Date/Time : 26 Feb 2026 15:00
Venue : S17 #04-05 (Seminar Room 2)
Speaker : Lingrui Ge, Peking University

We develop the dual based approach and introduce several new concepts and tools for the study of one-frequency quasiperiodic operators with analytic potentials. As applications we solve some long-standing arithmetic conjectures: the ten martini problem, sharp phase transition in frequency and absolute continuity of the integrated density of states, for the entire class of type I operators.

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Date/Time : 04 Feb 2026 14:00
Venue : S17 #04-05 (Seminar Room 2)
Speaker : Ngoc Cuong Nguyen, Kora Advanced Institute of Science & Technology

We study comprehensively local properties of functions in complex Sobolev spaces, introduced by Dinh and Sibony (2006), on a bounded open sub-set of C^n. The main tool is the corresponding functional capacity for the space which is inspired by the global one due to Vigny (2007). An inequality between this capacity and the Bedford-Taylor capacity for plurisubharmonic functions is proved, which is sharp as far as the exponents are concerned. Moreover, it is shown that the functional capacity is a Choquet capacity. The Alexander-Taylor type inequality for the capacity is also proved. This allows us to strengthen the results in the works of Dinh, Marinescu and Vu (2023), Vigny and Vu (2024).

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Date/Time : 04 Feb 2026 16:00
Venue : S17 #04-05 (Seminar Room 2)
Speaker : Dano Kim, Seoul National University

The theory of L2 extension theorems is a central topic in several complex variables with numerous applications to complex/algebraic geometry and complex analysis. They are analogous to vanishing theorems in algebraic geometry and often serve as a stronger counterpart of vanishing as exemplified in the proof of Siu’s invariance of plurigenera. In this talk, in the opposite direction, I will discuss how certain ideas from algebraic geometry are crucially used in answering a question raised by Demailly on understanding general L2 extension theorems, via the theory of log canonical pairs. This talk is partly based on joint work with Xu Wang (Trondheim).

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Date/Time : 04 Feb 2026 15:00
Venue : S17 #04-05 (Seminar Room 2)
Speaker : Asbjørn Nordentoft, University of Copenhagen

To any thin subgroup of a finite co-volume Fuchsian group one can associate a hyperbolic orbifold with geodesic boundary. The projection of the geodesic boundary gives a stratification (or partition) of the set of all thin subgroups. In this talk I will explain how in some cases one can understand the fibers of this stratification. This is related to the problem of lifting closed geodesics ‘simply and separating’. In the case of the modular group this gives a new and geometric perspective on a construction of Duke, Imamoglu and Toth using (minus) continued fractions.

This is joint work in progress with Ser Peow Tan

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Date/Time : 21 Jan 2026 14:00
Venue : S17 #04-04 (Seminar Room 3)
Speaker : Ming Hong Tee, Boston College

Given any Jordan domain U in the Riemann sphere equipped with the hyperbolic metric, one can construct the Epstein surface in hyperbolic 3 space corresponding to it. One important property of the Epstein surface is that its principal curvatures are related to the Schwazian derivative of the uniformization map of U. In this talk, we will exploit this property to relate the bending lamination of a pleated surface with the Schwazian derivative. Furthermore, if U is a domain for a Weil-Peterson curve, we will show that the hyperbolic metric and the quasi-hyperbolic metric are arbitrary closed and the two corresponding Epstein surfaces are arbitrary closed.

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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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