Departement Mathematik

Number theory seminar

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Frühjahrssemester 2019

Datum / Zeit Referent:in Titel Ort
22. Februar 2019
14:15-15:15 		Prof. Dr. Sandro Bettin
Università di Genova
Details

Number Theory Seminar

Titel The value distribution of quantum modular forms
Referent:in, Affiliation Prof. Dr. Sandro Bettin, Università di Genova
Datum, Zeit 22. Februar 2019, 14:15-15:15
Ort HG G 43
Abstract In a joint work with Sary Drappeau, we obtain results on the value distribution of quantum modular forms. As particular examples we consider the distribution of modular symbols, the Estermann function at the central point, and the Kashaev invariant at hyperbolic knots.
The value distribution of quantum modular formsread_more
HG G 43
1. März 2019
14:15-15:15 		Prof. Dr. Yves Martin
Universidad de Chile
Details

Number Theory Seminar

Titel On a collection of Fourier coefficients which determines Siegel cusp forms
Referent:in, Affiliation Prof. Dr. Yves Martin, Universidad de Chile
Datum, Zeit 1. März 2019, 14:15-15:15
Ort Hg G 43
Abstract We present a set of diagonal matrices which index enough Fourier coefficients for a complete characterization of all Siegel cusp forms of degree 2.
On a collection of Fourier coefficients which determines Siegel cusp formsread_more
Hg G 43
5. April 2019
14:15-15:15 		Dr. Pankaj Vishe
Durham University
Details

Number Theory Seminar

Titel Rational points on global fields and applications
Referent:in, Affiliation Dr. Pankaj Vishe, Durham University
Datum, Zeit 5. April 2019, 14:15-15:15
Ort HG G 43
Abstract We present analytic methods for counting rational points on complete intersections defined over function field F_q(t). The main ingredient is obtaining a version of Kloosterman refinement over function field for complete intersections.
Rational points on global fields and applicationsread_more
HG G 43
12. April 2019
14:15-15:15 		Prof. Dr. Raf Cluckers
Université de Lille
Details

Number Theory Seminar

Titel Igusa's conjecture on exponential sums
Referent:in, Affiliation Prof. Dr. Raf Cluckers, Université de Lille
Datum, Zeit 12. April 2019, 14:15-15:15
Ort HG G 43
Abstract I will present the recent progress with M. Mustata and K. H. Nguyen on Igusa's conjecture on exponential sums, which is about bounds for finite exponential sums with index sets consisting of integers modulo positive powers of primes, and where uniformity is key. The presented proof relies on recent results from the minimal model program in algebraic geometry, and is optimal in the case of non-rational singularities. Igusa intended to use his conjecture on exponential sums to advance the study of local-global principles, but these ideas remain mostly unachieved up to date.
Igusa's conjecture on exponential sumsread_more
HG G 43
19. April 2019
Details

Number Theory Seminar

Titel Easter holidays - no seminar
Referent:in, Affiliation
Datum, Zeit 19. April 2019,
Ort
Easter holidays - no seminar
26. April 2019
Details

Number Theory Seminar

Titel Easter holidays - no seminar
Referent:in, Affiliation
Datum, Zeit 26. April 2019,
Ort
Easter holidays - no seminar
3. Mai 2019
14:15-15:15 		Prof. Dr. Richard Pink
ETH Zurich, Switzerland
Details

Number Theory Seminar

Titel Reciprocal maps: Not so crazy, yet much ... useful
Referent:in, Affiliation Prof. Dr. Richard Pink, ETH Zurich, Switzerland
Datum, Zeit 3. Mai 2019, 14:15-15:15
Ort HG G 43
Reciprocal maps: Not so crazy, yet much ... useful
HG G 43
17. Mai 2019
14:15-15:15 		Prof. Dr. Shabnam Akhtari
University of Oregon and MPIM
Details

Number Theory Seminar

Titel Representation of integers by binary forms
Referent:in, Affiliation Prof. Dr. Shabnam Akhtari, University of Oregon and MPIM
Datum, Zeit 17. Mai 2019, 14:15-15:15
Ort HG G 43
Abstract Let F(x, y) be an irreducible binary form with integer coefficients and of degree at least 3. By a well-known result of Thue, the equation F(x, y) = m has only finitely many solutions in integers x and y. I will discuss some old and new quantitative results on the number of solutions to Thue equations. I will also talk about a joint work with Manjul Bhargava, where we use explicit upper bounds for the number of solutions of Thue equations to show that many such equations have no solutions.
Representation of integers by binary formsread_more
HG G 43
24. Mai 2019
14:15-15:15 		Prof. Dr. Adam Harper
University of Warwick
Details

Number Theory Seminar

Titel Riemann zeta function in short intervals
Referent:in, Affiliation Prof. Dr. Adam Harper, University of Warwick
Datum, Zeit 24. Mai 2019, 14:15-15:15
Ort HG G 43
Abstract I will describe some new results on the average and maximum size of the Riemann zeta function in a "typical" interval of length 1 on the critical line. A (hopefully) interesting feature of the proofs is that they reduce the problem for the zeta function to an analogous problem for a random model, which can then be solved using various probabilistic techniques.
Riemann zeta function in short intervalsread_more
HG G 43
31. Mai 2019
14:15-15:15 		Prof. Dr. Clément Dupont
Université de Montpellier
Details

Number Theory Seminar

Titel Single-valued integration and superstring amplitudes
Referent:in, Affiliation Prof. Dr. Clément Dupont, Université de Montpellier
Datum, Zeit 31. Mai 2019, 14:15-15:15
Ort HG G 43
Abstract The classical theory of integration concern integrals of differential forms over domains of integration. In geometric terms, this corresponds to a canonical pairing between de Rham cohomology and singular homology. For varieties defined over the reals, one can make use of complex conjugation to define a real-valued pairing between de Rham cohomology and its dual, de Rham homology. The corresponding theory of integration, that we call single-valued integration, pairs a differential form with a `dual differential form’. We will explain how single-valued periods are computed and give an application to superstring amplitudes in genus zero. This is joint work with Francis Brown.
Single-valued integration and superstring amplitudesread_more
HG G 43
* 2. August 2019
14:15-15:15 		Prof. Dr. Wenzhi Luo
Ohio State University
Details

Number Theory Seminar

Titel Automorphic shifted convolution and Vinogradov mean value conjecture
Referent:in, Affiliation Prof. Dr. Wenzhi Luo, Ohio State University
Datum, Zeit 2. August 2019, 14:15-15:15
Ort HG G 43
Abstract Linnik pioneered, by his dispersion method, the study of shifted convolution in the kth fold divisor function, which reveals fascinating connections between the theory of zeta functions and analytic properties of the Eisenstein series. In this talk, we will present an approach to the shifted convolution involving cubic or higher integral powers, and the Whittaker-Fourier coefficients of cuspidal automorphic forms on GL(n). It leads to strong asymptotic bounds, based on among other things the Weyl inequality and the Vinogradov mean value conjecture, the latter recently proved by Bourgain-Demeter-Guth via the decoupling techniques in harmonic analysis.
Automorphic shifted convolution and Vinogradov mean value conjectureread_more
HG G 43

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