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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Date/Time : 25 Sep 2025 16:00
Venue : S17 #04-05 (Seminar Room 2)
Speaker : Keiji Oguiso, The University of Tokyo

My talk is based on my joint work with Professor Koji Fujiwara (Kyoto University) and Professor Xun Yu (Tianjin University).

Main result of my talk is the finiteness of the Neron-Severi lattices of complex projective K3 surfaces whose automorphism groups are non-elementary hyperbolic under the assumption that the Picard number greater than or equal to 6 (which is optimal to ensure the finiteness). In this talk, after recalling the notion of hyperbolicity of group due to Gromov and its importance in mathematics, I would like to explain first why the non-elementary hyperbolicity of K3 surface automorphism group is the problem of the Neron-Severi lattices and next how one can deduce the above-mentioned finiteness, via the study of genus one fibrations on K3 surfaces and recent work of Kikuta and Takatsu on geometrically finiteness.

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Date/Time : 27 Aug 2025 16:00
Venue : S17 #04-04 (Seminar Room 3)
Speaker : Guolei Zhong, Institute for Basic Science, Korea

Let X be a smooth projective variety and G an abelian subgroup of automorphisms of X over the field of algebraic numbers. Suppose that G is of positive entropy. It was proved by Dinh and Sibony that the group is then free abelian of rank no more than dim(X)-1. In the past decade, from algebraic dynamics, the geometry of the extremal case when the rank achieves the maximal has been well-understood by Zhang. In this talk, we study the maximal rank case in the aspect of arithmetic dynamics. More precisely, we construct a canonical height function associated with the group, corresponding to a nef and big divisor, satisfying the Northcott property. By characterizing its null locus, we prove the Kawaguchi–Silverman conjecture for each group element. Some further discussion towards its application and the existence of Zariski dense orbits will also be presented. This is based on a joint work with Fei Hu.

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