Journées GAGC à Poitiers

18 - 20 October 2023 in Poitiers


Giuseppe Ancona (Strasbourg)
Chenyu Bai (Paris)
Anna Bot (Basel)
Hoang-Chinh Lu (Angers)
Matilde Manzaroli (Tübingen)
Anne Pichon (Marseille)
Rémi Reboulet (Göteborg)
Gabriele Rembado (Bonn)
Adrien Sauvaget (Cergy Pontoise)
Zhixin Xie (Nancy)

Registration: from 10 June until 20 September. Send an email to enrica.floris@univX-poiXtiers.Xfr (delete the letter X) with subject gagc 2023.

Schedule and location

Campus Futuroscope, Bâtiment H03, room Math 06, map of campus
From the train station: Take Bus 1 at the stop Gare Léon Blum, direction Futuroscope-Lycée Pilote, stop Gustave Eiffel
From the city center: Take Bus 1 at the stop Place Lepetit, direction Futuroscope-Lycée Pilote, stop Gustave Eiffel
The bus trip takes approximately 30 minutes.

 Wednesday  18 October  Thursday  19 October  Friday  20 October





   Anna Bot

   Adrien Sauvaget

   coffee break

   Matilde Manzaroli

  Gabriele Rembado

   Hoang-Chinh Lu

   coffee break

   Anne Pichon




   Chenyu Bai

   Giuseppe Ancona


   Rémi Reboulet

   Zhixin Xie

   social dinner




Titles and Abstracts

Click on the name of the speaker to see title and abstract of their talk

Lefschetz standard conjecture for some lagrangian fibrations

The Lefschetz standard conjecture predicts the existence of some specific algebraic classes on the square of an algebraic variety, namely the inverse of the Lefschetz operator should be induced by an algebraic correspondence. We will show this conjecture for the hyper-kähler varieties constructed by Laza-Saccà-Voisin. This will be a special case of a general criterion which will tell that hyper-kähler varieties admitting lagrangian fibrations « of Ngô type » satisfy this conjecture. I will start by recalling the conjecture and the known results.Then I will discuss how the conjecture behaves under fibration and explain why several difficulties appear. Finally I will explain why in the setting of lagrangian fibrations these difficulties can be treated. A crucial input is Ngô's support theorem, which I will recall as well. This is a joint work with Mattia Cavicchi, Robert Laterveer and Giulia Saccà.

Measures of Irrationality of Projective K3 Surfaces

My presentation will delve into the realm of measuring the degree of irrationality, fibering gonality, and fibering genus of projective K3 surfaces with Picard number 1. By exploring these measures, we gain insights into the anticipated asymptotic behaviors of these attributes for projective K3 surfaces in this category.

A smooth complex rational affine surface with uncountably many nonisomorphic real forms

A real form of a complex algebraic variety X is a real algebraic variety whose complexification is isomorphic to X. Many families of complex varieties have a finite number of nonisomorphic real forms, but up until recently no example with infinitely many had been found. In 2018, Lesieutre constructed a projective variety of dimension six with infinitely many nonisomorphic real forms, and last year, Dinh, Oguiso and Yu described projective rational surfaces with infinitely many as well. In this talk, I'll present the first example of a rational affine surface having uncountably many nonisomorphic real forms.

Monge-Ampère volume

We define and study two geometric objects attached to a compact complex manifold: the lower and upper bounds for Monge-Ampère volumes of quasi-plurisubharmonic functions. We prove that having Monge-Ampère volumes uniformly bounded from above and/or below is metric-independent and bimeromorphic invariant. As an application, we give an answer to a conjecture of Demailly-Paun saying that a nef class with positive intersection number contains a Kähler current. This is a joint work with Vincent Guedj.

Topology of totally real degenerations

In this talk, we study the topology of totally real semi-stable degenerations. The main result is a bound for the individual Betti numbers of a smooth real fiber in terms of the complex geometry of the degenerated fiber. The main ingredient is the use of real logarithmic geometry, which makes it possible to study degenerations that are not necessarily toric, and therefore to go beyond the case of smooth tropical degenerations, studied by Renaudineau-Shaw. This is a work in collaboration with Emiliano Ambrosi.

