CONFERENCE
Algebraic Geometry and Complex Geometry
Géométrie Algébrique et Géométrie Complexe
28 November – 2 December 2022
Scientific Committee
Comité scientifique
Stéphane Druel (CNRS, Université Lyon 1)
Andreas Höring (Université Côte d’Azur)
Laurent Manivel (CNRS, Université Paul Sabatier Toulouse)
Jorge Vitorio Pereira (Institute for Pure Applied Mathematics IMPA)
Organizing Committee
Comité d’organisation
Lionel Darondeau (Sorbonne Université)
Enrica Floris (Université de Poitiers)
The aim of this conference is to bring together algebraic geometers and complex geometers, around recent topics of interest. Participants are mostly researchers from european universities (french, english, german, italian, russian…) but everybody is welcome to participate.
It is organised by the GDR 3064 Géométrie Algébrique et Géométrie Complexe (Research Group of the CNRS, French Scientific Reseach Committee).
The mornings are devoted to 5 mini-courses, given by experts of cutting-edge topics in complex and algebraic geometry or in closely related research domains.
The afternoons are devoted to more specialized 50-minutes talks. They will be chosen by the scientific committee 3 to 6 months before the conference. A short talks (10-minutes) session will be also organized during the conference, most likely one evening, 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 sujets d’actualité. Les participants seront majoritairement des chercheurs (ou enseignants-chercheurs) travaillant dans des institutions européennes (notamment françaises, britanniques, allemandes, suisses et italiennes), mais tout le monde est invité à participer.
La rencontre sera organisée par le GDR 3064 Géométrie Algébrique et Géométrie Complexe. Les participants ne seront pas nécessairement membres du GDR (pour les chercheurs étrangers mais aussi certains français). La conférence a cependant un rôle fédérateur dans la communauté.
Le matin sera consacré à cinq mini-cours (divisés chacun en trois séances de 45 minutes) sur des travaux récents de grande importance en géométrie algébrique, en géométrie complexe ou dans des domaines proches.
Les après-midis sont consacrés à des exposés de recherche plus spécialisés d’environ 50 minutes, selectionnés par le comité scientifique 3 à 6 mois avant la conférence. Une séance d’exposés courts (10 minutes) sera aussi organisée pour permettre à des participants de présenter des questions ouvertes, ou pour donner l’opportunité à un plus grand nombre de participants d’exposer leurs travaux.
MINI-COURSES
Donaldson-Thomas (DT) invariants are counts of stable coherent sheaves or more generally stable complexes of coherent sheaves on Calabi-Yau 3-folds. In these lectures, I will focus on the case of the non-compact Calabi-Yau 3-fold known as local P2 and obtained as the total space of the canonical line bundle of the projective plane. I will describe recent advances towards the global understanding of the wall-crossing behavior of DT invariants, and concrete applications such as the modularity of generating series of Betti numbers of moduli spaces of one-dimensional sheaves on the projective plane. This will be partly based on previous work with Fan, Guo, Wu and work in progress with Descombes, Le Floch, Pioline.
Smooth complex projective hypersurfaces of a given degree enjoy two spectacular features: they all have the same volume and they share the same topology. Of course, these magical global properties vanish locally, i.e. the volume and topology of the intersection of a hypersurface with a fixed ball depend on the hypersurface. But if the latter is random (and of given degree), one can expect the global constant behaviour to have a local echo in the fixed ball. I will explain that this is the case, starting with the seminal work of Shiffman and Zelditch. Then, I will present more recent results about the local topology. A comparison with random real algebraic will be made.
We survey recent progress on the existence of Lagrangian fibrations on compact hyper-Kähler manifolds and on the classification for hyper-Kähler fourfolds. This is based on a joint work with Olivier Debarre, Daniel Huybrechts, and Claire Voisin.
These lectures aim at explaining a series of joint works with Javier Fresán and Jeng-Daw Yu, motivated by conjectures made by Broadhurst and Roberts on arithmetic properties of moments of Bessel functions. The purpose is to introduce the notion of irregular Hodge filtration, in the special case of an exponential mixed Hodge structure, and to illustrate the interest of considering this notion for computing Hodge filtrations of mixed Hodge structures related with Bessel or Airy moments. A Betti variant of this method is also introduced, in order to compute explicitly a period matrix of a pure motive associated to Bessel moments.
Which are the birational involutions of a variety? For the projective plane the first results are attributed to Bertini, although his results are considered incomplete, and the full classification over the field of complex numbers was achieved by L. Bayle and A. Beauville: an involution of the complex projective plane is conjugate to a linear map, a Jonquières map, a Geiser involution and or a Bertini involution. The latter three have a unique fixed curve, which is irrational. Bayle and Beauville showed that their conjugacy classes are in bijection with the isomorphism classes of their fixed curves. Unsurprisingly, it turns out that the classification of birational involutions of the real projective plane is more complicated than that. I will explain the classification of birational involutions of the real projective plane and present a large family of non-conjugate involutions with isomorphic fixed curve.
TALKS
Loïs Faisant (Université Grenoble-Alpes) Asymptotic behaviour of rational curves
Cécile Gachet (Université Côte d’Azur) Positivity of higher exterior powers of the tangent bundle
Liana Heuberger (University of Bath) Combinatorial Reid’s recipe for consistent dimer models
Simon Jacques (Université de Lorraine) Orbit closures in flag varieties for the centralizer of an order-two nilpotent element: normality and resolutions for types A, B, D
Inder Kaur (Loughborough University) Hodhe conjecture for singular varieties
Kuan-Wen Lai (University of Bonn) Bijective Cremona transformations of the plane
Wodson Mendson (Université de Rennes 1) Foliations over positive characteristic and irreducible components
Renata Picciotto (Université d’Angers) The derived moduli of sections and virtual pushforwards
Volodya Roubtsov (Université d’Angers) Multiplication Bessel Kernels: from addition laws to CY periods
Florent Schaffhauser (Université de Strasbourg) Hodge numbers of moduli stacks of principal bundles
Titouan Serandour (Université de Rennes 1) The monodromy map of meromorphic projective structures
Robert Śmiech (University of Warsaw) Singular contact varieties
SPONSORS
