Date: Fri Oct 16 10:12:00 GMT 2015

From: sumio yamada

Subject: 日仏共同研究（タイヒミュラー空間と写像類群）による小研究集会のご案内

皆様、 以下のお知らせを送らせていただきます。よろしくお願い致します。 山田澄生 //////////////////////////////////////////////////////////////////////// メーリングリストの皆様、 重複ご海容ください。 日仏共同研究（タイヒミュラー空間と写像類群）による小研究集会を １１月１６日（月）から２０日（金）まで 東京大学大学院数理科学研究科 002 号室で 以下の要領で行います。使用言語は英語です。 皆様奮ってご参加ください。 とりいそぎ 大鹿健一（阪大理） 逆井卓也（東大数理） 河澄響矢（東大数理） ========================= Atelier de travail franco-japonais sur la géométrie des groupes modulaires et des espaces de Teichmüller Les 16-20 novembre 2015 Salle 002, Faculté de sciences mathématiques, Université de Tokyo Le lundi 16 novembre (10:30-12:00 Salle 128 (Séminaire sur l'analyse géométrique complexe: (Hideki Miyachi (Université d’Osaka) 13:30-14:30 Athanase Papadopoulos (Université de Strasbourg/CNRS) Timelike geometry Le mardi 17 novembre 10:00-11:00 Athanase Papadopoulos (Université de Strasbourg/CNRS) Spherical geometry I 11:30-12:30 Takahito Naito (Université de Tokyo) Sullivan's coproduct on the relative loop homology 14:00-15:00 + 15:30-16:30 Gwénaël Massuyeau (Université de Strasbourg/CNRS) Fox pairings in Hopf algebras and Poisson structures (16:30-17:00 Salle commune(pause café pour Séminaire du mardi sur la topologie (17:00-18:30 Salle 056 (Séminaire du mardi sur la topologie (Atsuko Katanaga (Université de Shinshu) Le mercredi 18 novembre 10:00-11:00 Athanase Papadopoulos (Université de Strasbourg/CNRS) Spherical geometry II 11:30-12:30 Yasuo Wakabayashi (Université de Tokyo) A theory of dormant opers Le jeudi 19 novembre 10:00-11:00 Masatoshi Sato (Tokyo Denki University) On the cohomology ring of the handlebody mapping class group of genus two 11:30-12:30 Elena Frenkel (Université de Strasbourg) Area formula for Hyperbolic Triangles and Lexell problem 14:00-15:00 Yuanyuan Bao (Université de Tokyo) Heegaard Floer homology for transverse graphs with sinks and sources 15:30-16:30 Tadayuki Watanabe (Université de Shimane) An invariant of fiberwise Morse functions on surface bundle over S^1 by counting graphs Le vendredi 20 novembre 09:30-10:30 + 11:00-12:00 Olivier Guichard (Université de Strasbourg) Compactifications of certain locally symmetric spaces (Les 20 à 22 novembre Salle 123 (Rigidity School, Tokyo 2015 ======= Résumés des exposés Papadopoulos: Timelike geometry Papadopoulos: Spherical geometry I Naito: Sullivan's coproduct on the relative loop homology Sullivan's coproduct is the coproduct on the relative homology of the free loop space of a closed oriented manifold (called the relative loop homology). It is known that the relative loop homology is an infinitesimal bialgebra with respect to this coproduct and the loop product. In this talk, we will give a homotopical description of Sullivan's coproduct and introduce its properties. Moreover, we will compute the coalgebra structure of spheres over the rational number field by using the description. Massuyeau: Fox pairings in Hopf algebras and Poisson structures We will present the general theory of Fox pairings in Hopf algebras, which will be illustrated through several algebraic examples. Next, we will recall how such operations naturally appear in topology by considering intersections of curves in surfaces, and sketch how this generalizes to higher-dimensional manifolds. Finally, we will use Fox pairings to construct some natural Poisson structures on the affine scheme of representations of a cocommutative Hopf algebra in an arbitrary group scheme. (Based on joint works with Vladimir Turaev.) Wakabayashi: A theory of dormant opers A(n) (dormant) oper, being our central object of this talk, is a certain principal homogeneous space on an algebraic curve (in positive characteristic) equipped with an integrable connection. The study of dormant opers and their moduli may be linked to various fields of mathematics, e.g., the p-adic Teichmuller theory developed by Shinichi Mochizuki, Gromov-Witten theory, combinatorics of rational polytopes ( and spin networks), etc. In this talk, we would like to introduce the definition of a dormant oper and to present some related results, including an explicit formula for the generic number of dormant opers, which was conjectured by Kirti Joshi. Papadopoulos: Spherical geometry II Sato: On the cohomology ring of the handlebody mapping class group of genus two The genus two handlebody mapping class group acts on a tree constructed by Kramer from the disk complex, and decomposes into an amalgamated product of two subgroups. We determine the integral cohomology ring of the genus two handlebody mapping class group by examining these subgroups and the Mayer-Vietoris exact sequence. Using this result, ｗe estimate the orders of low dimensional homology groups of the genus three handlebody mapping class group. Frenkel: Area formula for Hyperbolic Triangles and Lexell problem My talk will be about an area formula in terms of side lengths for triangles in plane hyperbolic geometry and its geometrical interpretation . The proof of this formula is analogous to a proof given by Leonhard Euler in the spherical case. I will speak in particular about the Lexell problem, that is, the problem of finding the locus of vertices of triangle of fixed area and fixed base. Bao: Heegaard Floer homology for transverse graphs with sinks and sources We defined the Heegaard Floer homology (HF) for balanced bipartite graphs. Around the same time, Harvey and O’Donnol defined the combinatorial HF for transverse graphs without sink and source (see the definition in [arXiv:1506.04785v1]). In this talk, we compare these two methods and consider the HF for transverse graphs with the same number of sinks and sources in both analytic and combinatorial ways. Watanabe: An invariant of fiberwise Morse functions on surface bundle over S^1 by counting graphs We apply Lescop’s construction of Z-equivariant perturbative invariant of knots and 3-manifolds to the explicit equivariant propagator of “Z-paths”. We obtain an invariant of certain equivalence classes of fiberwise Morse functions on a 3-manifold fibered over S^1, which can be considered as a higher loop analogue of the Lefschetz zeta function and whose construction will be applied to that of finite type invariants of knots in such a 3-manifold. Guichard: Compactifications of certain locally symmetric spaces

