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Autumn Semester 2015

Date / Time Speaker Title Location
25 September 2015
14:15-15:15 		Ken Ono
Emory University
Details

Number Theory Seminar

Title Rogers-Ramanujan Identities and Umbral Moonshine
Speaker, Affiliation Ken Ono, Emory University
Date, Time 25 September 2015, 14:15-15:15
Location HG G 43
Abstract The Rogers-Ramanujan identities and Monstrous moonshine are important prototypes of results which occur at the interface of number theory, representation theory and physics. The speaker will discuss these identities, and describe recent work with Duncan, Griffin on Warnaar on their recent generalizations. This will include a comprehensive framework of Rogers-Ramanujan identities and singular moduli, and recent work umbral Moonshine.
Rogers-Ramanujan Identities and Umbral Moonshineread_more
HG G 43
23 October 2015
14:15-15:15 		Patrik Hubschmid
Universität Göttingen
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Number Theory Seminar

Title Equidistribution of Hecke orbits on Drinfeld moduli spaces
Speaker, Affiliation Patrik Hubschmid, Universität Göttingen
Date, Time 23 October 2015, 14:15-15:15
Location HG G 43
Abstract We consider Hecke orbits of functions on Drinfeld moduli spaces. We prove an equidistribution statement which is a positive characteristic analogue of a result of Clozel and Ullmo concerning equidistribution of Hecke orbits on PGL_n(Z)\PGL_n(R). The proof uses the spectral decomposition of the space of L^2-functions on the corresponding spaces in terms of adelic automorphic representations of GL_n over global function fields.
Equidistribution of Hecke orbits on Drinfeld moduli spacesread_more
HG G 43
30 October 2015
14:15-15:15 		Prof. Dr. Christian Elsholtz
Technische Universität Graz and FIM
Details

Number Theory Seminar

Title The maximal order of the iterated divisor function
Speaker, Affiliation Prof. Dr. Christian Elsholtz, Technische Universität Graz and FIM
Date, Time 30 October 2015, 14:15-15:15
Location HG G 43
Abstract We determine asymptotically the maximal order of log d(d(n)), where d(n) is the number of positive divisors of n. This solves a problem first put forth by Ramanujan in 1915.
The maximal order of the iterated divisor functionread_more
HG G 43
6 November 2015
14:15-15:15 		Prof. Dr. Philipp Habegger
Universität Basel
Details

Number Theory Seminar

Title Curves of Genus 2 with Bad Reduction and Complex Multiplication
Speaker, Affiliation Prof. Dr. Philipp Habegger, Universität Basel
Date, Time 6 November 2015, 14:15-15:15
Location HG G 43
Abstract If a smooth projective curve of positive genus which is defined over a number field has good reduction at some finite place, than so does its jacobian. But the converse already fails in genus 2. To study the extent of this failure we investigate jacobians that have complex multiplication. This forces the jacobians to have potentially good reduction at all finite places by a theorem of Serre and Tate. I will present a result which roughly speaking states that a genus 2 curve whose jacobian has complex multiplication usually has bad stable reduction at at least one finite place. This is joint work with Fabien Pazuki.
Curves of Genus 2 with Bad Reduction and Complex Multiplicationread_more
HG G 43
13 November 2015
14:15-15:15 		Prof. Dr. Emmanuel Kowalski
ETH Zurich, Switzerland
Details

Number Theory Seminar

Title Bilinear forms with Kloosterman sums
Speaker, Affiliation Prof. Dr. Emmanuel Kowalski, ETH Zurich, Switzerland
Date, Time 13 November 2015, 14:15-15:15
Location HG G 43
Abstract We will explain recent work with Ph. Michel and W. Sawin that leads to bounds for bilinear forms involving Kloosterman sums below the Polyá-Vinogradov range. We will also present some applications.
Bilinear forms with Kloosterman sumsread_more
HG G 43
20 November 2015
14:15-15:15 		Prof. Dr. Rainer Dietmann
Royal Holloway, University of London
Details

Number Theory Seminar

Title Random Diophantine problems
Speaker, Affiliation Prof. Dr. Rainer Dietmann, Royal Holloway, University of London
Date, Time 20 November 2015, 14:15-15:15
Location HG G 43
Abstract Applying the Hardy-Littlewood circle method to diagonal hypersurfaces of degree d one can establish the Hasse principle providing the dimension is at least d log d (1+o(1)). Using an averaging process, we can show that already for dimension at least 3d the Hasse principle holds true with probability 1 for a random diagonal hypersurface of degree d (joint work with Jörg Brüdern). If time permits, we also briefly want to mention related results on solutions of random Diophantine inequalities and random congruences.
Random Diophantine problemsread_more
HG G 43
4 December 2015
14:15-15:15 		Ting-Yu Lee
EPF Lausanne
Details

Number Theory Seminar

Title The Hasse principle for multinorm equations
Speaker, Affiliation Ting-Yu Lee, EPF Lausanne
Date, Time 4 December 2015, 14:15-15:15
Location HG G 43
Abstract Let k be a global field and let L_0 ,...,L_m be finite separable field extensions of k. In this talk, we are interested in the Hasse principle for the multinorm equation \prod_i N_{K_i/k}(t_i)=c. Under the assumption that L_0 is a cyclic extension, we will construct the Brauer-Manin map which gives an explicit description of the Brauer-Manin obstruction to the Hasse principle. It is a joint work with Eva Bayer-Fluckiger and Raman Parimala.
The Hasse principle for multinorm equationsread_more
HG G 43
11 December 2015
14:15-15:15 		Prof. Dr. Evelina Viada
ETH Zurich, Switzerland
Details

Number Theory Seminar

Title Rational points on explicit families of curves
Speaker, Affiliation Prof. Dr. Evelina Viada, ETH Zurich, Switzerland
Date, Time 11 December 2015, 14:15-15:15
Location HG G 43
Abstract We give explicit height bounds for the rational points on several families of curves, proving the effective Mordell Conjecture for these curves. We then give examples of curves with no rational points, and with 2 rational points. (Joint work with S. Checcoli and F. Veneziano)
Rational points on explicit families of curvesread_more
HG G 43

Organisers: Özlem Imamoglu, Peter Simon Jossen, Emmanuel Kowalski, Paul Nelson, Richard Pink, Evelina Viada, Gisbert Wüstholz

Archive: SS 25 AS 24 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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