CONFERENCE
Algebraic Geometry and Complex Geometry
Géométrie algébrique et géométrie complexe
17 - 21 December, 2018
Algebraic Geometry and Complex Geometry
Géométrie algébrique et géométrie complexe
17 - 21 December, 2018
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Scientific Committee
Comité scientifique Vincent Guedj (Université Paul Sabatier, Toulouse) Christophe Mourougane (Université Rennes 1) Angela Ortega (Humboldt Universität, Berlin) Nicolas Ressayre (Université Lyon 1) |
Organizing Committee
Comité d'organisation Olivier Benoist (CNRS/ENS Paris) Boris Pasquier (Université de Poitiers) |
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The aim of this conference is to get together algebraic geometers and complex geometers, around recent topics of interest.
It is organised by the GDR 3064 Géometrie Algebrique et Géometrie Complexe (Research Group of the CNRS). Mornings will be devoted to 5 mini-courses, given by experts, on important new developments. The afternoons are devoted to more specialized 50 minutes talks. They will be chosen by the scientific committee between 3 and 6 months before the conference. A short talks (10 minutes) session will be also organized during the conference to enable participants to talk about their works or about open questions. |
Le but de cette rencontre est de rassembler des géomètres algébristes et des géomètres complexes autour de thèmes d'actualité.
Elle est organisée par le GDR 3064 Géométrie Algébrique et Géometrie Complexe. Le format prévu pour cette rencontre est le suivant. Le matin sont donnés cinq mini-cours (divisés chacun en trois séances de 45 minutes) sur des travaux récents de grande importance en géométrie algébrique et géométrie complexe. Les après-midis sont consacrés à des exposés de 50 minutes. Une séance d'exposés courts (10 minutes) sera aussi organisée pour permettre aux participants qui le souhaitent de présenter rapidement leurs travaux ou des questions ouvertes. |
Mini-courses
Nicolas Addington (University of Oregon) : Cubic fourfolds
I will give three expository lectures on cubic fourfolds. I will discuss some classical geometry (rationality of cubics containing planes, quintic del Pezzo surfaces, or sextic elliptic ruled surfaces), some lattice theory (Torelli theorem, associated K3 surfaces), some hyperkähler geometry (the variety of lines, Lehn's 8-fold), and how Kuznetsov's K3 category clarifies these topics
I will give three expository lectures on cubic fourfolds. I will discuss some classical geometry (rationality of cubics containing planes, quintic del Pezzo surfaces, or sextic elliptic ruled surfaces), some lattice theory (Torelli theorem, associated K3 surfaces), some hyperkähler geometry (the variety of lines, Lehn's 8-fold), and how Kuznetsov's K3 category clarifies these topics
Hélène Esnault (Freie Universität Berlin) : Fundamental groups in algebraic and arithmetic geometry
Hélène Esnault (Freie Universität Berlin) : Fundamental groups in algebraic and arithmetic geometry
Gerard Freixas i Montplet (Institut de Mathématiques de Jussieu) : On the Arakelov theory of Shimura varieties
Gerard Freixas i Montplet (Institut de Mathématiques de Jussieu) : On the Arakelov theory of Shimura varieties
In these lectures I will discuss a recent theorem of Bruinier-Howard-Kudla-Rapoport-Yang on the modularity of generating series of arithmetic special cycles on unitary Shimura varieties. This is the kind of prototype result we seek in the Arakelov geometric study of Shimura varieties. For this, I will first present basic definitions in arithmetic intersection theory. Then I will review the construction of the Shimura varieties in question, their toroidal compactifications and special cycles. Finally, I will state and explain the modularity theorem.
https://webusers.imj-prg.fr/~gerard.freixas/Articles\%20de\%20Survol/Freixas-Fourier.pdf
https://webusers.imj-prg.fr/~gerard.freixas/Articles\%20de\%20Survol/Freixas-CIMPA.pdf
In these lectures I will discuss a recent theorem of Bruinier-Howard-Kudla-Rapoport-Yang on the modularity of generating series of arithmetic special cycles on unitary Shimura varieties. This is the kind of prototype result we seek in the Arakelov geometric study of Shimura varieties. For this, I will first present basic definitions in arithmetic intersection theory. Then I will review the construction of the Shimura varieties in question, their toroidal compactifications and special cycles. Finally, I will state and explain the modularity theorem.
https://webusers.imj-prg.fr/~gerard.freixas/Articles\%20de\%20Survol/Freixas-Fourier.pdf
https://webusers.imj-prg.fr/~gerard.freixas/Articles\%20de\%20Survol/Freixas-CIMPA.pdf
Stefan Kebekus (Albert-Ludwigs-Universität Freiburg) : Extension Theorems for differential forms and applications
Stefan Kebekus (Albert-Ludwigs-Universität Freiburg) : Extension Theorems for differential forms and applications
We present new extension theorems for differential forms on singular complex spaces, which are particularly useful in the study of minimal varieties, with the singularities of the minimal model program. We sketch the proof and survey a number of applications, pertaining to classification and characterisation of special varieties, non-Abelian Hodge Theory in the singular setting, and quasi-étale uniformization.
We present new extension theorems for differential forms on singular complex spaces, which are particularly useful in the study of minimal varieties, with the singularities of the minimal model program. We sketch the proof and survey a number of applications, pertaining to classification and characterisation of special varieties, non-Abelian Hodge Theory in the singular setting, and quasi-étale uniformization.
Colleen Robles (Duke University) : On degenerations of Hodge structures
Talks
Michele Ancona (Université Claude Bernard Lyon 1) Random section of line bundles over real Riemann surfaces - VIDEO -
Philippe Eyssidieux (Université Grenoble Alpes) Exemples de groupes Kählériens - VIDEO -
Andrea Fanelli (UVSQ Versailles) Fibrations de Fano en caractéristique positive - VIDEO -
Kevin Langlois (Heinrich Heine Universität, Düsseldorf) Intersection cohomology and torus actions of complexity one
Hsueh-Yung Lin (Universität Bonn) On the existence of algebraic approximations of compact Kähler manifolds (pdf) - VIDEO -
Frédéric Mangolte (Université d'Angers) Algebraic models of the line in the real affine plane (pdf) - VIDEO -
Adrien Sauvaget (Université Pierre et Marie Curie) Mazur-Veech volumes and intersection theory on the Hodge bundle
Junyi Xie (CNRS IRMAR, Université de Rennes I) The geometric Bogomolov conjecture
Michele Ancona (Université Claude Bernard Lyon 1) Random section of line bundles over real Riemann surfaces - VIDEO -
Philippe Eyssidieux (Université Grenoble Alpes) Exemples de groupes Kählériens - VIDEO -
Andrea Fanelli (UVSQ Versailles) Fibrations de Fano en caractéristique positive - VIDEO -
Kevin Langlois (Heinrich Heine Universität, Düsseldorf) Intersection cohomology and torus actions of complexity one
Hsueh-Yung Lin (Universität Bonn) On the existence of algebraic approximations of compact Kähler manifolds (pdf) - VIDEO -
Frédéric Mangolte (Université d'Angers) Algebraic models of the line in the real affine plane (pdf) - VIDEO -
Adrien Sauvaget (Université Pierre et Marie Curie) Mazur-Veech volumes and intersection theory on the Hodge bundle
Junyi Xie (CNRS IRMAR, Université de Rennes I) The geometric Bogomolov conjecture
SPONSORS
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ANR ECOVA ANR-15-CE40-0002-01
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