Seminare und Vorträge im WS 2018/2019

am Dienstag, 09. Oktober:

Oberseminar Zahlentheorie

Caner Nazaroglu (University of Cologne), Title: Mock Modular Forms in Physics I

14:00 Seminarraum 3 des Mathematischen Instituts

am Dienstag, 16. Oktober:

Oberseminar Zahlentheorie

No seminar

am Dienstag, 23. Oktober:

Oberseminar Zahlentheorie

No seminar

am Dienstag, 30. Oktober:

Oberseminar Zahlentheorie

Caner Nazaroglu (Universität zu Köln), Title: Mock Modular Forms in Physics II

14:00 Seminarraum 3 des Mathematischen Instituts

am Dienstag, 06. November:

Oberseminar Zahlentheorie

Jan Vonk (University of Oxford), Title: Rigid meromorphic cocycles and p-adic mock modular forms
Abstract: In joint work with Henri Darmon, we define the notion of a rigid meromorphic cocycle, and explain how to evaluate them at suitable real quadratic points. The resulting quantities bear a striking resemblance to the singular moduli from CM theory, and therefore suggest a p-adic approach to Hilbert's 12th problem for real quadratic fields which is close in spirit to Kronecker's Jugendtraum.

14:00 Seminarraum 3 des Mathematischen Instituts

am Dienstag, 13. November:

Oberseminar Zahlentheorie

Andreea Mocanu (University of Nottingham), Title: Newform theory for Jacobi forms of lattice index
Abstract: I will give a brief introduction to Jacobi forms of lattice index, including some examples and their relation to other types of modular forms. After that, I will discuss some of the ingredients that go into developing a theory of newforms for Jacobi forms of lattice index, namely Hecke operators, level raising operators and orthogonal groups of discriminant modules.

14:00 Seminarraum 3 des Mathematischen Instituts

am Dienstag, 20. November:

Oberseminar Zahlentheorie

Arash Arabi Ardehali (Uppsala University), Title: A walk through Quantum Field Theory's garden of exact partition functions
Abstract: Examples of exact partition functions of supersymmetric quantum field theories in 2, 3, and 4 dimensions will be discussed, and it will be explained how their asymptotic analysis sheds light on blackhole physics and gauge theory dynamics.

 13:45 Seminarraum 3 des Mathematischen Instituts

am Dienstag, 27. November:

Oberseminar Zahlentheorie

Sander Zwegers (Universität zu Köln), Title: On some indefinite theta functions related to McKay--Thompson series attached to M24
Abstract: In this talk we'll discuss the construction of certain indefinite theta functions involving the Niemeier lattice A124. We'll relate these indefinite theta functions to the McKay--Thompson series attached to the Mathieu group M24

 14:00 Seminarraum 3 des Mathematischen Instituts

am Dienstag, 04. Dezember:

Oberseminar Zahlentheorie

Valentin Reys (Università di Milano-Bicocca), Title: Mixed mock modular forms and supersymmetric black holes
Abstract: Understanding the microscopic structure of supersymmetric black holes has been a fertile testing ground for various ideas in string theory and theories of quantum gravity in general. Some time ago, it was realized that for the simplest black holes, the degeneracy of states are encoded by the Fourier coefficients of well-known modular and Jacobi forms. These results thus exhibited a deep connection between quantum black holes and analytic number theory. More recently, important progress has been made in understanding the structure of more complex black holes and generalizing this connection. In particular, the known physical phenomenon of wall-crossing manifests itself mathematically in the fact that the generating functions of microscopic degeneracies are mixed mock modular objects. In this talk, I will explain how a generalization of the Circle Method, first worked out by Bringmann and Manschot, allows us to compute the Fourier coefficients of the mixed mock modular forms relevant to specific supersymmetric black holes. In a second part, I will outline a method to derive these degeneracies using physics methods and discuss the challenges one faces along the way. Time permitting, I will also discuss some work in progress related to another class of supersymmetric black holes known as CHL models, where the relevant objects that appear are mixed mock modular with respect to certain congruence subgroups of the full modular group.

