Date/Time : 09 Dec 2024 14:00
Venue : S17 #05-12 (SR4)
Speaker : Daniel Mathews, Monash University

Work of Penrose and Rindler in the 1980s developed a formalism for spinors in relativity theory. In their work they gave geometric interpretations of 2-component spinors as flags in Minkowski space. We present some extensions of this work involving hyperbolic geometry. In particular, we give a correspondence between between spinors and horospheres with certain decorations, and show how spinors can be used to calculate a complex-valued, 3-dimensional generalisation of Penner’s lambda lengths. Time permitting, we may discuss some further applications, including inter-cusp distances in knot complements, higher-dimensional generalisations, and circle packings.

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Date/Time : 03 Dec 2024 15:30
Venue : S17 #04-04 (Seminar Room 3)
Speaker : Federico Rodriguez Hertz, The Pennsylvania State University

In a joint work in progress with Pablo Carrasco we show that to any quasi-morphism for a hyperbolic group can be associated a function with the Bowen property for some hyperbolic dynamics. In this talk I plan to describe the construction and how to prove the CLT for a quasi-morphism w.r.t. some length function.

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Date/Time : 02 Dec 2024 16:00
Venue : S17 #04-04 (SR3)
Speaker : Changguang Dong, Nankai University

We will discuss a dynamically defined zeta function for partially hyperbolic systems. This is a generalization of the classical Ruelle zeta function for Anosov (more generally Axiom A) diffeomorphisms/flows, which may reflect dynamical invariants such as entropy and pressure, as well as the geometry/topology of the manifolds. Based on an ongoing project with Qiujie Qiao.

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Date/Time : 27 Nov 2024 14:00
Venue : S17 #04-04 (SR3)
Speaker : Marco Vergamini, Scuola Normale Superiore

Let f be a complex Hénon map and µ its unique measure of maximal entropy. Recently, Bianchi-Dinh proved that µ is exponentially mixing of all orders for all Hölder observables, and that all such observables satisfy the central limit theorem with respect to µ. De Thélin-Vigny generalized these results for a certain class of bounded plurisubharmonic observables. We prove that these properties hold for all, not necessarily bounded, plurisubharmonic observables. This is a joint work with Hao Wu.

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Date/Time : 13 Nov 2024 14:00
Venue : S17 #04-04 (SR3)
Speaker : Duc-Bao Nguyen, National University of Singapore

We generalize previous diameter estimates and local non-vanishing of volumes for Kähler metrics to the case of big cohomology classes. In our proof, among other things, we will prove a uniform diameter estimate for a family of smooth Kähler metrics only involving an integrability condition. We also have to use fine stability properties of complex Monge-Ampere equations with prescribed singularities. This is joint work with Duc-Viet Vu

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Date/Time : 06 Nov 2024 14:00
Venue : S17 #04-04 (SR3)
Speaker : Lei Yang, National University of Singapore

In this talk, I will give a new (and shorter) proof of Strombergsson’s Theorem on effective equidistribution of unipotent orbits in ASL(2, R)/ASL(2,Z). The proof is based on a general framework developed in recent works by Lindenstrauss-Mohammadi-Wang and myself, which relates the problem to incidence geometry. It relies on the study of a Kakeya-type model. This is joint with Elon Lindenstrauss.

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Date/Time : 09 Oct 2024 14:00
Venue : S17 #04-04 (SR3)
Speaker : Enrique ARTAL BARTOLO, Universidad de Zaragoza

In this talk we discuss how algebraic (or arithmetic) and geometric properties of plane curves affect the topology. There are some classical results starting from Zariski where the position of some singular points with respect to curves of some fixed degree has surprising consequences on the topology of these curves. We discuss the state of art of the subject, leading to cases where for curves defined over a number field, the action of the Galois group has also influence on the topology. We will present recent discoveries on the subject, specially with my collaborators and from the Hiro Tokunaga’s team, and also open problems.

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Date/Time : 02 Oct 2024 14:00
Venue : S17 #04-04 (SR3)
Speaker : Hideo Kojima, Niigata University

A cuspidal curve means a projective curve whose singular points are locally irreducible. The study of rational cuspidal plane curves has had a long and interesting history. In the first half of the talk, I will introduce some of recent progress on the study. Then, I will give some results on rational cuspidal curves on Q-homology projective planes. Here, a Q-homology plane is a normal projective complex surface with quotient singularities having the same rational homology as the projective plane. Some results on rational cuspidal plane curves will be generalized.

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Date/Time : 09 Sep 2024 17:00
Venue : S17 #04-05 (SR2)
Speaker : Ichiro Shimada, Hiroshima University

The Ap\’ery-Fermi pencil is a certain one-dimensional family of complex affine surfaces related to a Fermi surface in solid state physics. This pencil is also connected to Ap\’ery’s proof of the irrationality of the zeta value at s=3.

A general member of the Ap\’ery-Fermi pencil is birational to a K3 surface with Picard number 19. We calculate the automorphism group of this K3 surface by means of Borcherds’ method.

I also present some general algorithms that may be useful in computational algebraic geometry.

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