Translation, Dilation, Affine and other Structures on Surfaces

Liste des contributions

1. Holomorphic dynamics in dimension 2 and geometry of surfaces

Jasmin Raissy

07/04/2025 09:30

In this introductory lecture I will present the connections between the dynamics of germs of biholomorphisms of ${\mathbb{C}}^2$ tangent to the identity at a fixed point, the real-time dynamics of homogeneous vector fields in ${\mathbb{C}}^2$ and the dynamics of the geodesic flow on affine surfaces, focusing on open problems.

2. Introduction to ... TBA

07/04/2025 11:00

3. Introduction to ... TBA

07/04/2025 14:30

4. TBA

Ferran Valdez

07/04/2025 16:00

5. TBA

Magali Jay

08/04/2025 09:30

6. Symmetric surfaces from dynamics on triangles

Pat Hooper

08/04/2025 11:00

Half-dilation surfaces are fun to build; you can snap together triangles like Magna-tiles®. I will describe a construction of half-dilation surfaces built from triangles produced by a (ℤ/2ℤ)(ℤ/2ℤ)(ℤ/2ℤ) action on homothety-equivalence classes of triangles in the plane. The advantage of this construction is that it produces surfaces with non-elementary Veech groups. Some of the surfaces that...

10. The topology of the moduli spaces of dilation surfaces

Jane Wang

08/04/2025 14:30

Dilation surfaces, which can be thought of as polygons whose sides are identified by translation and dilation, are a natural generalization of translation surfaces. While translation surfaces are well-studied, much less is known about dynamics on dilation surfaces and their moduli spaces. In this talk, we will survey recent progress in understanding the topology of moduli spaces of dilation...

8. TBA

Duc-Manh Nguyen

08/04/2025 16:00

9. Foliated affine and projective structures

Bertrand Deroin

09/04/2025 09:30

In this talk, I will report on some joint work with Adolfo Guillot on the existence of affine or projective structures along the leaves of one dimensional algebraic foliations. We will also discuss the problem of uniformizability of such structures.

7. TBA

Paul Apisa

09/04/2025 11:00

11. Lorentzian metrics with conical singularities and bi-foliations of the torus

Martin Mion -Mouton

10/04/2025 09:30

The constant curvature Lorentzian metrics having a finite number of conical singularities offer new examples of geometric structures on the torus, naturally generalizing the analogous Riemannian case. In the latter, works of Troyanov show that the data of the conformal structure and of the angles at the singularities entirely classify the metrics with conical singularities. In this talk, we...

12. TBA

Gabriela Weitze-Schmithüsen

10/04/2025 11:00

13. Sous-variétés bi-algébriques non-linéaires dans les espaces de modules de différentielles abéliennes

Carlos Matheus

10/04/2025 14:30

Les strates des espaces de modules de différentielles abéliennes sont des espaces non-homogènes portant des structures bi-algébriques naturelles. Klingler et Lerer ont montré qu'une courbe bi-algébrique dans un strate d'un espace de modules de différentielles abéliennes est linéaire pourvu qu'une certaine condition (*) soit satisfaite. Dans cet exposé, on discutera un travail en collaboration...

14. TBA

Guillaume Tahar

10/04/2025 16:00

15. Lengths of saddle connections for large genus

Anja Randecker

11/04/2025 09:00

Inspired by the well-studied case of hyperbolic surfaces, we can ask about the expected value of geometric properties of translation surfaces for large genus.
In this talk, we consider the number of saddle connections in a given length range as a random variable on a stratum and show that for genus going to infinity, this converges in distribution to a Poisson distributed random...

16. TBA

Charles Fougeron

11/04/2025 11:00