2025

Nov 18 (Tue) 4:00 pm

KIAS (Room 1424) & Zoom https://kimsh.kr/vz

Balthazar Fléchelles (Institut Fourier, Université Grenoble Alpes) 

Title: Convex projective geometry and relatively Anosov representations

Abstract: In hyperbolic geometry, geometrically finite and convex-cocompact representations into PO(n,1) enjoy good geometric and dynamical properties. Anosov representations are a generalization of hyperbolic convex-cocompactness to the higher rank setting which retains the most interesting features of the hyperbolic case. Surprisingly however, Anosov representations seem to mainly generalize the dynamical aspects of convex-cocompactness, leaving the geometrical picture aside. More recently, several relativizations of Anosov representations were introduced in order to generalize hyperbolic geometric finiteness.

In a celebrated work, Danciger, Guéritaud and Kassel showed that Anosov representations could be understood in purely geometrical terms in convex projective geometry, by generalizing a geometric characterization of hyperbolic convex-cocompactness. In this talk, I will explain a theorem obtained in collaboration with Mitul Islam and Feng Zhu which generalizes Danciger-Guéritaud-Kassel's result to the geometrically finite case. More precisely, we prove that a geometrical definition of geometric finiteness in convex projective geometry corresponds to relatively Anosov representations. I will explain what are the consequences of this theorem for the theory of relatively Anosov representations. This includes the definition of a new, more general version of relatively Anosov representations, which we call asymmetrically relatively Anosov representations.

Nov 19 (Wed) 2:00 pm

KIAS (Room TBA) & Zoom https://kimsh.kr/vz

Mladen Bestvina (University of Utah) 

Title: Tame homeomorphisms of surfaces of infinite type

Abstract: A cornerstone of low-dimensional topology is the Nielsen–Thurston classification theorem, which provides a blueprint for understanding homeomorphisms of finite-type surfaces up to homotopy. However, extending this theory to surfaces of infinite type remains an elusive goal. A key difficulty is the behavior of curves under iteration, which can exhibit pathologies that do not arise in the finite-type setting. To address these challenges, we introduce the notion of tame homeomorphisms, a class of homeomorphisms with non-mixing dynamics. In this talk, I will present some recent progress on extending the classification theory to such homeomorphisms. This is joint work with Federica Fanoni and Jing Tao.

Dec 2 (Wed) 11:00 am

SNU (Room TBA) & Zoom https://kimsh.kr/vz

Donggyun Seo (Seoul National University) 

Title: TBA

Abstract: TBA