2025

July 17 (Thurs), 11 am

KIAS 1424 & Zoom https://kimsh.kr/vz

Ken'ichi Ohshika

Convex structures of unit tangent spheres of Teichmüller spaces with Thurston’s metric

I will talk about how the unit tangent spheres look in Teichmüller space with Thurston’s metric. I will first briefly review the definition of Thurston’s metric and how its geodesics behave. Then we show that faces of the unit sphere can be characterised in terms of geodesic laminations.

July 23 (Wed), 11 am

KIAS ? & Zoom https://kimsh.kr/vz

Hyein Choi

Quasi-isometric embeddings of Ramanujan complexes

Euclidean buildings (a.k.a affine buildings and Bruhat-Tits buildings) are considered as a p-adic analogue of symmetric spaces. It is natural to ask how the symmetric space of SL(n,R) differs from the Euclidean building of SL(n,Q_p). We show that there is no quasi-isometric embedding between them. Generalizing this, we distinguish Ramanujan complexes constructed by Lubotzky-Samuels-Vishne as finite quotients of Euclidean buildings of PGL(n,F_p((y))) up to quasi-isometric embeddings. These complexes serve as high dimensional analogues of the optimal expanders, Ramanujan graphs, with fruitful applications in mathematics and computer science.

August 5 (Tue), 11 am

KIAS 1423 & Zoom https://kimsh.kr/vz

Ryoo, Seung-Yeon (Caltech)

TBA

TBA

August 8 (Fri), 11 am

KIAS 1423 & Zoom https://kimsh.kr/vz

Jang, Seung-Uk (Rennes)

Dynamics of the Sturmian Trace Skew Product

In this talk, we focus on the spectrum of the discrete Schrödinger equation with a quasi-periodic potential called Sturmian potential. Eigenvector problem with a Sturmian potential is associated to a dynamics of the Markov surface, together with a control variable of "rotation angle," leading us to a study of a skew product system.

Our understanding is that this skew product system exhibits a sort of hyperbolicity. As a first step to establish it, we have shown that there exists a cone field on the Markov surface that contracts by the dynamics, which is independently defined by the angle variable. The discovery is more or less elementary, initiated by some geometric observations of the Markov dynamics. After sketching the tricks, we will announce some prospective after having a cone field, including the "holonomy" between Sturmian spectra.

This talk is based on a joint work with Anton Gorodetski and Victor Kleptsyn.