On September 20 and 21, the next meeting of the BelgianDutch Algebraic Geometry seminar will be held at Radboud University Nijmegen. A special 2day event this time! The lectures are given in the Huygensgebouw (Heijendaalseweg 135), room HG00.071.
Programme (click a title to show/hide the abstract) 

Thursday, 20 September  
13:3014:30  ChingLi Chai (University of Pennsylvania)  Sustained pdivisible groups and the foliation on moduli spaces of abelian varieties
Abstract: We will explain joint work with Frans Oort on the notion of 'sustained pdivisible groups' and its application to the foliation structure on moduli spaces of abelian varieties in positive characteristic p. This notion is a schemetheoretic version of the concept of 'geometrically fiberwise constant pdivisible group' introduced by Frans Oort in 2001 in order to define the central foliation structure on moduli spaces of abelian varieties. Thus we get a
schemetheoretic definition of central leaves in moduli spaces of abelian varieties. This updated definition facilitates the analysis of differential properties of central leaves and reveals their fine local structure. If time permits we will also discuss recent progress on local rigidity for formal completions of central leaves.

15:0016:00  Jörg Wildeshaus (Université Paris 13)  Weights and conservativity
Abstract: After an introduction to weight structures, and a comparison to tstructures, we shall concentrate on conservativity of functors whose source is a triangulated category with a weight structure. Two questions will be of interest to us: (1) Does conservativity of the restriction
of the functor to the heart of the weight structure imply conservativity of the functor itself? (2) Is it possible to control the weights of an object from its image under the functor (this principle will be referred to as "weight conservativity")? It turns out that (1) and (2) admit a common answer. It is based on the notion of "minimal weight filtration". Our main application concerns the étale realization of motives of Abelian type.

16:3017:30  Kestutis Cesnavicius (CNRS / Université ParisSud)  Purity for the Brauer group
Abstract: A purity conjecture due to Grothendieck and AuslanderGoldman predicts that the Brauer group of a regular scheme does not change after removing a closed subscheme of codimension at least 2. The combination of several works of Gabber settles the conjecture except for some cases that concern ptorsion Brauer classes in mixed characteristic (0,p). We will discuss an approach to the mixed characteristic case via the tilting equivalence for perfectoid rings.

Friday, 21 September  
09:3010:30  Claire Voisin (Collège de France)  Gonality and zerocycles of abelian varieties
Abstract: The gonality of a variety is defined as the minimal gonality of a curve sitting in the variety. We prove that the gonality of a very general abelian variety of dimension g goes to infinity with g. We use for this a generalization of a method of Pirola that we will describe, and rests on the notion of naturally defined subsets of abelian varieties. The method also leads to a number of other applications concerning 0cycles modulo rational equivalence on very general abelian varieties. For example, for a general abelian variety A of dimension at least 2k – 1, the orbit of k{x} is countable for any point x of A. Furthermore, the set of divisors D such that D^{k} = 0 in CH^{k}(A) is countable.

11:0012:00  Victoria Hoskins (Freie Universität Berlin)  On the motive of the stack of vector bundles on a curve
Abstract: Following Grothendieck's vision that a motive of an algebraic variety should capture many of its cohomological invariants, Voevodsky introduced a triangulated category of motives which partially realises this idea. After describing some of the properties of this category, I will explain how to define the motive of certain algebraic stacks by generalising a construction of Totaro. I will then focus on defining and studying the motive of the moduli stack of vector bundles on a smooth projective curve and show that this motive can be described in terms of the motive of this curve and its symmetric powers. If there is time, I will give a conjectural formula for this motive, and explain how this follows from a conjecture on the intersection theory of certain Quot schemes. This is joint work with Simon Pepin Lehalleur.

13:0014:00  Richard Thomas (Imperial College London)  Refined VafaWitten invariants for projective surfaces
Abstract: I'll describe how to define VafaWitten invariants – and refined VafaWitten invariants – of projective surfaces. Then I'll explain how to calculate some parts of the theory via degeneracy loci and "CarlssonOkounkov operators". The talk describes different projects joint with Yuuji Tanaka, Davesh Maulik and Amin Gholampour.

14:3015:30  Piotr Achinger (IMPAN, Warsaw)  SerreTate theory for CalabiYau varieties
Abstract: Classical Serre–Tate theory describes deformations of ordinary abelian varieties. It implies that every such variety has a canonical lift to characteristic zero and equips the moduli space with a Frobenius lifting and canonical multiplicative coordinates. I will discuss a construct canonical liftings modulo p^2 of varieties with trivial project, joint with Maciej Zdanowicz (EPFL), whose aim is canonical class which are ordinary in the weak sense that the Frobenius acts bijectively on the top cohomology of the structure sheaf. Consequently, we obtain a Frobenius lifting on the moduli space of such varieties. The quite explicit construction uses Frobenius
splittings and a relative version of Witt vectors of length two.

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 NéronOggShafarevich 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)  Quasiunipotent 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)  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 