15th edition: Charmey January 12-16, 2026
Tentative Schedule
Monday
January 12 |
Tuesday
January 13 |
Wednesday
January 14 |
Thursday
January 15 |
Friday
January 16 |
|
breakfast |
8:45-9:45
mini-course |
8:45-9:45
mini-course |
8:45-9:45
mini-course |
8:45-9:45
mini-course |
10:15-11:15
mini-course |
10:15-11:15
mini-course |
10:15-11:15
mini-course |
10:00-11:00
mini-course |
12:30
welcome |
11:45-12:45
mini-course |
11:45-12:45
mini-course |
11:45-12:45
mini-course |
11:15-12:15
mini-course |
| lunch |
bus at 12:40 |
14:30-15:30
Yasinsky |
time for discussion /
enjoying the mountain side |
|
16:00-17:00
Poineau |
17:20-18:10
Baudin |
17:20-18:10
short talks |
17:20-18:10
Bockondas |
17:30-18:30
Dutta |
18:30-19:20
Paiva |
18:30-19:20
Modin |
18:30-19:20
van Santen |
19h
dinner |
19:30
dinner |
Mini-courses
-
Intermediate Jacobians
Yajnaseni Dutta (Leiden)
Abstract
The intermediate Jacobian associated to a smooth projective odd-dimensional variety is a geometric structure that captures essential information about the geometry of the variety. For example, Clemens and Griffiths used this gadget to prove that smooth cubic threefolds defined over the complex numbers are not rational. Classically constructed using Hodge theory, its definition over arbitrary base remained a mystery until recently. In this talk, I will introduce this wonderful gadget, review Clemens and Griffiths' technique and discuss some of the recent developments on its definition over arbitrary fields.
-
Berkovich spaces and applications
Jérôme Poineau (Caen)
Abstract
Berkovich theory is often presented as a way to develop a notion of analytic space in the p-adic setting that is analogous to its familiar complex counterpart. However, Berkovich’s original definition actually allows arbitrary Banach rings as base rings, e.g. Z endowed with the usual absolute value, which results in spaces naturally containing complex analytic spaces as well as p-adic analytic spaces for every prime number p. This course will provide an introduction to the classical Berkovich theory (over a p-adic, or more generally non-Archimedean, field), and its global version. The last sessions will present applications to degenerations of complex invariants, and to arithmetic dynamics.
-
Equivariant birational invariants
Egor Yasinsky (Bordeaux)
Abstract
A classical problem in algebraic geometry is to determine when two varieties are birationally equivalent. This question can be naturally refined by assuming that a group, say a finite one, acts on both varieties and then asking whether they are equivariantly birational. In this setting, the notion of "equivariant rationality" becomes the problem of "linearizing" the group action — that is, finding an equivariant birational map to projective space where the group acts linearly. In recent years, a number of new techniques have been developed to show that such equivariant birationalities do not exist. This course will survey some of these methods. We will try to cover the equivariant Sarkisov program, the Bogomolov–Prokhorov and Reichstein–Youssin invariants, the Amitsur group, and the Burnside-type invariants introduced in recent works of Tschinkel and collaborators.
Talks
-
On the Euler characteristic of ordinary irregular varieties
Jefferson Baudin (Lausanne)
Abstract
Informally, a variety is "irregular" if it is closely related to an abelian variety (that is, a smooth projective variety which also admits the structure of a group). This is for example the case of non-rational curves, which embed in their Jacobian.
Over the complex numbers, several methods gave rise to a remarkable results in this field: characterization of abelian varieties by only fixing a few invariants, deeper understanding of the Euler characteristic of irregular varieties, study of their pluricanonical systems, and so on (in any dimension!).
These theorems all rely on analytic techniques, making this whole topic harder to reach in positive characteristic. Our goal in this talk will be to explain purely positive characteristic methods that allow us to "approximate well enough the complex theory", in order to deduce geometric consequences. We will achieve this through presenting the following theorem: if X is a smooth projective ordinary variety of maximal Albanese dimension (i.e. dim(alb(X)) = dim(X)), then the Euler characteristic of the sheaf of top forms is non-negative. If in addition this quantity is zero, then the Albanese image of X is fibered by abelian varieties.
-
Triple lines and Eckardt points on a cubic threefold
Gloire Grâce Bockondas (Neuchâtel)
Abstract
The variety that parametrizes the lines on a smooth cubic threefold is a smooth surface of general type known as the Fano surface. Among these lines, those of the second type are of particular interest: their locus in the associated Fano surface is an algebraic curve whose study goes back to Murre’s work in 1972. In this talk, we will investigate the role of triple lines in the geometry of this curve and explore the relationships between these lines and Eckardt points.
