Aachen-Bonn-Koeln-Lille-Siegen seminar on automorphic formsNovember 23, Utrecht. Location: Minnaert Building, room 201
|13:15-14:15||Peter Bruin (Leiden), On explicit computations with modular Galois representations|
Abstract. I will explain a compact way of encoding representations of the absolute Galois group of a field K on finite Abelian groups as dual pairs of finite K-algebras. These are in principle equivalent to finite commutative group schemes or Hopf algebras, but are easier to compute and to store. I will show how to compute these objects and to work with them, with a focus on representations attached to modular forms over finite fields. Work is ongoing to include such representations in the L-Functions and Modular Forms Database.
|14:15-15:15||Alexandru Ciolan (Köln), Asymptotics and inequalities for partitions into squares|
Abstract. In this talk we show that the number of partitions into squares with an even number of parts is asymptotically equal to that of partitions into squares with an odd number of parts. We further prove that, for n large enough, the two quantities are different and which of the two is bigger depends on the parity of n. This solves a recent conjecture formulated by Bringmann and Mahlburg (2012).
|15:45-16:45||Jan-Willem van Ittersum (Utrecht), A symmetric Bloch-Okounkov theorem|
Abstract. Bloch and Okounkov showed that the generating series associated to a wide class of functions on partitions of integers are quasimodular forms. We consider a different class of functions on partitions. In this class the functions are symmetric in the parts and multiplicities of the parts of the partitions. We show that the associated generating series are quasimodular forms as well.
|16:45-17:45||Annalena Wernz (Aachen), On Hermitian modular forms - Theta series and Maass spaces|
Abstract. It is well known (Cohen, Resnikoff 1978 and Hentschel, Nebe 2009) that Hermitian theta series of an even unimodular theta lattice of rank k belong to [U(2,2;OK),k] where U(2,2;OK) is the full Hermitian modular group of degree 2. In this talk, we consider the normalizer U*(2,2;OK) of U(2,2;OK) in the special unitary group SU(2,2;C) and examine the behavior of Hermitian theta series under its action. Furthermore, we consider the Hermitian Maaß spaces S(k,OK) and M(k,OK) introduced by Sugano (1985) and Krieg (1991) respectively. In an approach which is similar to the paramodular case (Heim, Krieg 2018), we prove that a Maaß form in the Sugano sense is an element of Krieg's Maaß space if and only if it is a modular form with respect to U*(2,2;OK).
Intercity Seminar Number TheoryDecember 7, Eindhoven. In Metaforum 14 (6e verdieping); PhD defense Guus Bollen in Senaatszaal of Auditorium.
|11:45-12:30||Wieb Bosma (Nijmegen), Enumerating self-complementary graphs|
Abstract. Graphs that are isomorphic to their complement are among
the objects to which Polya's counting method has been most
successfully applied. We will discuss methods for counting and
enumerating self-complementary graphs (both ordinary and
directed, with and without particular structure) on small
numbers of points, and interaction between the two.
On the way we will also encounter some interesting
properties and problems of these graphs.
|13:15-14:00||Winfried Hochstättler (Hagen), The Varchenko Determinant of an Oriented Matroid|
Abstract. The Varchenko matrix M of a hyperplane arrangement is a symmetric square
matrix indexed by the full dimensional regions of the arrangement, where
Mij equals the product of the hyperplanes seperating the cells i and j.
Varchenko proved 1993 that the determinant of this matrix has a nice
factorization. Using a proof strategy suggested by Denham and Henlon in
1999 we show that the same factorization works in the abstract setting
of oriented matroids. For that purpose we show that every T-convex
region of the set of topes, considered as a subcomplex of the Edelman
poset, has a contractible order complex, which might be of independent
|14:15-15:00||Dustin Cartwright (Tennessee), One-dimensional groups and algebraic matroids|
Abstract. I will talk about a construction of algebraic matroids from modules over
endomorphism rings of 1-dimensional algebraic groups, which generalizes
both linear and monomial realizations of matroids. The algebraic matroid
constructed in this way coincides with a linear matroid over the
endomorphism ring. I will explain how this relationship also extends to
the Lindström valuation and the Frobenius flock of the algebraic
matroid. This is joint work with Jan Draisma and Guus Bollen.
|16:00-17:00||Guus Bollen (Eindhoven), PhD defense|
Intercity Number Theory SeminarDecember 18, Leiden. In Snellius 412; PhD defense Erik Visse in the Academiegebouw in the center of Leiden.
Belgian-Dutch Algebraic Geometry seminarFebruary 1, Utrecht.
Intercity Number Theory SeminarMarch 15, Utrecht.