Upcoming lectures
Intercity Number Theory Seminar
22 March,
UvA and
VU Amsterdam. Room 11A33 in the main building of the VU.
- 11:00–12:00
- Duco van Straten Johannes Gutenberg-Universität Mainz, Siegel paramodular forms and pencils of Calabi-Yau threefolds
The search for the automorphic origin of Galois-representations arising from geometry is central to the Langlands program and arithmetic algebraic geometry. The understanding of the relation between elliptic curves and classical modular forms arose from the systematic study of examples and culminated in the modularity theorem of Wiles and others.
Calabi-Yau 3-folds form a class of varieties with rich and intriguing properties that come next to elliptic curves and K3 surfaces. In the talk I will report on joint work with V. Golyshev and describe some examples of Calabi-Yau 3-folds Y for which the Galois representation H3(Y) is related to weight 3 Siegel paramodular modular forms.
- 13:00–14:00
- Rob de Jeu Vrije Universiteit Amsterdam, K2 of elliptic curves over non-Abelian cubic and quartic fields
After a review of some earlier results on (mostly) K2 of curves, we give constructions of families of elliptic curves over certain cubic or quartic fields with three, respectively four, ‘integral’ elements in the kernel of the tame symbol on the curves. The fields are in general non-Abelian, and the elements linearly independent. For their integrality, we discuss a new criterion that does not ignore any torsion. We also verify Beilinson’s conjecture numerically for some of the curves. This is joint work with François Brunault, Liu Hang, and Fernando Rodriguez Villegas.
- 14:15–15:15
- Valentijn Karemaker Universiteit Utrecht, Unique decomposition and automorphisms of abelian varieties
We will discuss unique decomposition results for polarised abelian varieties over any field, that follow from studying indecomposable idempotents in algebras with involution. For abelian varieties that are governed by lattices, in particular superspecial abelian varieties, we also derive unique decomposition statements for the abelian varieties from those of the lattices. We will give some consequences for the automorphism groups of the abelian varieties.This is based on joint work with Tamagawa-Yu and Ibukiyama-Yu.
- 15:45–16:45
- Tian Wang MPIM Bonn, On the distribution of supersingular primes for abelian surfaces
In 1976, Lang and Trotter made a conjecture that predicts the number of primes p up to x, for which the reduction of a non-CM elliptic curve E/mathbbQ at p is supersingular. Though the conjecture is still open, we now have unconditional upper and lower bounds thanks to the work of several mathematicians in the past few decades. However, less has been studied for the distribution of supersingular primes for abelian surfaces (even conjecturally). In this talk, I will present my recent work on unconditional upper bounds for the number of primes p up to x, for which the reduction of a fixed abelian surface at p is supersingular.
Intercity Number Theory Seminar
19 April,
Leiden.
Intercity Number Theory Seminar
10 May,
Groningen.
Intercity Number Theory Seminar
24 May,
Utrecht.
Intercity Number Theory Seminar
7 June,
Utrecht.