Date/Time : 16 Jan 2026 16:00
Venue : S17 #04-05 (Seminar Room 2)
Speaker : Dou Dou, Nanjing University

Ranging from irrational rotations to mixing transformations like horocycle flows, zero entropy systems exhibit very rich and diverse complex structures and dynamical behaviors. In this talk, we will introduce recent developments in the theory of complexity and entropy-type invariants for zero entropy systems, along with our related work on entropy dimensions.

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Date/Time : 14 Jan 2026 14:00
Venue : S17 #04-04 (Seminar Room 3)
Speaker : Pierre-Louis Blayac, Strasbourg University

Given a closed surface S of genus at least 2 and an integer d>2, the space of marked hyperbolic structures, called Teichmüller space T(S), can be seen as the space of representations of the fundamental group of S into PSL(2,R) modulo conjugation.

By postcomposing with the irreducible representation of PSL(2,R) in PSL(d,R), T(S) embeds in representations valued in PSL(d,R). The connected component containing T(S) is the Hitchin component H(S), which is homeomorphic to a vector space and consists of discrete and faithful representations by work of Hitchin, Labourie, Fock and Goncharov.

A decade ago, Bridgeman, Canary, Labourie and Sambarino constructed on H(S) several metrics, called pressure metrics, that extend the famous Weil–Petersson metric on T(S). Their construction uses a characterisation of the WP metric in terms of hyperbolic lengths due to Thurston and Wolpert. We will describe the pressure metrics on certain subspaces of H(S) that are transverse to T(S), consisting of deformations through the famous bending procedure. This will allow us, in genus>2, to show that T(S) is distorted in H(S), in the sense that there is a sequence of points in T(S) whose distance to the origin diverge for the WP metric, but remains bounded for the pressure metrics.

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Date/Time : 11 Dec 2025 15:00
Venue : S17 #05-11 (Seminar Room 5)
Speaker : Ivan Fesenko, Westlake University, China

Zeta functions are the central object in number theory.

Iwasawa and Tate independently described how using adelic structures from class field theory one can obtain an integral presentation for zeta functions of number fields and prove their key properties (except the generalised Riemann hypothesis). They used Haar measure on abelian locally compact groups and associated harmonic analysis.

Modern number theory often works with two-dimensional objects such as elliptic curves over number fields and their proper regular models. Associated 2d local and adelic structures are far from locally compact. It was an open problem to produce a 2d version of the Iwasawa-Tate theory. The speaker introduced higher Haar measure and integration on 2d local and adelic objects and used them to establish such a 2d generalisation. This talk will briefly present this 2d theory and how it further leads to a new approach to the Birch and Swinnerton-Dyer conjecture.

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Date/Time : 25 Nov 2025 16:00
Venue : S17 #04-04 (Seminar Room 3)
Speaker : Davide Ravotti, Université de Lille

Translation flows are a simple kind of motion on geometric surfaces built by gluing polygons edge-to-edge. In certain special cases, called self-similar, the flow repeats its behavior in a precise way when the surface is stretched and folded by a symmetry known as a pseudo-Anosov map. When this happens, we can understand the flow by studying this symmetry. A powerful method for doing this, pioneered in a work by Giulietti and Liverani, uses a tool called transfer operator. By analyzing how the transfer operator acts on a carefully chosen space of distributions, it is possible to deduce fine dynamical and statistical properties of self-similar flows on compact surfaces. This strategy was successfully carried out by Faure, Gouëzel, and Lanneau.

In this talk, I will describe how we extend this approach to self-similar translation flows on certain non-compact surfaces, namely Abelian covers. By introducing a family of weighted transfer operators, we obtain precise formulas describing the long-term behavior of time averages of observables, for points that are typical with respect to the natural measure lifted to the cover (joint work with Henk Bruin, Charles Fougerons, and Dalia Terhesiu). If time allows, I will also discuss ongoing work (with Mauro Artigiani, Roberto Castorrini, and Yuriy Tumarkin) that goes beyond the natural area measure and treats a broader class of ergodic invariant measures, known as Maharam measures.

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Date/Time : 19 Nov 2025 16:00
Venue : S17 #04-04 (Seminar Room 3)
Speaker : Arpan Kabiraj, Indian Institute of Technology Palakkad

In 80’s, Goldman introduced a Lie bracket on the linear span of the free homotopy classes of directed closed curves on a surface called the Goldman Lie bracket. In this talk we will discuss some properties of Goldman Lie bracket using hyperbolic geometry. We will use these properties to give characterizations of simple closed curves. This is a joint work with Moira Chas.

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Date/Time : 18 Nov 2025 15:00
Venue : S17 #04-05 (Seminar Room 2)
Speaker : Fernando Camacho Cadena, Strasbourg University

A hyperbolic structure on a surface S can be deformed by cutting along a curve c without self—intersections, twisting, and re-gluing. Such a deformation can also be seen as the Hamiltonian flow of the length function of c on the Teichmüller space of S, equipped with the Weil—Petersson symplectic form. In this talk, I will discuss Hamiltonian flows associated to length functions of self—intersecting curves, and their generalizations to higher rank Teichmüller spaces. This is partially joint work with J. Farre and A. Wienhard.

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Date/Time : 11 Nov 2025 13:00
Venue : S17 #06-11 (Seminar Room 6)
Speaker : Amir Mohammadi, University of California, Berkeley

There is a profound connection between homogeneous dynamics and number theory, particularly in the study of Diophantine approximation. A landmark example is Margulis’s resolution of the Oppenheim conjecture in the mid-1980s using tools from dynamics, followed by further strengthenings by Eskin, Margulis, and Mozes based on Ratner’s seminal work. In this talk, we will present effective results in this direction, with an emphasis on obtaining polynomial rates. This is based on joint works with Elon Lindenstrauss, Zhiren Wang, and Lei Yang.

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Date/Time : 22 Oct 2025 14:00
Venue : S17 #06-11 (Seminar Room 6)
Speaker : Richard Canary, University of Michigan

Margulis proved asymptotic counting results for the number of closed geodesics less than a fixed length in the quotient of a uniform lattice in a rank one Lie group. Patterson and Sullivan developed a technology to generalize his results to convex cocompact and geometrically finite subgroups of rank one Lie groups.

An element of a higher rank Lie group has a vector-valued translation length function, which gives rise to more than one reasonable notion of the length of an element. Anosov groups of higher rank semi-simple Lie groups are the natural analogue of convex cocompactness in rank one. Sambarino proved counting results for all well-behaved length functions in this setting.

Relatively Anosov subgroups of higher rank Lie groups are one generalization of geometrically finite subgroups of rank one Lie groups. In this talk we obtain counting results in this setting. The crucial new difficulty is that the relevant flow spaces are non-compact, whereas they were compact in the Anosov setting. These results are based on work with Zhang and Zimmer on Poincare series of relatively Anosov groups and a rather general formulation of Patterson-Sullivan theory which was developed with Blayac, Zhu and Zimmer.

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Date/Time : 01 Oct 2025 15:00
Venue : S17 #04-05 (Seminar Room 2)
Speaker : Homin Lee, Korea Institute for Advanced Study

In this talk, we will discuss about smooth higher rank lattice actions on manifolds with positive entropy. For instance, when lattices in SL(n,R) act on an n-dimensional manifold with positive entropy with n at least 3, we will see that the lattice is commensurable with SL(n,Z) and a topological information on manifolds. This is a joint work with Aaron Brown.

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