Organizers: Ben Moonen (Nijmegen), Johannes Nicaise (Imperial College/Leuven), Lenny Taelman (Amsterdam), Nero Budur (Leuven), Martijn Kool (Utrecht), David Holmes (Leiden)

Next meeting: April 26, 2024, at Utrecht University

On April 26, 2024, the next meeting of the Belgian-Dutch Algebraic Geometry seminar will be held at Utrecht University. Location: Ruppert Rood (Utrecht Science Park).

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

13:15-14:15 Soumya Sankar (Utrecht) On the rationality of conic bundle threefolds
Abstract: One of the major programs in algebraic geometry seeks to understand when a given variety is rational, and what the obstructions to rationality are. From this perspective, conic bundles are a geometrically rich class of varieties. Hassett—Tschinkel and Benoist—Wittenberg recently introduced a rationality obstruction that can be translated into a question about curve classes on threefolds. I will talk about joint work with Sarah Frei, Lena Ji, Bianca Viray and Isabel Vogt, where we study curve classes on certain conic bundle threefolds over arbitrary fields of odd characteristic. We then use the description of these classes to study the rationality of such varieties
14:45-15:45 Dimitri Wyss (EPFL) Non-archimedean integration on quotients
Abstract: Motivated by mirror symmetry, Batyrev defines 'stringy' Hodge numbers for a variety X with Gorenstein canonical singularities using motivic integration. While in general it is an open question, whether these numbers are related to a cohomology theory, the orbifold formula shows, that if X has quotient singularities, they agree with Chen-Ruan's orbifold Hodge numbers. I will explain how to generalize this orbifold formula to quotients of smooth varieties by linear algebraic groups. As an application we obtain identifications of stringy Hodge numbers with enumerative invariants, so-called BPS-invariants, in the case when X is the moduli space of a CY1 category. This is joint work with Michael Groechenig and Paul Ziegler.
16:15-17:15 Jef Laga (Cambridge) Ceresa cycles of Picard curves
Abstract: The Ceresa cycle is a canonical algebraic 1-cycle in the Jacobian of a curve with a marked point. In some sense it is the simplest non-trivial canonical algebraic cycle 'beyond homology' and as such it is a natural testing ground for our knowledge of cycles on abelian varieties. The Ceresa cycle vanishes for all hyperelliptic curves, but beyond this little is known about the locus of curves in Mg where this cycle is torsion. In this talk I will discuss joint work with Ari Shnidman where we find this torsion locus for a special family of genus-3 curves called Picard curves.

Previous meetings of the seminar (in reverse chronological order)

October 27, 2023, at Leiden University

Rahul Pandharipande (ETH Zürich) Abelian varieties, curves, and the Hilbert scheme of points of the plane. (See here for detailed notes.)
Farbod Shokrieh (Univ. of Washington) Arakelov invariants and non-archimedean geometry
Yajnaseni Dutta (Leiden University) Birational self-maps on Hyperkähler (HK) manifolds

March 24, 2023, at Radboud University Nijmegen

Alexander Petrov (Harvard and MPI Bonn) Decomposability of the de Rham complex in positive characteristic
Sabrina Pauli (Duisburg-Essen)) Counting curves over an arbitrary field using tropical geometry
Emanuele Macrì (Orsay) Hyper-Kähler manifolds and Lagrangian fibrations

December 9, 2022, at the University of Amsterdam

Piotr Achinger (IMPAN) The Riemann-Hilbert correspondence for rigid spaces
Laura Pertusi (Milan) Moduli spaces of stable objects in Enriques categories
Dustin Clausen (Copenhagen) Algebraic geometry from the solid perspective

September 30, 2022, at the KU Leuven

Javier de Bobadilla (BCAM) Monodromy at radius zero and equimultiplicity of families with constant Milnor number
Valentijn Karemaker (Utrecht) The Gauss problem for central leaves
Gebhard Martin (Bonn) On the non-degeneracy of Enriques surfaces

November 8, 2019, at the University of Antwerp

Lie Fu (Lyon and Nijmegen) Orbifold products on motivic cohomology and hyper-Kaehler resolution conjectures
Špela Špenko (UL Bruxelles) Perverse schobers in geometric invariant theory
Stefan Kebekus (Freiburg) Extension Theorems for differential forms and applications

June 21, 2019, at the University of Amsterdam

Diletta Martinelli (Edinburgh) On the geometry of contractions of the Moduli Space of sheaves of a K3 surface
Zsolt Patakfalvi (EPFL) On the Beauville-Bogomolov decomposition in positive characteristic
Yichao Tian (Strasbourg) Geometry of unitary Shimura varieties at non-quasi-split primes and arithmetic applications

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