 14:00 Seminarraum 3 des Mathematischen Instituts

am Dienstag, 11. Dezember:

Oberseminar Zahlentheorie

Olivia Beckwith (University of Bristol), Title: Indivisibility and divisibility of class numbers of imaginary quadratic fields
Abstract: For any prime p > 3, the strongest lower bounds for the number of imaginary quadratic fields with discriminant down down to -X for which the class group has trivial (non-trivial) p-torsion are due to Kohnen and Ono (Soundararajan). I will discuss recent refinements of these classic results in which we consider the imaginary quadratic fields whose class number is indivisible (divisible) by p such that a given finite set of primes factor in a prescribed way. We prove a lower bound for the number of such fields with discriminant down to -X which is of the same order of magnitude as in Kohnen and Ono's (Soundararajan's) results. For the indivisibility case, we rely on a result of Wiles establishing the existence of imaginary quadratic fields with trivial p-torsion in their class groups satisfying almost any given finite set of local conditions, and a result of Zagier which says that the Hurwitz class numbers are the Fourier coefficients of a mock modular form.

 14:00 Seminarraum 3 des Mathematischen Instituts

am Dienstag, 18. Dezember:

Oberseminar Zahlentheorie

Massimo Bertolini (Universität Duisburg-Essen), Title: Reciprocity laws for triple product L-functions and the arithmetic of elliptic curves

14:00 Seminarraum 3 des Mathematischen Instituts

am Dienstag, 08. Januar:

Oberseminar Zahlentheorie

Judith Ludwig (Universität Heidelberg), Title: An introduction to p-adic automorphic forms
Abstract: This talk is an introduction to the theory of p-adic automorphic forms. After explaining Serre's definition of a p-adic modular form, I will give an overview of the theory for more general groups. I will explain how to organize p-adic automorphic forms into geometric families, which opens up the theory to the toolbox of non-archimedean geometry. Towards the end of the talk we will catch a glimpse of the p-adic Langlands program.

14:00 Seminarraum 3 des Mathematischen Instituts

am Dienstag, 15. Januar:

Oberseminar Zahlentheorie

Steffen Loebrich (University of Amsterdam) Title: On cycle integrals of meromorphic modular forms
Abstract: In joint work in progress with Markus Schwagenscheidt, we study cycle integrals of meromorphic modular forms associated to quadratic forms of negative discriminant. In particular, we relate them to evaluations of locally harmonic Maass forms at CM-points. This allows us to generalize a recent theorem of Alfes-Neumann, Bringmann, and Schwagenscheidt on the rationality of these cycle integrals in several directions.

14:00 Seminarraum 3 des Mathematischen Instituts

am Dienstag, 22. Januar:

Oberseminar Zahlentheorie

Jolanta Marzec (TU Darmstadt/University of Silesia), Title: Maass relations for Saito-Kurokawa lifts of higher levels
Abstract: Classically, Saito-Kurokawa lifting is an injective mapping from the space of modular forms of level 1 to the space of Siegel modular forms of degree 2 such that the functions in the image violate generalized Ramanujan-Petersson conjecture. The first construction of such a lifting was given by Maass who exploited correspondences between various modular forms. The image consisted of functions whose Fourier coefficients satisfied what we now call the Maass relations. One can generalize this mapping to include modular forms of higher levels. However, then the classical constructions become fairly complicated and it is not clear whether they still imply (a version of) Maass relations. We show that this is indeed the case by generalizing a representation theoretical approach of Pitale, Saha and Schmidt from level 1 to higher levels.

 14:00 Seminarraum 3 des Mathematischen Instituts

am Dienstag, 29. Januar:

Oberseminar Zahlentheorie

Talk cancelled due to illness of the speaker.

Archiv

Seminare und Vorträge im SS 2018
Seminare und Vorträge im WS 2017/2018
Seminare und Vorträge im SS 2017
Seminare und Vorträge im WS 2016/2017
Seminare und Vorträge im SS 2016
Seminare und Vorträge im WS 2015/2016
Seminare und Vorträge im SS 2015
Seminare und Vorträge im WS 2014/2015
Seminare und Vorträge im SS 2014
Seminare und Vorträge im WS 2013/2014
Seminare und Vorträge im SS 2013
Seminare und Vorträge im WS 2012/2013
Seminare und Vorträge im SS 2012
Seminare und Vorträge im WS 2011/2012
Seminare und Vorträge im SS 2011
Seminare und Vorträge im WS 2010/2011
Seminare und Vorträge im SS 2010
Seminare und Vorträge im WS 2009/2010
Seminare und Vorträge im SS 2009
Seminare und Vorträge im WS 2008/2009
Seminare und Vorträge im SS 2008 und früher