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

June 21, 2019, at the University of Amsterdam

On June 21, 2019, the next meeting of the Belgian-Dutch Algebraic Geometry seminar will be held at the University of Amsterdam. Location: room G2.10 at Science Park 904, Amsterdam.

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

13:00-14:00 Diletta Martinelli (Edinburgh) On the geometry of contractions of the Moduli Space of sheaves of a K3 surface
Abstract: I will describe how recent advances have made possible to study the birational geometry of hyperkaehler varieties of K3-type using the machinery of wall-crossing and stability conditions on derived categories as developed by Tom Bridgeland. In particular Bayer and Macrì relate birational transformations of the moduli space M of sheaves of a K3 surface X to wall-crossing in the space of Bridgeland stability conditions Stab(X). I will explain how it is possible to refine their analysis to give a precise description of the geometry of the exceptional locus of any birational contraction of M.
14:30-15:30 Zsolt Patakfalvi (EPFL) On the Beauville-Bogomolov decomposition in positive characteristic
Abstract: I will present a work in progress joint with Maciej Zdanowicz aiming to prove a positive characteristic version of the Beauville-Bogomolov decomposition. Over the complex numbers this decomposition was shown using differential geometry methods in the 70's and the 80's. It concerns varieties with trivial canonical bundle, which we call K-trivial here. The main statement over the complex number is that smooth projective K-trivial varieties admit an étale cover which splits as a product of three types of varieties: abelian, Calabi-Yau and symplectic. I will present a similar statement in positive characteristic for (weakly) ordinary K-trivial varieties, the proof of which uses purely positive characteristic methods.
16:00-17:00 Yichao Tian (Strasbourg) Geometry of unitary Shimura varieties at non-quasi-split primes and arithmetic applications
Abstract: Let E/Q be an imaginary quadratic number field, and G be the unitary group associated to a Hermitian space over E of dimension n of signature type (1,n-1). We consider a prime number p inert in E such that the Hermitian space is not quasi-split at p. In this talk, I will explain the geometry in characteristic p of the Shimura variety attached to G of maximal level at p. It turns out that the Shimura variety has semi-stable reduction and one has a very explicit description of its supersingular locus. The intersection of the irreducible components of the supersingular locus encodes interesting arithmetic information. This is part of my joint work in progress with Yifeng Liu, Liang Xiao, Wei Zhang and Xinwen Zhu.

Previous meetings of the seminar (in reverse chronological order)

February 1, 2019, at Utrecht University

Dan Petersen (Stockholm University) Tautological classes with twisted coefficients
Donatella Iacono (Università di Bari) DG-Lie algebras and deformation of pairs
Georg Oberdieck (University of Bonn) Quantum cohomology of the Hilbert scheme of pairs

September 20 and 21, 2018 at Radboud University Nijmegen

Ching-Li Chai (UPenn) Sustained p-divisible groups and the foliation on moduli spaces of abelian varieties
Jörg Wildeshaus (Paris 13) Weights and conservativity
Kestutis Cesnavicius (CNRS/Paris-Sud) Purity for the Brauer group
Claire Voisin (Collège de France) Gonality and zero-cycles of abelian varieties
Victoria Hoskins (FU Berlin) On the motive of the stack of vector bundles on a curve
Richard Thomas (Imperial College) Refined Vafa-Witten invariants for projective surfaces
Piotr Achinger (IMPAN, Warsaw) Serre-Tate theory for Calabi-Yau varieties

June 8, 2018 at the KU Leuven

Arend Bayer (Edinburgh) Families of Hyperkaehler varieties via families of stability conditions
Christian Liedtke (Technische Universität München) A Néron-Ogg-Shafarevich criterion for K3 Surfaces
José Burgos Gil (ICMAT, Madrid) Grothendieck's period conjecture and zeta values

March 23, 2018 at Leiden University

Videos of the lectures are available via youtube.
Florian Ivorra (FRIAS, Freiburg) Quasi-unipotent motives
Peter Jossen (ETH Zürich) Galois groups and Motivic Fundamental groups
Lionel Darondeau (KU Leuven) Jet differentials and hyperbolicity

December 15, 2017 at Radboud University Nijmegen

Johannes Nicaise (Imperial College and Leuven) Specialization of (stable) rationality in families with mild singularities
Javier Fresán (École Polytechnique) Exponential motives
Michael Groechenig (FU Berlin) p-adic integration for the Hitchin system

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