Lipschitz geometry of complex analytic germs

Let (X,0)⊆ (ℂn,0) be a germ of analytic set. For all sufficiently small ε >0 the intersection of X with the sphere S2n-1ε of radius ε about 0 is transverse, and X is locally ''topologically conical'', i.e., homeomorphic to the cone on its link Lε=X∩ S2n-1ε. However, it is in general not metrically conical: there are parts of the link Lε with non-trivial topology which shrink faster than linearly when ε tends to 0. A natural problem is then to build classifications of the germs up to local bi-Lipschitz homeomorphism, and what we call Lipschitz geometry of a singular space germ is its equivalence class in this category. There are different approaches for this problem depending on the choice of the metric. A germ (X,0) has actually two natural metrics induced from any embedding in ℂn with a standard euclidean metric: the outer metric is defined by the restriction of the euclidean distance, while the inner metric is defined by the infimum of lengths of paths in V. I will give an introductive talk on the topic and review some of the recent results on Lipschitz classifications of complex germs. Some of these results are joint works with Lev Birbrair and Walter Neumann. I will also present a recent logarithmic version of the link of a complex analytic germ which is equipped with an ultrametric. This non-archimedean object reflects the behavior of the inner and outer metrics of the germ and it enables to describe its Lipschitz geometries through some decompositions of the logarithmic link into ultrametric balls. This last part is a work in progress with Lorenzo Fantini and Walter Neumann.

Transcendental Okounkov bodies and toric degenerations

It is a well-known fact, dating back to the work of Atiyah--Guillemin--Sternberg, that there exists a correspondence between Delzant polytopes in ℝn and polarised toric projective varieties (X,L) of dimension n. A generalisation of one direction of this construction, the Okounkov body, associates to any pair (X,L) (without assuming existence of any group action, and with L possibly being big rather than ample) a convex body in ℝn that captures the volume of L. We prove an open conjecture stating that a similar construction also holds on Kähler manifolds endowed with a big cohomology class, generalising prior work of Deng from surfaces to manifolds of arbitrary dimension. In this talk, I will give an informal introduction to these topics and our result, and explain a new geometric interpretation of these convex bodies based on the construction of toric degenerations of Kähler manifolds. This is joint work with T. Darvas, D. W. Nyström, M. Xia, and K. Zhang.

Meromorphic connections and wild mapping class groups

Moduli spaces of holomorphic connections on principal/vector bundles over Riemann surfaces have a rich geometric structure: they are complex symplectic manifolds, and their monodromy data lead to the standard character varieties. Moreover, as certain natural deformation parameters are deformed, they assemble into local systems over the space of deformation parameters, bringing about actions of the mapping class groups. (After quantisation, such objects are relevant to the mathematical formalisation of quantum field theory with gauge/conformal symmetries.) In this talk we will aim at a review of part of this story, and then present a generalisation for moduli spaces of meromorphic connections with arbitrary singularities. These are still complex symplectic manifolds, leading to wild character varieties and (after deformation) to actions of new wild mapping class groups. This is joint work with P. Boalch, J. Douçot, G. Felder, M. Tamiozzo and R. Wentworth.

Isomonodromic foliations and Witten-Kontsevich theorem

The psi-classes are cohomology classes that occur naturally in moduli spaces of curves. Witten suggested a conjectural approach to calculate them, which was later proven by Kontsevich (1992). Various proofs of this theorem have been presented over time. Here, I will present a new proof that relies on the existence of isomonodromic deformations on surfaces with cone singularities, or, alternatively, on the existence of isomonodromic foliations on moduli spaces of cone surfaces.

Cones of divisors on ℙ3 blown up at eight very general points

Let X be the blowup of ℙ3 at eight very general points. Then X is a smooth projective threefold whose anticanonical divisor is nef but not semiample. In this talk we describe explicitly the cone of nef divisors and the cone of effective divisors on X. Moreover, we show that a certain Weyl group acts with a rational polyhedral fundamental domain on the effective movable cone of X. This is joint work with I. Stenger.



Eduardo Alves da Silva
Giuseppe Ancona
Chenyu Bai
Pietro Beri
Gustave Billon
Samuel Boissière
Aurore Boitrel
Antoine Boivin
Anna Bot
Michel Brion
Maxime Cazaux
Louis Dailly
Rémi Danain
Romain Demelle
Bruno Dewer
Stéphane Druel
Adrien Dubouloz
Laurent Evain
Loïs Faisant
Enrica Floris
Pascal Fong
Franco Giovenzana
Crislaine Kuster
Hoang-Chinh Lu
Matilde Maccan
Matthieu Madera
Matilde Manzaroli
Yann Millot
Martina Monti
Mattia Morbello
Wayne Ng Kwing King
Boris Pasquier
Anne Pichon
Ana Quedo
Eloan Rapion
Rémi Reboulet
Gabriele Rembado
Xavier Roulleau
Claude Sabbah
Adrien Sauvaget
Egor Yasinski
Zhixin Xie
Sokratis Zikas
Susanna Zimmermann



Stéphane Druel (Lyon)
Enrica Floris (Poitiers)



Scientific commitee:

Sébastien Boucksom (Paris)
Damien Calaque (Montpellier)
Antoine Chambert-Loir (Paris-Diderot)
Andreas Höring (Nice)
Laurent Manivel (Toulouse)
Anne Moreau (Paris-Sud)
Christophe Mourougane (Rennes)

Financial support:

We gratefully acknowledge support from:
LMA de Poitiers