皆様、

以下のお知らせを送らせていただきます。よろしくお願い致します。

山田澄生

////////////////////////////////////////////////////////////////////////

メーリングリストの皆様、

重複ご海容ください。

日仏共同研究（タイヒミュラー空間と写像類群）による小研究集会を

１１月１６日（月）から２０日（金）まで

東京大学大学院数理科学研究科 002 号室で

以下の要領で行います。使用言語は英語です。

皆様奮ってご参加ください。

とりいそぎ

大鹿健一（阪大理）

逆井卓也（東大数理）

河澄響矢（東大数理）

=========================

Atelier de travail franco-japonais sur la géométrie

des groupes modulaires et des espaces de Teichmüller

Les 16-20 novembre 2015

Salle 002, Faculté de sciences mathématiques, Université de Tokyo

Le lundi 16 novembre

(10:30-12:00 Salle 128

(Séminaire sur l'analyse géométrique complexe:

(Hideki Miyachi (Université d’Osaka)

13:30-14:30

Athanase Papadopoulos (Université de Strasbourg/CNRS)

Timelike geometry

Le mardi 17 novembre

10:00-11:00

Athanase Papadopoulos (Université de Strasbourg/CNRS)

Spherical geometry I

11:30-12:30

Takahito Naito (Université de Tokyo)

Sullivan's coproduct on the relative loop homology

14:00-15:00 + 15:30-16:30

Gwénaël Massuyeau (Université de Strasbourg/CNRS)

Fox pairings in Hopf algebras and Poisson structures

(16:30-17:00 Salle commune <premier étage>

(pause café pour Séminaire du mardi sur la topologie

(17:00-18:30 Salle 056

(Séminaire du mardi sur la topologie

(Atsuko Katanaga (Université de Shinshu)

Le mercredi 18 novembre

10:00-11:00

Athanase Papadopoulos (Université de Strasbourg/CNRS)

Spherical geometry II

11:30-12:30

Yasuo Wakabayashi (Université de Tokyo)

A theory of dormant opers

Le jeudi 19 novembre

10:00-11:00

Masatoshi Sato (Tokyo Denki University)

