On June 8, the next meeting of the BelgianDutch Algebraic Geometry seminar will be held in Leuven. The lectures are given in the Landbouwinstituut Hoofdgebouw, room 00.215  aula Jozef Heuts
Programme (click a title to show/hide the abstract) 

13:4514:45  Arend Bayer (Edinburgh)  Families of Hyperkaehler varieties via families of stability conditions
Abstract: Bridgeland stability conditions on derived categories of algebraic varieties and their wallcrossings have recently been used extensively to study the geometry of moduli spaces of stable sheaves. In work in progress with Macri, Lahoz, Nuer, Perry and Stellari, we are extending this toolkit to the "relative" setting, i.e. for a family of varieties. Our construction comes with relative moduli spaces of stable objects; this gives additional ways of constructing new families of varieties from a given family, thereby potentially relating different moduli spaces of varieties. Our main application is for families of cubic fourfolds; in particular, this produces many new examples of algebraically constructed families of Hyperkaehler varieties over a base of maximal dimension 20.

15:0016:00  Christian Liedtke (Technische Universität München)  A NéronOggShafarevich criterion for K3 Surfaces
Abstract: Let R be complete local ring with field of fractions K and residue field k, let X be a K3 surface over K, and assume that X has potential
semistable reduction (which is automatic if char(k)=0). If char(K)=0, then we show that the following are equivalent:
(1) the ladic Galois representation on H^{2}(X,Q_{l}) is unramified for one l different from p;
(2) the ladic Galois representation on H^{2}(X,Q_{l}) is unramified for all l different from p;
(3) the padic Galois representation on H^{2}(X,Q_{p}) is crystalline;
(4) the surface has good reduction after an unramified extension of K.
For example, if R is a power series over the complex numbers, then this says that a family of K3 surfaces over a pointed disk can be filled in smoothly over the origin (that is, has good reduction) if and only the monodromy representation on H^{2} is trivial. However, in the arithmetic situation, where the residue field k might not be algebraically closed, then an unramified base change might be needed. We show by example that sometimes, a nontrivial basechange is necessary. In any case, we show that if (1) to (3) hold, then there always exists a model over R whose special fiber X_{0} has at worst canonical singularities. Then, good reduction of X is equivalent to having an isomorphism between H^{2} of X and the minimal resolution of singularities of X_{0}, such that this isomorphism is compatible with the natural Galoisactions (or Fisocrystal structures). In my talk, I will introduce all the above notions, which will not give me much time to explain proofs. Part of this is joint with Matsumoto, part of this is joint with Chiarellotto and Lazda. 
16:3017:30  Lionel Darondeau (KUL)  Jet differentials and hyperbolicity
Abstract: Hyperbolicity is the study of the geometry of holomorphic entire curves f: C→ X with values in a given complex manifold. In this talk, we will give some definitions and provide motivating historical examples. Then, we will describe the formalism of jets, that can be viewed as a coordinate free description of the differential equations that entire curves may satisfy, and explain a successful general strategy to study hyperbolicity due to Bloch, Demailly, Siu. We will end the talk with a quick review of some recent results on hyperbolicty and related topics.

March 23, 2018 at Leiden University 

Videos of the lectures are available via youtube.  
Florian Ivorra (FRIAS, Freiburg)  Quasiunipotent motives  
Peter Jossen (ETH Zürich)  Galois groups and Motivic Fundamental groups  
José Burgos Gil (ICMAT, Madrid)  Grothendieck's period conjecture and zeta values  
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)  padic 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 blowups 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 biarrangements  
Misha Verbitsky (ULB, Bruxelles)  Transcendental Hodge algebra  
June 11 and 12, 2015 in Nijmegen, joint with NoGAGS 

Daniel Greb (DuisburgEssen)  Movable curves and semistable sheaves  
Klaus Künnemann (Regensburg)  A tropical approach to nonarchimedean Arakelov geometry  
Kevin Buzzard (Imperial College)  Preadic 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 Dmodules in positive characteristic  
Christian Lehn (Hannover)  Rational curves on singular cubic fourfolds  
Ulf Kühn (Hamburg)  A geometric approach to constructing elements of K_{2} of curves  
November 14, 2014 at the University of Amsterdam 

Minhyong Kim (Oxford)  Nonabelian reciprocity laws and Diophantine geometry  
Mingmin Shen (UvA)  Multiplicative ChowKünneth 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  
FrankOlaf 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  
JeanBenoît 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 Sarithmetic groups  
Matthieu Romagny (Jussieu)  Models of groups schemes of roots of unity  
Mircea Mustaţă (Michigan)  Adjoint line bundles in positive characteristic 