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4/29/24, 9:00 AM
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Sanghyun Kim4/29/24, 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...
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Kathryn Mann4/29/24, 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.
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Isabelle Liousse4/29/24, 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.
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In this talk, I will discuss an analogous result, obtained with Nancy Guelman, for groups of interval exchange transformations. -
Andres Navas4/29/24, 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.
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Lvzhou Chen4/29/24, 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...
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Sebastian Hurtado4/30/24, 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...
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Kathryn Mann4/30/24, 11:00 AM
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Bruno Duchesne4/30/24, 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....
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Hélène Eynard-Bontemps4/30/24, 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...
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Frédéric Le Roux4/30/24, 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...
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Filippo Calderoni5/2/24, 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...
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Emmanuel Militon5/2/24, 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...
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Maxime Wolff5/2/24, 2:00 PM
In joint work with Frédéric Le Roux and Kathryn Mann, we
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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. -
Thomas Barthelmé5/2/24, 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.
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Such actions were first introduced as an axiomatization, and... -
KyeongRo Kim5/2/24, 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....
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Jonathan Bowden5/3/24, 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...
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Emmanuel Militon5/3/24, 11:00 AM
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Camilo Arosemena5/3/24, 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....
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Michele Triestino5/3/24, 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...
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Joaquin Brum5/3/24, 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...
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Aaron Brown5/4/24, 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...
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Victor Kleptsyn5/4/24, 11:00 AM
My talk will follow a joint work with Maximiliano Escayola, devoted
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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....
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