Tuesday Seminar on Topology

[Japanese]   [Past Programs]
17:00 -- 18:30 Graduate School of Mathematical Sciences, The University of Tokyo (with live streaming on Zoom)
or
17:00 -- 18:00 Online seminar on Zoom.

Last updated September 27, 2023
Information :　
Kazuo Habiro
Nariya Kawazumi
Takahiro Kitayama
Takuya Sakasai

Pre-registration is required.
Once you register, you can attend all our seminars until the end of March, 2024.
The zoom meeting will be opened 15 minutes before start.
Making audio and video recordings is prohibited.
October 10, 17:30-18:30 -- Room 056 with live streaming on Zoom

Masato Mimura (Tohoku University)

Invariant quasimorphisms and coarse geometry of scl

Abstract: The topic of this talk is completely independent from that of the intensive lecture (the Green--Tao theorem) from 9th to 13th, Oct. This talk is based on the series of the joint work with Morimichi Kawasaki, Mitsuaki Kimura, Takahiro Matsushita and Shuhei Maruyama. Quasimorphisms on a group are interesting objects, but for many naturally constructed groups the space of quasimorphisms tends to be either 'trivial' or infinite dimensional. We study the setting of a pair of a group and its normal subgroup, not of a single group, and invariant quasimorphisms. Then, we can obtain a non-zero finite dimensional vector space from this setting. The celebrated Bavard duality theorem is extended to this framework, and the resulting theorem yields some outcome on the coarse geometry of scl (stable commutator length). I will present an overview of the developments of this theory.

October 17, 17:00-18:00 -- Online on Zoom

Shunsuke Kano (MathCCS, Tohoku University)

Train track combinatorics and cluster algebras

Abstract: The concepts of train track was introduced by W. P. Thurston to study the measured foliations/laminations and the pseudo-Anosov mapping classes on a surface. In this talk, we translate some concepts of train tracks into the language of cluster algebras using the tropicalization of Goncharov--Shen's potential function. Using this, we translate a combinatorial property of a train track associated with a pseudo-Anosov mapping class into the combinatorial property in cluster algebras, called the sign stability which was introduced by Tsukasa Ishibashi and the speaker.