17:00 -- 18:30 数理科学研究科棟(東京大学駒場キャンパス)
Tea: 16:30 -- 17:00 コモンルーム

Last updated October 11, 2016
河野 俊丈
河澄 響矢
北山 貴裕
逆井 卓也

9月27日 -- 056号室, 17:00 -- 18:30

藤内 翔太 (東京大学大学院数理科学研究科)

CAT(0) properties for orthoscheme complexes

Abstract: Gromov showed that a cubical complex is locally CAT(0) if and only if the link of every vertex is a flag complex. Brady and MacCammond introduced an orthoscheme complex as a generalization of cubical complexes. It is, however, difficult to tell whether an orthoscheme complex is (locally) CAT(0) or not. In this talk, I will discuss a translation of Gromov's characterization for orthoscheme complexes. As a generalization of Gromov's characterization, I will show that the orthoscheme complex of locally distributive semilattice is CAT(0) if and only if it is a flag semilattice.

10月11日 -- 056号室, 17:00 -- 18:30

河澄 響矢 (東京大学大学院数理科学研究科)

The Kashiwara-Vergne problem and the Goldman-Turaev Lie bialgebra in genus zero

Abstract: In view of results of Goldman and Turaev, the free vector space over the free loops on an oriented surface has a natural Lie bialgebra structure. The Goldman bracket has a formal description by using a special (or symplectic) expansion of the fundamental group of the surface. It is natural to ask for a formal description of the Turaev cobracket. We will show how to obtain a formal description of the Goldman-Turaev Lie bialgebra for genus 0 using a solution of the Kashiwara-Vergne problem. A similar description was recently obtained by Massuyeau using the Kontsevich integral. Moreover we propose a generalization of the Kashiwara-Vergne problem in the context of the Goldman-Turaev Lie bialgebra. This talk is based on a joint work with A. Alekseev, Y. Kuno and F. Naef.

10月18日 -- 056号室, 17:30 -- 18:30

橋本 義武 (東京都市大学)


Abstract: This talk is based on a joint work with A. Tsuchiya (Kavli IPMU) and T. Matsumoto (Nagoya Univ). In 2006 Feigin-Gainutdinov-Semikhatov-Tipunin introduced vertex operator algebras M called extended W-algebras. Tsuchiya-Wood developed representation theory of M by the method of "infinitesimal deformation of parameter" and Jack symmetric polynomials.

In this talk I will discuss the following subjects:
1. "factorization" in conformal field theory,
2. tensor structure of the category of M-modules and "module-bimodule correspondence".

11月1日 -- 056号室, 17:00 -- 18:30

大場 貴裕 (東京工業大学)

Higher-dimensional contact manifolds with infinitely many Stein fillings

A Stein fillings of a given contact manifold is a Stein domain whose boundary is contactomorphic to the given contact manifold. Open books, Lefschetz fibrations, and mapping class groups of their fibers in particular help us to produce various contact manifolds and their Stein fillings. However, little is known about mapping class groups of higher-dimensional manifolds. This is one of the reasons that it was unknown whether there is a contact manifold of dimension > 3 with infinitely many Stein fillings. In this talk, I will choose a certain symplectic manifold as fibers of open books and Lefschetz fibrations and by using them, construct an infinite family of higher-dimensional contact manifolds with infinitely many Stein fillings.

11月8日 -- 056号室, 17:00 -- 18:30

秋田 利之 (北海道大学)

Second mod 2 homology of Artin groups

Abstract: After a brief survey on the K(π,1) conjecture and homology of Artin groups, I will introduce our recent result: we determined second mod 2 homology of arbitrary Artin groups without assuming the K(π,1)-conjecture. The key ingredients are Hopf's formula and a result of Howlett on Schur multipliers of Coxeter groups. This is a joint work with Ye Liu.