Low Dimensional Actions

Contribution List

23. Registration/ Welcome coffee

4/29/24, 9:00 AM

1. First order rigidity of manifold homeomorphism groups

Sanghyun Kim

4/29/24, 9:30 AM

Two groups are elementarily equivalent if they have the same sets of true first order group theoretic sentences. We prove that if the homeomorphism groups of two compact connected manifolds are elementarily equivalent, then the manifolds are homeomorphic. This generalizes Whittaker’s theorem on isomorphic homeomorphism groups (1963) without relying on it. We also establish the analogous result...

2. Minicourse: big mapping class groups

Kathryn Mann

4/29/24, 11:00 AM

This course will introduce mapping class groups of surfaces of infinite types, and present a perspective due to Calegari, that we might use these to study groups acting on (finite type) surfaces.

3. Free IET-Actions

Isabelle Liousse

4/29/24, 2:00 PM

Hölder's theorem states that a group acting freely by circle homeomorphisms is isomorphic and semi-conjugate to a subgroup of rotations.
In this talk, I will discuss an analogous result, obtained with Nancy Guelman, for groups of interval exchange transformations.

4. On the geometry of diffeomorphisms groups in dimension 1

Andres Navas

4/29/24, 3:00 PM

In this talk I will discuss some geometric properties of diffeomorphisms groups that are hard to tackle via classical methods because of the lack of local compactness. In particular, I will elaborate on Gromov's notion of distortion in this context. I will mostly concentrate in the case of 1-manifolds, which is surprisingly rich and hard to tackle.

5. Rigidity of big mapping class groups acting on the circle

Lvzhou Chen

4/29/24, 4:30 PM

Surfaces of infinite type, such as the plane minus a Cantor set, occur naturally in dynamics. However, their mapping class groups are much less understood compared to the mapping class groups of surfaces of finite type. For the mapping class group G of the plane minus a Cantor set, we show that any nontrivial G-action on the circle is semi-conjugate to its action on the so-called simple...

6. Groups with full limit set vs Lattices

Sebastian Hurtado

4/30/24, 9:30 AM

Based on work in progress with Subhadip Dey.

We discuss the question whether a discrete subgroup in a Lie group of higher rank with full limit set in its boundary is necessarily a lattice. We find some necessary conditions for this to be true and discuss some new and old results pointing towards an affirmative answer. Hopefully, we will also relate this discussion to questions about groups...

7. Minicourse: big mapping class groups and dynamics

Kathryn Mann

4/30/24, 11:00 AM

8. Homeomorphism groups of the Airplane and the Basilica Julia sets

Bruno Duchesne

4/30/24, 2:00 PM

The airplane and the Basilica Julia sets are two compact fractal sets that appear in different parts of group theory. In this talk, we will be interested in their full homeomorphism groups. We will show that these groups can be identified with a specific universal Burger-Mozes group (this was proved by Y. Neretin for the Basilica) and a specific kaleidoscopic group for the Airplane....

9. Deformations of Z^2-actions in dimension 1 (joint with Andrés Navas)

Hélène Eynard-Bontemps

4/30/24, 3:00 PM

Can any pair of commuting diffeomorphisms of a compact 1D manifold be connected to the trivial pair (id,id) via a path of such pairs ? This question plays an important role in the classification of foliations of 3-manifolds by surfaces. It can be asked in any differentiability class, and we will see that the phenomena at play and the techniques involved to answer it highly depend on the...

10. Around the fine curve graph of the torus

Frédéric Le Roux

4/30/24, 4:30 PM

Lan, Margalit, Pham, Verbene and Yao showed in 2021 that the group of automorphisms of the fine curve graph of a surface of genus at least 2 identifies with the group of homeomorphisms of the surface. With Maxime Wolff, we generalise this result to any surface, and describe the smooth version. The torus case is of special interest since recent work by Bowden, Hansel, Militon, Man, and Webb...

11. Spaces of left-orderings and their Borel complexity

Filippo Calderoni

5/2/24, 9:30 AM

In this talk we will discuss the problem of determining the Borel complexity of the space of left-orders LO(G) of a countable left-orderable group G modulo the conjugacy G-action. We will see how this problem is connected to some well-studied topological properties of LO(G) such as the existence of dense orbits, and condensed orders. We will give an overview of our results showing that certain...

