Seminare und Vorträge im WS 2017/18

am Dienstag, 10. Oktober:

Oberseminar Zahlentheorie

Stephan Ehlen (Universität zu Köln), Title: Minicourse on vector-valued modular forms I

14:00 Seminarraum 3 des Mathematischen Instituts

am Dienstag, 17. Oktober:

Oberseminar Zahlentheorie

Stephan Ehlen (Universität zu Köln), Title: Minicourse on vector-valued modular forms II

14:00 Seminarraum 3 des Mathematischen Instituts

am Dienstag, 24. Oktober:

Oberseminar Zahlentheorie

Kein Oberseminar

am Dienstag, 7. November:

Oberseminar Zahlentheorie

Stephan Ehlen (Universität zu Köln), Title: Minicourse on vector-valued modular forms III

14:00 Seminarraum 3 des Mathematischen Instituts

am Dienstag, 14. November:

Oberseminar Zahlentheorie

Samuele Anni (MPIM Bonn), Title: Modular forms, congruences and graphs
Abstract: The theory of congruences of modular forms is a central topic in contemporary number theory, lying at the basis of the proof of Mazur's theorem on torsion in elliptic curves, Fermat's Last Theorem, and Sato-Tate, amongst others.
Congruences are a display of the interplay between geometry and arithmetic. In order to study them, in a joint work with Vandita Patel (University of Toronto), we are constructing graphs encoding congruence relations between classical newforms. These graphs have extremely interesting features: they help our understanding on the structure of Hecke algebras, and they are also a new tool in the study of numerous conjectures.
In this talk I will describe these new objects, show examples and explain some of the possible applications.

 14:00 Seminarrraum 3 des Mathematischen Instituts

am Dienstag, 21. November:

Oberseminar Zahlentheorie

No seminar because of a workshop at the MPIM Bonn (see here for further information)

am Dienstag, 28. November:

Oberseminar Zahlentheorie

Cancelled upon further notice because of a workshop at the MPIM Bonn (see here for further information)

am Dienstag, 5. Dezember:

Oberseminar Zahlentheorie

Damaris Schindler (Universiteit Utrecht), On integral solutions to systems of two quadratic equations
Abstract: In this talk we discuss the local-global principle for integral solutions to systems of two (inhomogeneous) quadratic equations. In particular we will see concrete examples of Brauer classes obstructing the Hasse principle and discuss obstructions to the local-global principle in more general. This is joint work with Joerg Jahnel.

 14:00 Seminarraum 3 des Mathematischen Instituts

am Dienstag, 12. Dezember:

Oberseminar Zahlentheorie

Matija Kazalicki (University of Zagreb), Title: Supersingular zeros of divisor polynomials of elliptic curves of prime conductor and Watkins' conjecture

11:30 Seminarraum 3 des Mathematischen Instituts

Oberseminar Zahlentheorie

David Alexander McGady (University of Copenhagen, Niels Bohr Institute), Title: Hagedorn growth, Casimir energies, and meromorphic modular forms
Abstract: I will introduce the notion of a path integral in quantum field theory, with a particular emphasis on models of the strong interaction. Path integrals for these models have a characteristic ``Hagedorn'' growth in the number of states with a given energy. Such path integrals have isolated poles at finite temperature. They are also believed to be modular forms, which I will also discuss. Considering modular-invariant path integrals with poles naturally suggests that physical observables for toy models of the strong interaction -- such as Casimir energies -- are governed by special values of L-functions for meromorphic modular forms. Borcherds products provide an interesting analogy for many of these salient features.

14:15 Seminarraum 3 des Mathematischen Instituts

am Dienstag, 19. Dezember:

Oberseminar Zahlentheorie

Steffen Loebrich (Universität zu Koeln), Title: Selected Topics on Modular Forms (PhD Defense)

14:00 Seminarraum 3 des Mathematischen Instituts

am Dienstag, 9. Januar:

Oberseminar Zahlentheorie

Henrik Bachmann (Nagoya University/MPIM Bonn), Title: Multiple harmonic q-series at roots of unity
Abstract: In this talk we will discuss multiple harmonic q-series evaluated at roots of unity. These series can also be seen as functions from the rationals to the complex numbers and in the smallest depth, they give simple examples of quantum modular forms. The motivation to study these series comes from a recent results on the connection of finite multiple zeta values (FMZV) and symmetrized multiple zeta values (SMZV). We start by giving a small introduction into theory of multiple zeta values and then discuss their finite analogues, which were recently introduced by Kaneko and Zagier. After this we introduce the notion of finite multiple harmonic q-series at roots of unity and show that these specialize to the FMZV and the SMZV through an algebraic and analytic operation, respectively. This talk is based on a joint work with Y. Takeyama and K. Tasaka.

