Departement Mathematik

Number theory seminar

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Herbstsemester 2018

Datum / Zeit Referent:in Titel Ort
21. September 2018
14:15-15:15 		Prof. Dr. Dinesh Thakur
University of Rochester
Details

Number Theory Seminar

Titel A tale of two congruences
Referent:in, Affiliation Prof. Dr. Dinesh Thakur, University of Rochester
Datum, Zeit 21. September 2018, 14:15-15:15
Ort HG G 43
Abstract This will be a colloquium style talk which does not assume more background than a little elementary number theory. It explores the concepts of Wieferich primes and Wilson primes in the polynomial setting. Most of the talk will be accessible to students from the third bachelor year onwards.
A tale of two congruencesread_more
HG G 43
28. September 2018
14:15-15:15 		Prof. Dr. Alexander Gorodnik
Universität Zürich
Details

Number Theory Seminar

Titel Period Integrals and Randomness in the Geometry of Numbers
Referent:in, Affiliation Prof. Dr. Alexander Gorodnik, Universität Zürich
Datum, Zeit 28. September 2018, 14:15-15:15
Ort HG G 43
Abstract It turns out that some lattice-point counting functions exhibit random-like behavior. We explain how to prove results in this direction by analysing diagonal period integrals on suitable homogeneous spaces. This is a joint work with M. Björklund.
Period Integrals and Randomness in the Geometry of Numbersread_more
HG G 43
5. Oktober 2018
14:15-15:15 		Prof. Dr. Jens Funke
Durham University
Details

Number Theory Seminar

Titel Indefinite theta series via incomplete theta integrals
Referent:in, Affiliation Prof. Dr. Jens Funke, Durham University
Datum, Zeit 5. Oktober 2018, 14:15-15:15
Ort HG G 43
Indefinite theta series via incomplete theta integrals
HG G 43
* 19. Oktober 2018
Details

Number Theory Seminar

Titel No Seminar: Fields Medals day in Bern
Referent:in, Affiliation
Datum, Zeit 19. Oktober 2018,
Ort University of Bern
No Seminar: Fields Medals day in Bern
University of Bern
26. Oktober 2018
14:15-15:15 		Dr. Arthur Forey
ETH Zürich
Details

Number Theory Seminar

Titel Uniform bounds for points of bounded degree in function fields of finite characteristic
Referent:in, Affiliation Dr. Arthur Forey, ETH Zürich
Datum, Zeit 26. Oktober 2018, 14:15-15:15
Ort HG G 43
Abstract I will establish a bound for the number of F_q[t]-points of bounded degree in a variety defined over Z[t], uniform in q. This generalizes work by Sedunova for fixed q. The proof uses model theory of valued fields and uniform non-Archimedean Yomdin-Gromov parametrizations. This is joint work with Raf Cluckers and François Loeser.
Uniform bounds for points of bounded degree in function fields of finite characteristicread_more
HG G 43
9. November 2018
14:15-15:15 		Prof. Dr. Javier Fresán
École Polytechnique de Palaiseau
Details

Number Theory Seminar

Titel L-functions of symmetric power moments of Kloosterman sums
Referent:in, Affiliation Prof. Dr. Javier Fresán, École Polytechnique de Palaiseau
Datum, Zeit 9. November 2018, 14:15-15:15
Ort HG G 43
Abstract This talk will revolve around a global family of L-functions built up by assembling symmetric power moments of Kloosterman sums over finite fields. We prove that they arise from potentially automorphic motives over the rational numbers, hence admit a meromorphic extension to the complex plane which satisfies the expected functional equation. Although the motives turn out to be “classical”, the strategy consists in first realizing them as exponential motives and computing the Hodge numbers by means of the irregular Hodge filtration. Joint work with Claude Sabbah and Jeng-Daw Yu.
L-functions of symmetric power moments of Kloosterman sumsread_more
HG G 43
16. November 2018
14:15-14:19 		Dr. Job Kuit
Universität Paderborn
Details

Number Theory Seminar

Titel Discrete series representations for real spherical homogeneous spaces
Referent:in, Affiliation Dr. Job Kuit, Universität Paderborn
Datum, Zeit 16. November 2018, 14:15-14:19
Ort HG G 43
Abstract Let G/H be a homogeneous space and assume that it admits a G-invariant Radon measure. A discrete series representation for G/H is an irreducible subrepresentation of the space of square integrable functions on G/H. In this talk I will focus on a specific class of homogeneous spaces, the so-called real spherical homogeneous spaces. I will discuss recent results on discrete series representations for such spaces, in particular a theorem on the infinitesimal characters of discrete series representations. This work is joint with Bernhard Krötz, Eric Opdam and Henrik Schlichtkrull.
Discrete series representations for real spherical homogeneous spacesread_more
HG G 43
30. November 2018
14:15-15:15 		Prof. Dr. Farrell Brumley
Université Paris 13
Details