-
Non-reductive quotients via multiplicative actions
Ludvig Modin (Hannover)
Abstract
The U-hat theorem of Bérczi, Doran, Hawes and Kirwan gives conditions for when a linear action of a complex graded unipotent group admits a geometric quotient, it is one of the key results non-reductive geometric invariant theory is built on.
We extend this theorem to actions over a Noetherian base scheme using generalizations of Białynicki-Birula's structure theorem for varieties with a multiplicative action and Halpern-Leistner's notion of Θ-strata of algebraic stacks.
-
The generalized Gizatullin’s problem
Daniela Paiva (Basel)
Abstract
The problem of determining which automorphisms of a smooth quartic surface S ⊂ P3 are induced by birational maps of P3 remains open. This question is known as Gizatullin’s problem.
In this talk, we will discuss this problem and a generalized version, where we pose the same question for projective K3 surfaces contained in Fano threefolds. I we will provide a general overview of the theory of K3 surfaces and the birational geometry of Fano threefolds, and explain how the interaction between these two areas can be used to approach Gizatullin’s problem.
The results I will present are part of several joint works with Carolina Araujo, Michela Artebani, Alice Garbagnati, Ana Quedo, and Sokratis Zikas.
-
Algebraic families of automorphisms and solvability
Immanuel van Santen (Basel)
Abstract
This talk is based on joint work in progress with Serge Cantat, Hanspeter Kraft, and Andriy Regeta. We investigate the following question for a variety X: given an irreducible family of automorphisms of X that contains the identity, under which conditions does this family generate an algebraic subgroup of Aut(X)?
When the members of the family commute pairwise and X is affine, a result of Serge Cantat, Andriy Regeta, and Junyi Xie shows that such a family indeed generates an algebraic subgroup. We extend this theorem to the case where the family generates a solvable subgroup and X is only assumed to be quasi-affine. We also present several applications of this result, for example to Borel subgroups in Aut(X).
In addition, we had a session of short talks by Tobias Bisang, Gabriel Frey, Yijue Hu, Keyao Peng, Gianni Petrella, Antoine Pinardin, Alois Schaffler, and Renpeng Zheng.
Participants
- Marc Abboud (Neuchâtel)
- Jefferson Baudin (Lausanne)
- Beatrice Bernasconi (Zurich)
- Mebarka Bettayeb (Basel)
- Angelo Bianchi (Sao Paulo)
- Tobias Bisang (Basel)
- Jérémy Blanc (Neuchâtel)
- Gloire Grâce Bockondas (Neuchâtel)
- Alessio Cangini (Basel)
- Mattia Cavicchi (Dijon)
- Victor Chachay (Dijon)
- Simone Coccia (Basel)
- Tiago Duarte Guerreiro (Basel)
- Yajnaseni Dutta (Leiden)
- Andrea Fanelli (Bordeaux)
- Mattias Ferreira-Filoramo (Paris)
- Pascal Fong (Hannover)
- Gabriel Frey (Warwick)
- Hang Fu (Basel)
- Brais Gerpe Vilas (Sheffield)
- Pietro Gigli (Dijon)
- Gianluca Grassi (Ferrara)
- Lyalya Guseva (Dijon)
- Yijue Hu (Nottingham)
- Gwendal Jahier (Paris)
- Andrés Jaramillo Puentes (Catania)
- Dongchen Jiao (Basel)
- Elias Kurz (Neuchâtel)
- Stéphane Lamy (Toulouse)
- Matilde Maccan (Bochum)
- Irène Meunier (Toulouse)
- Ludvig Modin (Hannover)
- Daniela Paiva (Basel)
- Keyao Peng (Dijon)
- Gianni Petrella (Esch-sur-Alzette)
- Antoine Pinardin (Basel)
- Jérôme Poineau (Caen)
- Quentin Posva (Neuchâtel)
- Alois Schaffler (Zurich)
- Anne Schnattinger (Neuchâtel)
- Julia Schneider (Dijon)
- Claudia Stadlmayr (Neuchâtel)
- Marc Truter (Warwick)
- Christian Urech (Zürich)
- Immanuel van Santen (Basel)
- Henrik Wehrheim (Neuchâtel)
- Yaoqi Yang (Warwick)
- Egor Yasinsky (Bordeaux)
- Yang Zhang (Lausanne)
- Renpeng Zheng (Nottingham)
Organizers
Andrea Fanelli (Bordeaux)
Julia Schneider (Dijon)
Philipp Habegger (Basel)
Susanna Zimmermann (Basel)
Logistic support: Adrien Dubouloz (Poitiers)
Support
ANR Fracasso
SERI Saphidir
Swiss Mathematical Society
Swiss Academy of Sciences
University of Basel