14:00 Seminarraum 3 des Mathematischen Instituts

am Dienstag, 16. Januar:

Oberseminar Zahlentheorie

Michalis Neururer (TU Darmstadt), Mahler measures of elliptic surfaces
Abstract: The (logarithmic) Mahler measure of a polynomial P in n variables is defined as the mean of log |P| on the n-th power of the unit circle. In 1997 Boyd and Deninger noticed a remarkable connection between Mahler measures of polynomials and L-values of the associated algebraic variety. Boyd conjectured, under certain conditions, explicit relations between Mahler measures of polynomials in 2 variables that define an elliptic curve E and L-values of E. I will discuss joint work with François Brunault, in which we study Mahler measures of polynomials in 3 variables that define modular elliptic surfaces and prove higher dimensional analogues of Boyd's relations. Such relations where previously studied by Bertin and with out new approach, based on the Rogers-Zudilin method, we reprove one of her results along with numerous new identities.

14:00 Seminarraum 3 des Mathematischen Instituts

am Dienstag, 23. Januar:

Oberseminar Zahlentheorie

Robert Pollack (Boston University/MPIM Bonn), Title: Slopes of modular forms and the ghost conjecture
Abstract: The Fourier coefficients of cuspidal modular forms are subtle invariants which contain a wealth of arithmetic information. Even bounding the size of these coefficients involve very deep mathematics -- the best bounds follow from Deligne's proof of the Weil conjectures. In this talk, rather than looking at complex absolute values, we will instead focus on the p-adic size of p-th Fourier coefficient of an eigenform. We give a conjectural description of the variation of these sizes over all weights (classical and p-adic). This conjecture (the ghost conjecture) then has implications regarding the shape and structure of the eigencurve. This is a joint project with John Bergdall.

 14:00 Seminarraum 3 des Mathematischen Instituts

am Dienstag, 30. Januar:

Oberseminar Zahlentheorie

Anna Medvedovsky (MPIM Bonn), The distribution of prime Fourier coefficients of modular forms mod p
Abstract: The distribution of prime Fourier coefficients of mod-p eigenforms can be understood by analyzing the image of the associated Galois representation over a finite field. Eigenforms mod p are not enough, however, to understand all forms -- there are simply too few of them. But one can use similar methods to study the distribution of prime Fourier coefficients of *generalized* mod-p eigenforms, at the price of working with a Galois pseudocharacter over an artinian ring. Building on recent work of Bellaïche, we will discuss some results and conjectures, focusing closely on the case p = 3 in level one.

14:00 Seminarraum 3 des Mathematischen Instituts

am Dienstag, 6. Februar:

Oberseminar Zahlentheorie

Nils-Peter Skoruppa (Universität Siegen), Title Hurwitz class numbers and automorphic forms, and an extension to number fields
Abstract: Hurwitz class numbers occur in various places in the theory of classical modular and Jacobi forms. Recently, in joint work with H. Boylan, we found an extension of this theory to (totally real) number fields. In this talk we explain the context for these considerations, introduce the pendants of Hurwitz class numbers in totally real number fields and the appearance of these new numbers in the theory of Jacobi forms over number fields.

 14:00 Seminarraum 3 des Mathematischen Instituts

am Dienstag, 27. Februar:

Oberseminar Zahlentheorie

Anna Haensch (Duquesne University), Title: Spinor regular ternary quadratic forms
Abstract: It is well known that there is no direct integral analogue to Hasse’s local-global principle. An integral lattice which satisfies a local-global principle (that is, a lattice that represents everything globally which is represented locally at every prime) is called regular. Extending this notion of regularity introduced by Dickson in 1939, a positive definite ternary integral quadratic form is said to be spinor regular if it represents all the positive integers represented by its spinor genus (that is, all positive integers represented by any form in its spinor genus). Jagy conducted an extensive computer search for primitive ternary quadratic forms that are spinor regular, but not regular, resulting in a list of 29 such forms. In this talk, I will discuss recent work with A. G. Earnest in which we verify the completeness of this list.

14:00 Seminarraum 3 des Mathematischen Instituts

Archiv

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
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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