Date/Time : 06 Feb 2025 13:30
Venue : S17 #04-06 (SR1)
Speaker : Asbjørn Christian Nordentoft, Université Paris-Saclay

In the case of the modular surface Duke-Imamouglu-Toth defined a thin subgroup associated to each closed geodesic and studied the equidistribution of the projection of the associated hyperbolic orbifold with boundary (i.e. the partial coverings). In this talk, I will give a purely geometric generalization to any hyperbolic surface. Furthermore, I will explain that the equidistribution of closed geodesics in the unit tangent bundle implies equidistribution of the associated partial coverings. This yields a new proof of the result of Duke-Imammouglu-Toth as well as many other new equidistribution results.

This is joint work with Ser Peow Tan.

Add to calendar :

Date/Time : 22 Jan 2025 14:00
Venue : S17 #04-04 (SR3)
Speaker : Gaofeng Huang, University of Bern

In this talk we survey a few results in the study of large holomorphic automorphism groups. First we give a short historical development of the so-called Andersen–Lempert theory, namely the study of large holomorphic automorphism groups. This field nowadays focuses on the so-called density property and a criterion for discovering more examples, many of which are smooth affine algebraic varieties.

In the second part we will consider the symplectic setting, namely complex symplectic manifolds with large group of holomorphic symplectic automorphisms. An example is the even dimensional Euclidean space endowed with the standard complex symplectic form. As a new example, the Calogero–Moser space, also admits the symplectic density property, which in turn leads to a strong approximation result for symplectic automorphisms in the Carleman sense.

Add to calendar :

Date/Time : 21 Jan 2025 14:00
Venue : S17 #04-05 (SR2)
Speaker : Ara Basmajian, City University of New York

There are many topological invariants one can associate with homotopy classes of closed curves. These include algebraic and geometric self-intersection number, intersection with curves in a class of curves (for example, simple ones), the Goldman bracket, complementary component types of a curve, mapping class group stabilizers of a curve, and many others. How these invariants interact and determine the curve type (mapping class group orbit) is an active area of research today. In this talk, we focus on the so called inf invariant (shortest length metric) associated to a filling curve, its relationship with the geometric self-intersection number, and its relation to the optimal metric that is tailored to produce the minimum length. While clearly the geometric self-intersection number is a type invariant, we address whether the inf invariant can distinguish between curves that have the same self-intersection. This is joint work with Sayantika Mondal.

Add to calendar :

Date/Time : 17 Jan 2025 15:30
Venue : S17 #04-05 (SR2)
Speaker : Hao Wu, University of Zurich

Dynamical systems are deterministic systems. However, in chaotic systems where the entropy is positive, the ergodic sums often behave similarly to the sums of independent random variables and satisfy the spatial central limit theorems (CLT).

In zero-entropy systems, the spatial CLT often fails due to the lack of (fast) mixing properties. But in some cases, such as irrational rotations of bounded type, we can retrieve the central limit theorem if we study single orbit statistics. Here we fix the starting point but randomise time, hence the word “temporal” in the title. In this talk, I will present an ongoing joint work with Bromberg and Ulcigrai, where we make effective the method in their previous work, coding and Markov chains, to obtain a temporal central limit theorem for a broader class of observables over bounded irrational rotations.

Add to calendar :

Date/Time : 16 Jan 2025 14:00
Venue : S17 #04-05 (SR2)
Speaker : Weisheng Wu, Xiamen University

Geodesic flows in (and beyond) nonpositive curvature are important examples of nonuniformly hyperbolic dynamical systems. We discuss some ergodic properties of geodesic flows including the ergodicity of Liouville measure and the uniqueness of measure of maximal entropy, and the applications to the problem of counting closed geodesics.

Add to calendar :

Date/Time : 15 Jan 2025 14:00
Venue : S17 #04-05 (SR2)
Speaker : Anh Duc Vo, Harvard University

In this talk, I will discuss the notion of Du Bois complexes and provide an overview of classical notions such as rational and Du Bois singularities. I will then discuss their recent extensions to k-rational and k-Du Bois singularities, both for local complete intersections (LCIs) and non-LCI varieties. This talk is based on joint work with Wanchun Shen, and Sridhar Venkatesh.

Add to calendar :

Date/Time : 15 Jan 2025 16:00
Venue : S17 #04-05 (SR2)
Speaker : Han Zhang, Soochow University

In 1984, Mahler proposed the following question on Diophantine approximation : How close can irrational numbers in the middle-thirds Cantor set be approximated by rational numbers? One way to reformulate Mahler’s question is to ask if Khintchine’s theorem extends to the middle-thirds Cantor set.

It turns out that random walks on homogenous sapces and slicing theorems in fractal geometry play crucial roles in answering Mahler’s question. In this talk, I will survey works regarding Khintchine’s theorem on fractals, discuss the connection between homogeneous dynamics and Diophantine approximation, and sketch the proof of Khintchine’s theorem on the middle-thirds Cantor set using tools from homogeneous dynamics and certain slicing theorem from fractal geometry.

This is based on a joint work with Timothée Bénard and Weikun He.

Add to calendar :

Date/Time : 26 Dec 2024 14:00
Venue : S17 #04-04 (SR3)
Speaker : Sang-hyun Kim, Korea Institute for Advanced Study

Given a topological (C0) action of a group on a manifold, one can ask the best possible regularity (Cr) with which the group may act smoothly. Estimation of such regularities involve interplays among group theory (nilpotence, solvability and so forth), analysis (Hölder regularity) and dynamics (tracing orbits). In this talk, We prove that if a countable group does not contain a finitely generated subgroup of exponential growth, then every topological action of the group on a compact connected one-manifold can be blown-up to a C1 action. The proof is based on a functional characterisation of such groups. Joint work with Mikael de la Salle, Nicolas Matte Bon and Michele Triestino.

Add to calendar :

Date/Time : 10 Dec 2024 15:00
Venue : S17 #04-04 (SR3)
Speaker : Gianluca Faraco, University of Milano Bicocca

A translation surface is the datum of an abelian differential on a Riemann surface. Every such pair determines a representation called absolute period representation or period character. In this talk we discuss the realization of a given representation as the period character of some translation surface.

Add to calendar :