 43
21 May 2010
14:15-15:15 		Prof. Dr. Lynne Walling
Univ. of Bristol
Event Details

Number Theory Seminar

Title Explicit Hecke theory for Siegel modular forms, and applications
Speaker, Affiliation Prof. Dr. Lynne Walling, Univ. of Bristol
Date, Time 21 May 2010, 14:15-15:15
Location HG G 43
Explicit Hecke theory for Siegel modular forms, and applications
HG G 43
NaN undefined NaN
09:00-17:00
Event Details

Number Theory Seminar

Title Workshop "Rational Points - Theory & Experiment"
Speaker, Affiliation
Date, Time NaN undefined NaN, 09:00-17:00
Location HG
Abstract This conference will take place at FIM and is organized by U. Derenthal (University of Freiburg) and G. Wüstholz (ETH Zurich). For further information follow the link above.
Workshop "Rational Points - Theory & Experiment"read_more
HG
16 July 2010
14:15-15:15 		Dr. Sergey Rybakov
Russian Academy of Sciences
Event Details

Number Theory Seminar

Title The groups of points on abelian surfaces over finite fields
Speaker, Affiliation Dr. Sergey Rybakov, Russian Academy of Sciences
Date, Time 16 July 2010, 14:15-15:15
Location HG G 43
Abstract Let A be an abelian surface over a finite field k. The k-isogeny class of A is uniquely determined by a Weil polynomial f_A of degree 4. I give a classification of the groups of k-rational points on varieties from this class in terms of f_A(1-t).
The groups of points on abelian surfaces over finite fieldsread_more
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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