On March 24, 2023, the next meeting of the Belgian-Dutch Algebraic Geometry seminar will be held at Radboud University Nijmegen. Location: room HG00.303 (ground floor) in the Huygens Building, Heyendaalseweg 135, Nijmegen.
Note: participation is free (including an informal dinner after the talks); but for practical reasons we ask that you register, no later than March 17, via this link. Thank you!
Programme (click a title to show/hide the abstract) |
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13:15-14:15 | Alexander Petrov (Harvard and MPI Bonn) | Decomposability of the de Rham complex in positive characteristic
Abstract: Deligne and Illusie proved that if a smooth variety over Fp admits a lift over Z/p2 then the truncation of its de Rham complex in degrees < p is quasi-isomorphic to the direct sum of its cohomology sheaves. As a consequence, the Hodge-to-de Rham spectral sequence of a smooth proper liftable variety degenerates, provided that the dimension of the variety is ≤ p.
It turns out that further truncations of the de Rham complex of a liftable variety need not be decomposable. I will describe the obstruction to decomposing the truncation of the de Rham complex in degrees ≤ p in terms of other invariants of the variety, and will use this to give an example of a smooth projective variety over Fp that lifts to Zp but whose Hodge-to-de Rham spectral sequence does not degenerate at the first page. The proof proceeds by first understanding the obstruction to the formality of the de Rham complex as a commutative algebra (in the appropriate derived sense) using an analog of Steenrod operations from algebraic topology. |
14:45-15:45 | Sabrina Pauli (Duisburg-Essen) | Counting curves over an arbitrary field using tropical geometry
Abstract: A tropical curve is a graph embedded in R^2 satisfying a number of conditions.
Mikhalkin's celebrated correspondence theorem establishes a correspondence between algebraic curves and tropical curves.
This translates the difficult question of counting plane rational curves of degree d through 3d-1 points to the question of counting tropical curves with a given notion of multiplicity through 3d-1 points which can be solved using combinatorics. There are two versions of this correspondence, one for the count of complex curves and one for the real count.
In the talk, I will present work in progress joint with Andrés Jaramillo Puentes in which we provide a version Mikhalkin's correspondence theorem over an arbitrary base field k.
I will also give a short introduction to counting curves over different fields and tropical geometry.
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16:15-17:15 | Emanuele Macrì (Orsay) | Hyper-Kähler manifolds and Lagrangian fibrations
Abstract: A hyper-Kähler manifold is a complex Kähler manifold that is simply connected, compact, and has a unique holomorphic symplectic form, up to constants. This important class of manifolds has been studied in the past in many contexts, from an arithmetic, algebraic, geometric point of view, and in applications to physics and dynamics. The theory in dimension two, namely K3 surfaces, is well understood.
The aim of the seminar is to give an introduction to the theory of hyper-Kähler manifolds in higher dimension, from a point of view of their classification; in particular, about existence of Lagrangian fibrations.
We will present some results in dimension four, obtained recently in collaboration with Olivier Debarre, Daniel Huybrechts and Claire Voisin.
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December 9, 2022, at the University of Amsterdam |
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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 |
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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 |
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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 |
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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 |
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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 |
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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 |
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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 |
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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 |
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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 |
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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 |
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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 |
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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 |
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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 |
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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 |
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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 |
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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 |
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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 |
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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 |
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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 |