IHP, September 22-25, 2025

Registration

The registration is free, but mandatory. Please register via this link.

Program

The talks will be in room Perrin/Yvette Cauchois.

Monday

14:30-15:30: Xenia Flamm
15:30-16:00: coffee break
16:00-17:30: Minicourse Thibault Lefeuvre

Tuesday

9:30-11:00: Minicourse Thibault Lefeuvre
11:00-11:30: coffee break
11:30-12:30: Anne Vaugon

14:30-16:00: Minicourse Nastaran Einabadi and Pierre-Antoine Guihéneuf
16:00-16:30: coffee break
16:30-17:30: Nolwenn Le Quellec

Wednesday

9:30-11:00: Minicourse Nastaran Einabadi and Pierre-Antoine Guihéneuf
11:00-11:30: coffee break
11:30-13:00: Minicourse Thibault Lefeuvre

14:00-16:00: Collaboration GALS
16:00-16:30: coffee break
16:30-18:00: Discussion GALS

Thursday

9:30-11:00: Minicourse Nastaran Einabadi and Pierre-Antoine Guihéneuf
11:00-11:30: coffee break
11:30-12:30: Kai Fu

Titles and abstracts

Minicourses

Nastaran Einabadi and Pierre-Antoine Guihéneuf
Title: Classification of actions on the fine curve graph for homeomorphisms of surfaces of genus at least 2.
Abstract: The fine curve graph is a Gromov-hyperbolic space associated to a surface S, whose definition is very simple, on which the set of homeos of S acts by isometries. These actions are of three types: elliptic, parabolic and loxodromic. Establishing in which category the action of a homeo on the fine curve graph falls in is a problem which could help to understand the algebraic structure of the whole group of homeos of S. This classification is essentially established for S=the torus, in terms of rotational behaviour of the homeo, but is only partially solved for higher genus surfaces. In this minicourse, we will review some of those partial results:

• we will introduce some results about rotation theory on higher genus surfaces;
• we will explain a criterion of loxodromicity for the homeos homotopic to the identity;
• we will give one ellipticity, and one non-ellipticity condition.

Thibault Lefeuvre
Title: The marked length spectrum of Anosov surfaces
Abstract: Anosov surfaces are surfaces whose geodesic flow is uniformly hyperbolic (Anosov), and they generalize negatively curved surfaces. On such surfaces, there exists a unique closed geodesic in each free homotopy class, and the collection of all lengths of closed geodesics marked by the free homotopy defines what is known as the marked length spectrum. I will explain the proof of the marked length spectrum rigidity theorem for Anosov surfaces (Guillarmou-L.-Paternain), namely that the marked length spectrum of an Anosov surface determines its metric up to isometries.


Talks

Kai Fu
Title: Siegel–Veech Measures of Convex Flat Cone Spheres
Abstract: A classical theorem of Siegel gives the average number of lattice points in bounded subsets of $\mathbb{R}^n$. Motivated by this result, Veech introduced an analogue for translation surfaces, now known as the Siegel–Veech formula. However, no such formula is known for flat surfaces with irrational cone angles. A convex flat cone sphere is a Riemann sphere equipped with a conformal flat metric with conical singularities, all of whose cone angles are less than $2\pi$. In this talk, I will present recent work extending the Siegel–Veech theory to this setting, and outline the strategy of the proof.


Xenia Flamm:
Title: Convex projective geometry, degenerations and non-Archimedean fields
Abstract: Convex projective manifolds are a generalisation of hyperbolic manifolds, where the convex set is the unit ball. They are endowed with a natural metric: the Hilbert metric. The study of degenerations of convex projective structures naturally leads to replacing the reals by a non-Archimedean ordered field. The aim of this talk is to introduce convex sets over such a field, study their Hilbert geometry through several examples, and see how they arise as limits of convex projective structures. This is joint work with Anne Parreau.

Nolwenn Le Quellec:
Title: Parabolic and first kind flute surfaces
Abstract: In this talk we are going to describe ways to tell if a flute surface is parabolic and/or of first kind. This extends results by Pandazis and Šarić shown in 2023 and use the concept of visible end coined by Basmajian and Šarić.

Anne Vaugon:
Title: Entropy of H-flows on non-compact manifolds
Abstract: In a work in progress with Anna Florio and Barbara Schapira, we prove the existence of a measure of maximal entropy for flows of a class of dynamics that we call H-flows under an assumption of entropy control at infinity. These flows can be seen as a generalization of Anosov flows on non-compact manifolds and include geodesic flows with pinched negative curvature. This generalizes results of Gouëzel, Schapira, and Tapie for the geodesic flow on non-compact manifolds.
The goal of this presentation is to state this existence result while explaining the definition of H-flow and the assumption of entropy control at infinity.

Participants

1. Anne Broise
2. Indira Chatterji
3. Salammbo Connolly
4. Nguyen-Thi Dang
5. Nastaran Einabadi
6. Hélène Eynard-Bontemps
7. Federica Fanoni
8. Xenia Flamm
9. Anna Florio
10. Kai Fu
11. Pierre-Antoine Guihéneuf
12. Magali Jay
13. Fanny Kassel
14. Ekaterina Kuritsina
15. Thibault Lefeuvre
16. Nolwenn Le Quellec
17. Frédéric Le Roux
18. Yusen Long
19. Tianyi Lou
20. Achille Méthivier
21. Alexander Nolte
22. Alejandro Passeggi
23. Françoise Pène
24. Barbara Schapira
25. Giorgos Stamatiou
26. Nicolas Tholozan
27. Roméo Troubat
28. Anne Vaugon
29. Lasse Wolf