On the cohomology ring of the handlebody mapping class group of genus two

11:30-12:30

Elena Frenkel (Université de Strasbourg)

Area formula for Hyperbolic Triangles and Lexell problem

14:00-15:00

Yuanyuan Bao (Université de Tokyo)

Heegaard Floer homology for transverse graphs with sinks and sources

15:30-16:30

Tadayuki Watanabe (Université de Shimane)

An invariant of fiberwise Morse functions on surface bundle over S^1 by counting graphs

Le vendredi 20 novembre

09:30-10:30 + 11:00-12:00

Olivier Guichard (Université de Strasbourg)

Compactifications of certain locally symmetric spaces

(Les 20 à 22 novembre Salle 123

(Rigidity School, Tokyo 2015

=======

Résumés des exposés

Papadopoulos: Timelike geometry

Papadopoulos: Spherical geometry I

Naito: Sullivan's coproduct on the relative loop homology

Sullivan's coproduct is the coproduct on the relative homology of the

free loop space of a closed oriented manifold (called the relative loop

homology). It is known that the relative loop homology is an

infinitesimal bialgebra with respect to this coproduct and the loop

product. In this talk, we will give a homotopical description of

Sullivan's coproduct and introduce its properties. Moreover, we will

compute the coalgebra structure of spheres over the rational number

field by using the description.

Massuyeau: Fox pairings in Hopf algebras and Poisson structures

We will present the general theory of Fox pairings in Hopf algebras, which will be illustrated through several algebraic examples. Next, we will recall how such operations naturally appear in topology by considering intersections of curves in surfaces, and sketch how this generalizes to higher-dimensional manifolds. Finally, we will use Fox pairings to construct some natural Poisson structures on the affine scheme of representations of a cocommutative Hopf algebra in an arbitrary group scheme. (Based on joint works with Vladimir Turaev.)

Wakabayashi: A theory of dormant opers

A(n) (dormant) oper, being our central object of this talk, is a certain

principal homogeneous space on an algebraic curve (in positive

characteristic) equipped with an integrable connection. The study of

dormant opers and their moduli may be linked to various fields of

mathematics, e.g., the p-adic Teichmuller theory developed by Shinichi

Mochizuki, Gromov-Witten theory, combinatorics of rational polytopes (

and spin networks), etc. In this talk, we would like to introduce the

definition of a dormant oper and to present some related results,

including an explicit formula for the generic number of dormant opers,

which was conjectured by Kirti Joshi.

Papadopoulos: Spherical geometry II

Sato: On the cohomology ring of the handlebody mapping class group of genus two

The genus two handlebody mapping class group acts on a tree constructed by Kramer from the disk complex,

and decomposes into an amalgamated product of two subgroups.

We determine the integral cohomology ring of the genus two handlebody mapping class group

by examining these subgroups and the Mayer-Vietoris exact sequence.

Using this result, ｗe estimate the orders of low dimensional homology groups

of the genus three handlebody mapping class group.

Frenkel: Area formula for Hyperbolic Triangles and Lexell problem

My talk will be about an area formula in terms of side lengths for triangles in plane hyperbolic geometry and its geometrical interpretation . The proof of this formula is analogous to a proof given by Leonhard Euler in the spherical case. I will speak in particular about the Lexell problem, that is, the problem of finding the locus of vertices of triangle of fixed area and fixed base.

Bao: Heegaard Floer homology for transverse graphs with sinks and sources

We defined the Heegaard Floer homology (HF) for balanced bipartite graphs. Around the same time, Harvey and O’Donnol defined the combinatorial HF for transverse graphs without sink and source (see the definition in [arXiv:1506.04785v1]). In this talk, we compare these two methods and consider the HF for transverse graphs with the same number of sinks and sources in both analytic and combinatorial ways.

Watanabe: An invariant of fiberwise Morse functions on surface bundle over S^1 by counting graphs

We apply Lescop’s construction of Z-equivariant perturbative invariant

of knots and 3-manifolds to the explicit equivariant propagator of “Z-paths”.

We obtain an invariant of certain equivalence classes of fiberwise Morse

functions on a 3-manifold fibered over S^1, which can be

considered as a higher loop analogue of the Lefschetz zeta function and whose

construction will be applied to that of finite type invariants of knots in such

a 3-manifold.

Guichard: Compactifications of certain locally symmetric spaces