Organizers: Arne Smeets and Ben Moonen (Nijmegen), Johannes Nicaise (Imperial College/Leuven), Lenny Taelman (Amsterdam), Nero Budur (Leuven) and Bas Edixhoven (Leiden)

Next meeting: December 15, 2017 at Radboud University Nijmegen

The 12th Belgian-Dutch Algebraic Geometry Day will be held on Friday, December 15 in Nijmegen. The speakers are Javier Fresán, Michael Groechenig and Johannes Nicaise.

Venue: Radboud University Nijmegen, Huygens building, room HG00.062 (ground floor). Address: Heyendaalseweg 135, Nijmegen. Travel directions.

Programme (click a title to show/hide the abstract)

13:00-14:00 Johannes Nicaise (Imperial College and Leuven) Specialization of (stable) rationality in families with mild singularities
Abstract: I will present joint work with Evgeny Shinder, where we use Denef and Loeser's motivic nearby fiber and a theorem by Larsen and Lunts to prove that stable rationality specializes in families with mild singularities. I will also discuss an improvement of our results by Kontsevich and Tschinkel, who defined a birational version of the motivic nearby fiber to prove specialization of rationality.
14:30-15:30 Javier Fresán (École Polytechnique) Exponential motives
Many interesting numbers, such as the special values of the gamma and the Bessel functions or the Euler constant, are not expected to be periods in the usual sense of algebraic geometry. However, they all appear as coefficients of the comparison isomorphism between two cohomology theories for varieties together with a regular function. Following ideas of Katz, Kontsevich and Nori, this point of view allows one to construct a Tannakian category of exponential motives and to produce Galois groups which conjecturally govern all algebraic relations among exponential periods. Joint work with Peter Jossen.
16:00-17:00 Michael Groechenig (FU Berlin) Rigid local systems
An irreducible representation of an abstract group is called rigid, if it defines an isolated point in the moduli space of all representations. Complex rigid representations are always defined over a number field. According to a conjecture by Simpson, for fundamental groups of smooth projective varieties one should expect furthermore that rigid representations are of geometric origin, and hence should be defined over the ring of algebraic integers. I will report on joint work with H. Esnault where we prove this integrality property for so-called cohomologically rigid representations. Our argument is mostly arithmetic and passes through fields of positive characteristic and the p-adic numbers.

Previous meetings of the seminar (in reverse chronological order)

December 9, 2016 at the University of Amsterdam

June Huh (Princeton) Enumeration of points, lines, planes, etc.
Dieter Kotschick (München) and Stefan Schreieder (Bonn) The Hodge ring of Kähler manifolds
Bhargav Bhatt (Ann Arbor) Derived splinters in mixed characteristic

April 22, 2016 at KU Leuven

Sho Tanimoto (Copenhagen) Towards a refinement of Manin's conjecture
John Christian Ottem (Oslo) Effective cones of cycles on blow-ups of projective space
Bruno Chiarellotto (Padova) Monodromy action and special fiber for semistable schemes over a DVR

December 11, 2015 at Leiden University

David Holmes (Leiden) Models of degenerating jacobians
Clément Dupont (MPIM Bonn) Motives of bi-arrangements
Misha Verbitsky (ULB, Bruxelles) Transcendental Hodge algebra

June 11 and 12, 2015 in Nijmegen, joint with NoGAGS

Daniel Greb (Duisburg-Essen) Movable curves and semistable sheaves
Klaus Künnemann (Regensburg) A tropical approach to non-archimedean Arakelov geometry
Kevin Buzzard (Imperial College) Pre-adic spaces and adic spaces
Tim Dokchitser (Bristol) Local arithmetic of hyperelliptic curves
David Rydh (KTH Stockholm) The local structure of Artin stacks
Lars Kindler (FU Berlin) Ramification theory for D-modules in positive characteristic
Christian Lehn (Hannover) Rational curves on singular cubic fourfolds
Ulf Kühn (Hamburg) A geometric approach to constructing elements of K2 of curves

November 14, 2014 at the University of Amsterdam

Minhyong Kim (Oxford) Non-abelian reciprocity laws and Diophantine geometry
Mingmin Shen (UvA) Multiplicative Chow-Künneth decompositions
Jakob Stix (Frankfurt) Gorenstein orders and abelian varieties over finite fields

May 16, 2014 in Leuven

Olivier Benoist (Strasbourg) Complete families of smooth space curves
Frank-Olaf Schreyer (Saarbrücken) Matrix factorizations and families of curves of genus 15
Carel Faber (Utrecht) On the cohomology of the moduli spaces of pointed curves of genus three

November 22, 2013 in Nijmegen

Nero Budur (Leuven) Cohomology jump loci
Stefan Schröer (Düsseldorf) Wild quotient surface singularities
René Schoof (Rome) Finite group schemes and abelian varieties with good reduction outside one prime

June 14, 2013 in Leiden

Walter Gubler (Regensburg) Normal toric varieties over valuation rings of rank 1
Gaël Rémond (Bordeaux) Isogenies and polarizations
Jean-Benoît Bost (Orsay) Pluripotential theory, heights, and algebraization on arithmetic threefolds
José Ignacio Burgos Gil (ICMAT Madrid) The singularities of the invariant metric of the sheaf of Jacobi forms on the universal elliptic curve

April 19, 2013 in Leuven

Alejandro Soto (Regensburg) Toric Varieties over a Valuation Ring
Sébastien Boucksom (Jussieu) A uniform version of Izumi's theorem
Ariyan Javanpeykar (Leiden) Bounds for Arakelov invariants - algorithmic and Diophantine applications

December 7, 2012 at the UvA

Andrei Caldararu (Wisconsin) Derived intersections
Eduard Looijenga (Utrecht) Cohomological dimension of moduli spaces of curves
Daniel Huybrechts (Bonn) Cycles on K3 surfaces

June 15, 2012 in Leuven

Ted Chinburg (UPenn) Small generators for S-arithmetic groups
Matthieu Romagny (Jussieu) Models of groups schemes of roots of unity
Mircea Mustaţă (Michigan) Adjoint line bundles in positive characteristic