12. Minicourse: Dynamics of homeomorphisms of surfaces and fine curve graph

Emmanuel Militon

5/2/24, 11:00 AM

The fine curve graph of a closed surface is a Gromov hyperbolic graph on which the group of homeomorphisms of the surface acts faithfully by isometry. In this mini-course, we will explore the links between the dynamics of a homeomorphism of the surface and the isometry type of its action on the fine curve graph. The first talk will be devoted to a dynamical characterization of homeomorphisms...

13. The group of germs at infinity of homeomorphisms of the real line has no outer automorphisms

Maxime Wolff

5/2/24, 2:00 PM

In joint work with Frédéric Le Roux and Kathryn Mann, we
prove that every automorphism of the group of germs at infinity
of homeomorphisms of the real line is given by the conjugation by
some homeomorphism of the line.

14. Bifoliated planes, Anosov-like actions and rigidity

Thomas Barthelmé

5/2/24, 3:00 PM

A bifoliated plane is a topological plane equipped with two transverse (possibly singular) foliations. Given a group G, an Anosov-like action is an action of G on a bifoliated plane satisfying a few axioms, first among them is the fact that each point in the plane fixed by an element of the group is a hyperbolic fixed point.
Such actions were first introduced as an axiomatization, and...

15. Laminar groups and Kleinian groups

KyeongRo Kim

5/2/24, 4:30 PM

Thurston showed the universal circle theorem as a first step of the proof of the geometrization conjecture of tautly foliated three manifolds. The theorem says that the fundamental group of a closed three manifold slithering over the circle acts on the circle preserving a pair of laminations. In this talk, I talk about the converse of the universal circle theorem in terms of laminar groups....

16. Towards the boundary of the fine curve graph

Jonathan Bowden

5/3/24, 9:30 AM

The fine curve graph was introduced as a geometric tool to homeomorphism groups of surfaces. One then wishes to establish a dictionary between the underlying surface dynamics and the action of elements on the fine curve graph. For this it is key to have a geometric interpretation of points on the Gromov boundary in analogy to Klarreich’s description for classical curve graphs. We describe...

17. Minicourse: Dynamics of homeomorphisms of surfaces and fine curve graph

Emmanuel Militon

5/3/24, 11:00 AM

18. Rigidity of Codimension One Higher Rank Actions

Camilo Arosemena

5/3/24, 2:00 PM

We classify all closed manifolds admitting a smooth locally free action by a higher rank split simple Lie group with codimension 1 orbits. Namely, if a closed manifold M admits such an action by a Lie group G as above, M is finitely and equivariantly covered by G/Gamma x S^1, for some cocompact lattice Gamma of G, where G acts by left translations on the first factor, and trivially on S^1....

19. Laminations and structure theorems for group actions on the line (1)

Michele Triestino

5/3/24, 3:00 PM

A lamination of the real line is a closed collection of pairwise unlinked, finite intervals. They appear naturally when studying certain classes of group actions on the line. More precisely, we will discuss actions of solvable groups, and of locally moving groups (these are subgroups of Homeo(R) such that for any open interval I, the subgroups of elements fixing the complement of I acts...

20. Laminations and structure theorems for group actions on the line (2)

Joaquin Brum

5/3/24, 4:30 PM

A lamination of the real line is a closed collection of pairwise unlinked, finite intervals. They appear naturally when studying certain classes of group actions on the line. More precisely, we will discuss actions of solvable groups, and of locally moving groups (these are subgroups of Homeo(R) such that for any open interval I, the subgroups of elements fixing the complement of I acts...

21. Stationary measures for groups acting on surfaces

Aaron Brown

5/4/24, 9:30 AM

For a group acting on a surface, one may want to classify orbit closures or invariant/stationary measures. I’ll discuss an older result of myself and Rodriguez-Hertz—adapting the exponential drift methods of Benoit-Quint and Eskin-Mirzakhani—to classify stationary measures under certain dynamical hypotheses on the action. I’ll also discuss more recent related works, work in progress, and...

22. Critical regularity for nilpotent group actions in dimension one

Victor Kleptsyn

5/4/24, 11:00 AM

My talk will follow a joint work with Maximiliano Escayola, devoted
to the study of critical regularities for nilpotent group actions.
The questions of critical regularities have been studied
by many authors in many different contexts: starting from the
classical Denjoy theorem and example, there are works by M. Herman, J.-C. Yoccoz,
N. Kopell, B. Deroin, A. Navas, C. Rivas, E....