Special day for Teichmueller theory

October 3 (Tue), 2017

Room 126, Graduate School of Mathematical Sciences,
University of Tokyo (Komaba) access

invited speakers (alphabetical order):
Tsukasa Ishibashi (Univ. Tokyo)
Hidenori Ishihara (Univ. Tokyo)
Hidetoshi Masai (Tohoku Univ.)
Shogo Matsuba (Univ. Tokyo)
Athanase Papadopoulos (IRMA, Univ. Strasbourg/CNRS)


10:00--11:00, at Room 126,
Hideki Ishihara (Univ. Tokyo)
Weil-Petersson isometries of the developed Teichmueller space

11:20--12:20, at Room 126,
Shogo Matsuba (Univ. Tokyo)
Thompson groups corresponding to dynamical systems

14:10--15:10, at Room 126,
Tsukasa Ishibashi (Univ. Tokyo)
On a Nielsen-Thurston classification theory on cluster modular groups

15:30--16:30, at Room 126,
Hidetoshi Masai (Tohoku Univ.)
Symmetry of mapping classes and outer automorphisms

16:30--17:00, at Common Room on the 2nd floor,
Tea for Tuesday Seminar on Topology

17:00--18:00, Tuesday Seminar on Topology at Room 056
Athanase Papadopoulos (IRMA, Univ. Strasbourg/CNRS)
Transitional geometry

supported by:
Invitation Fellowship Short-term FY2017: Synthetic study on convex geometries of moduli spaces
Grant-in-Aid for Scientific Research (B) 15H03617

organizers (alphabetical order):
Nariya Kawazumi (Univ. Tokyo)
Yuske Kuno (Tsuda Univ.)
Takuya Sakasai (Univ. Tokyo)

schedule with abstracts: pdf-file

Titles and Abstracts:

Tsukasa Ishibashi (University of Tokyo)

On a Nielsen-Thurston classification theory on cluster modular groups

It is known that each element of the mapping class group of a orientable
surface is classified into three types.
These types are characterized by fixed point properties of a natural
action on a closed disk, which is the Thurston compactification of the
Teichmuller space. These are the Nielsen-Thurston classification thoery.
On the other hand, by Fock-Goncharov, the mapping class group and the
Teichmuller space are generalized to cluster modular groups and cluster
ensembles respectively. For particular choices of the
input data, these concepts can describe higher Teichmuller spaces and
the mapping class group action on them in a combinatorial language.
In this talk, I will give a classification of elements of the cluster
modular group, which is an analogue of the Nielsen-Thurston
classification. Then they are related with fixed point properties of the
action on the tropical compactification of the cluster ensemble.

Hidenori Ishihara (University of Tokyo)

Weil-Petersson isometries of the developed Teichm\"uller space

Sumio Yamada constructed the development of Teichm\"uller
space by using the Coxeter group and named the space Teichm\"uller
Coxeter complex. The development is the Weil-Petersson geodesic
completion of Teichm\"uller space and a CAT(0) space. On the other hand,
Koji Fujiwara and Jason Fox Manning gave an example of isometries of
Teichm\"uller Coxeter complex which differs from the natural isometric
action of the development. I will talk about the above and the main
theorem on the expression of the isomety group of Teichm\"uller Coxeter
complex based on the idea of Koji Fujiwara and Jason Fox Manning.

Hidetoshi Masai (Tohoku University)

Symmetry of mapping classes and outer automorphisms

We consider notion called fibered commensurability, which allows us to study symmetry of maps.
Fibered commensurability is first defined by Calegari-Sun-Wang on mapping classes group.
We first recall known facts of fibered commensurability of mapping classes.
Then we discuss analogy for outer automorphism groups of free groups.
A part of this talk is based on the joint work with Ryosuke Mineyama.

Shogo Matsuba (University of Tokyo)

Thompson groups corresponding to dynamical systems

We will introduce Thompson groups that come from dynamical systems.
Belk and Forrest defined the basilica Thompson group T_B,
where the basilica is the Julia set of the dynamical system f(z) = z^2-1.
T_B is naturally embedded into Thompson group T and
has finite generators but is not finitely presentable.
As they said, we can also construct Thompson groups for other dynamical systems.
In this talk we will see the concrete generators of the Thompson group
for the Julia set called "rabbit" and some properties parallel to or different from T_B.

Athanase Papadopoulos (IRMA, University of Strasbourg/CNRS)
(Tuesday seminar on Topology)

Transitional geometry

I will describe transitions, that is, paths between hyperbolic and spherical geometry,
passing through the Euclidean. This is based on joint work with Norbert A’Campo
and recent joint work with A’Campo and Yi Huang.

Nariya Kawazumi (kawazumi_ATMARK_ms.u-tokyo.ac.jp)