Number Theory Seminar

Titel Large periods of theta lifts
Referent:in, Affiliation Prof. Dr. Farrell Brumley, Université Paris 13
Datum, Zeit 30. November 2018, 14:15-15:15
Ort HG G 43
Abstract In recent years there has been a flowering of results on largeand small values of discrete periods of automorphic forms, usually expressed as upper and lower bounds on their sup norms. In this talk we shall present some new results on large values of geodesic periods of automorphic forms on compact congruence quotients of higher dimensional hyperbolic spaces. Joint work with Simon Marshall.
Large periods of theta liftsread_more
HG G 43
* 5. Dezember 2018
16:15-17:15 		Prof. Dr. Ching-Li Chai
University of Pennsylvania
Details

Number Theory Seminar

Titel Sustained p-divisible groups: foliation of moduli spaces of p-divisible groups revisited
Referent:in, Affiliation Prof. Dr. Ching-Li Chai, University of Pennsylvania
Datum, Zeit 5. Dezember 2018, 16:15-17:15
Ort HG G 19.1
Abstract We will explain joint work with Frans Oort on the notion of "sustained p-divisible groups" and its application to the foliation structure on moduli spaces of abelian varieties in positive characteristic p. In a nutshell, a family of p-divisible groups X over a scheme S in characteristic p is said to be sustained if, for every natural number n, the kernel of the endomorphism "multiplication by p^n on X" is locally constant for the flat topology of S. This notion is a scheme-theoretic version of the concept of "geometically fiberwise constant p-divisible group" introduced by Frans Oort in 2001 in order to define the central foliation structure on moduli spaces of abelian varieties in characteristic p. It turns out that that central leaves in moduli spaces of polarized abelian varieties thus defined are smooth, for any polarization degree, a phenomenon which perhaps is unexpected. This talk will begin with a quick review of the definition of commutative group schemes and p-divisible groups, to make it accessible to graduate students familiar with basic algebraic geometry (say the first three chapters of Hartshorne's book), including the definition of faithfully flat morphisms.
Sustained p-divisible groups: foliation of moduli spaces of p-divisible groups revisitedread_more
HG G 19.1
7. Dezember 2018
14:15-15:15 		Prof. Dr. Morten Risager
University of Copenhagen
Details

Number Theory Seminar

Titel Counting lattices and geodesics
Referent:in, Affiliation Prof. Dr. Morten Risager, University of Copenhagen
Datum, Zeit 7. Dezember 2018, 14:15-15:15
Ort HG G 43
Abstract The circle problem seeks to estimate the number of points of an orbit Gz inside a disc of growing radius R, where G acts discontinuously on a metric space X. Analogously the prime geodesic theorem seeks to estimate the number of prime geodesics on a Riemann surface with length less than R We review various results connected to these problems in the arithmetic case emphasizing the connection to a conjecture on a spectral exponential sum. This is work in progress.
Counting lattices and geodesicsread_more
HG G 43
14. Dezember 2018
14:15-15:15 		Prof. Dr. Ernst-Ulrich Gekeler
Universität Saarbrücken
Details

Number Theory Seminar

Titel A Survey of recent developments in the theory of Drinfeld modular forms
Referent:in, Affiliation Prof. Dr. Ernst-Ulrich Gekeler, Universität Saarbrücken
Datum, Zeit 14. Dezember 2018, 14:15-15:15
Ort HG G 43
Abstract In the last few years, Pink, Basson-Breuer-Pink, Häberli and myself started to work out a theory of Drinfeld modular forms of rank r >= 2. This will generalize the now well-established theory in rank 2, which is an analogue in positive characteristic of the classical theory of elliptic modular forms. In the talk, I will focus on the rigid-analytic aspects of such modular forms, which are holomorphic functions on the Drinfeld symmetric space Omega^r, and the relationship of Omega^r with the Bruhat-Tits building of PGL(r).
A Survey of recent developments in the theory of Drinfeld modular formsread_more
HG G 43
21. Dezember 2018
14:15-15:15 		Dr. Jessica Fintzen
Cambridge University
Details

Number Theory Seminar

Titel Representations of p-adic groups
Referent:in, Affiliation Dr. Jessica Fintzen, Cambridge University
Datum, Zeit 21. Dezember 2018, 14:15-15:15
Ort HG G 43
Abstract In the 1990s Moy and Prasad revolutionized p-adic representation theory by showing how to use Bruhat-Tits theory to assign invariants to p-adic representations. The tools they introduced resulted in rapid advancements in both representation theory and harmonic analysis -- areas of central importance in the Langlands program. A crucial ingredient for many results is an explicit construction of (types for) representations of p-adic groups. In this talk I will indicate why, survey what constructions are known (no knowledge about p-adic groups assumed) and present recent developments based on a refinement of Moy and Prasad's invariants.
Representations of p-adic groupsread_more
HG G 43

Hinweise: mit einem Stern gekennzeichnete Ereignisse (*) zeigen an, dass die Zeit und/oder der Ort von der üblichen Zeit und/oder dem üblichen Ort abweichen.

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