Intercity Number Theory Seminar

Upcoming lectures

Intercity Number Theory

November 1, Leiden. Room 312 of the Snellius building

11:00-12:00Martin Bright (Leiden), A walk on the wild side: p-torsion in the Brauer group
Abstract. The Brauer group of a variety over a number field is a powerful tool for studying failures of the Hasse principle. To apply this, one needs to understand the function obtained by evaluating a given element of the Brauer group at the p-adic points of the variety. For elements of order coprime to p, this evaluation map factors through reduction modulo p. For elements of order p, the situation is much more intricate: one may need to look at the points to higher p-adic precision. We relate the resulting filtration on the Brauer group to one defined by Bloch–Kato, and show that Kato's refined Swan conductor controls the local behaviour of the evaluation map. This is joint work with Rachel Newton.
13:30-14:30Leila Schneps (Jussieu, Paris), Grothendieck-Teichmüller theory, a crossroads between geometry and number theory.
Abstract. Grothendieck-Teichmüller theory was originated by Alexander Grothendieck as a way to study the absolute Galois group of the rationals by considering its action on fundamental groups of varieties, in particular of moduli spaces of curves with marked points: the special properties of the Galois action with respect to inertia generators and the fact of respecting the relations in the fundamental group gave rise to the definition of the group GT which contains GQ.

The group GT is profinite, but its defining relations can also be used to give a pro-unipotent avatar, and an associated graded Lie algebra grt. The study of the Lie algebra grt reveals many unexpected relations with number theory that are completely invisible in the profinite situation. We will show how Bernoulli numbers, cusp forms on SL2(Z) and multiple zeta values arise in the Lie algebra context.

14:50-15:50Pierre Lochak (Jussieu, Paris), A topological version of Grothendieck-Teichmüller theory.
Abstract. After recalling some basic features of G.-T. theory, mainly with a view to emphasize its "nonlinear" versus "linear" aspects, I will take the topological (and nonlinear) path, introducing in particular the profinite completions of various simplicial complexes (curve an arc complexes mainly, as well as some closely related graphs) which feature far-reaching generalizations of the so-called "dessins d'enfants" and enable one to build a topological version of G.-T. (valid in every genus) which may (or may not) be rather close to the blueprint appearing in Grothendieck's famous Esquisse d'un programme.
16:10-17:10Igor Shparlinski (Sydney), Integers of prescribed arithmetic structure in residue classes
Abstract. We give an overview of recent results about the distribution some special integers in residues classes modulo a large integer q. Questions of this type were introduced by Erdos, Odlyzko and Sarkozy (1987), who considered products of two primes as a relaxation of the classical question about the distribution of primes in residue classes. Since that time, numerous variations have appeared for different sequences of integers. The types of numbers we discuss include smooth, square-free, square-full and almost primes integers. We also expose the wealth of different techniques behind these results: sieve methods, bounds of short Kloosterman sums, bounds of short character sums and many others.

Belgian Dutch Algebraic Geometry Day

November 8, Antwerpen.

DIAMANT Symposium

November 29, De Bilt. The is part of a two-day event, November 28-29.

Intercity Number Theory Seminar

December 13, UvA and VU Amsterdam. At the VU.

Intercity Number Theory Seminar / Getaltheorie in het vlakke land

December 11, Utrecht. (2020)