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

Last updated March 1, 2013
世話係 
河野俊丈
河澄響矢


10月2日 -- 056号室, 16:30 -- 18:00

二木 昭人 (東京大学大学院数理科学研究科)

Geometric flows and their self-similar solutions

Abstract: In the first half of this expository talk we consider the Ricci flow and its self-similar solutions, namely the Ricci solitons. We then specialize in the Kähler case and discuss on the Kähler-Einstein problem. In the second half of this talk we consider the mean curvature flow and its self-similar solutions, and see common aspects of the two geometric flows.


10月9日 -- 056号室, 16:30 -- 18:00

藤井 道彦 (京都大学大学院理学研究科)

The growth series of pure Artin groups of dihedral type

Abstract: In this talk, I consider the kernel of the natural projection from the Artin group of dihedral type to the corresponding Coxeter group, that we call a pure Artin group of dihedral type, and present rational function expressions for both the spherical and geodesic growth series of the pure Artin group of dihedral type with respect to a natural generating set. Also, I show that their growth rates are Pisot numbers. This talk is partially based on a joint work with Takao Satoh.


10月16日 -- 056号室, 17:10 -- 18:10

吉川 謙一 (京都大学大学院理学研究科)

Analytic torsion of log-Enriques surfaces

Abstract: Log-Enriques surfaces are rational surfaces with nowhere vanishing pluri-canonical forms. We report the recent progress on the computation of analytic torsion of log-Enriques surfaces.


10月23日 -- 056号室, 16:30 -- 18:00

河澄 響矢 (東京大学大学院数理科学研究科)

A geometric approach to the Johnson homomorphisms

Abstract: 久野雄介氏(津田塾大学芸)との共同研究。 ジョンソン準同型を、完備化されたゴールドマン・トゥラエフ・リー双代数への トレリ群の 埋め込みとして捉え直す。その際、ジョンソン準同型像はトゥラエフ余括弧積の 核に含まれる。 境界成分が1の場合、このことから森田トレースの幾何的な意味が明らかになる。 時間が許せば、穴あき円板の場合についても議論する。


10月30日 -- 126号室, 16:30 -- 18:00

下川 航也 (埼玉大学大学院理工学研究科)

Applications of knot theory to molecular biology

Abstract: In this talk we discuss applications of knot theory to studies of DNA and proteins. Especially we will consider
(1)topological characterization of mechanisms of site-specific recombination systems,
(2)modeling knotted DNA and proteins in confined regions using lattice knots, and
(3)mechanism of topoisomerases and signed crossing changes.


11月6日 -- 056号室, 16:30 -- 18:00

古庄 英和 (名古屋大学多元数理科学研究科)

結び目へのガロア作用

Abstract: 結び目に定まるモティーフの構造について説明する。 その後、有理数体の絶対ガロア群が'結び目全体が張る空間'に 非自明な方法で非自明に作用することを説明する。


11月13日 -- 056号室, 16:30 -- 18:00

北山 貴裕 (京都大学数理解析研究所,日本学術振興会PD)

The virtual fibering theorem and sutured manifold hierarchies

Abstract: In 2007 Agol showed that every irreducible 3-manifold whose fundamental group is nontrivial and virtually residually finite rationally solvable (RFRS) is virtually fibered. In the proof he used the theory of least-weight taut normal surfaces introduced and developed by Oertel and Tollefson-Wang. We give another proof using complexities of sutured manifolds. This is a joint work with Stefan Friedl (University of Cologne).


11月20日 -- 056号室, 16:30 -- 18:00

長尾 健太郎 (名古屋大学多元数理科学研究科)

3次元双曲幾何と団代数

Abstract: クラスター代数は2000年にFomin-Zelevinskyによって発見された代数系である. 近年,クラスター代数の構造は量子群の理論,低次元トポロジー・離散可積分系・Donaldson-Thomas理論・弦理論など様々な分野で発見され,ダイナミックに研究が進展している. 今回は弦理論におけるある種の双対性を背景とした,3次元双曲幾何とクラスター代数の関係について紹介する.


11月27日 -- 056号室, 16:30 -- 18:00

野澤 啓 (JSPS-IHES フェロー)

葉層構造の特性類の有限的側面について

Abstract: Thurstonの例により、葉層構造の二次特性類は有界でないことが知られている。本講演では、横断的な共形平坦構造などを持つ葉層構造に対しては(例外的な場合を除き)二次特性類が有限性を持つことを、非有界性や葉層構造の剛性との関連と共に説明する。 (本講演はSantiago de Compostela大学のJesús Antonio Álvarez López氏との共同研究 arXiv:1205.3375に基づく。)


12月4日 -- 056号室, 16:30 -- 18:00

橋本 義武 (東京都市大学)

Conformal field theory for C2-cofinite vertex algebras

Abstract: This is a jount work with Akihiro Tsuchiya (Kavli IPMU). We consider sheaves of covacua and conformal blocks over parameter spaces of n-pointed Riemann surfaces for a vertex algebra of which the category of modules is not necessarily semi-simple. We assume the C2-cofiniteness condition for vertex algebras. We define "tensor product" of two modules over a C2-cofinite vertex algebra.


12月11日 -- 056号室, 16:30 -- 18:00

Ismar Volic (Wellesley College)

Homotopy-theoretic methods in the study of spaces of knots and links

Abstract: I will survey the ways in which some homotopy-theoretic methods, manifold calculus of functors main among them, have in recent years been used for extracting information about the topology of spaces of knots and links. Cosimplicial spaces and operads will also be featured. I will end with some recent results about spaces of homotopy string links and in particular about how one can use functor calculus in combination with configuration space integrals to extract information about Milnor invariants.


1月21日 (月) -- 002号室

16:30 -- 17:30

加藤 直樹 (東京大学大学院数理科学研究科)

ベキ零リー環を横断構造に持つリー葉層構造について

Abstract: リー$\mathfrak{g}$-葉層構造が与えられたとき,それに付随した構造リー環と呼 ばれる$\mathfrak{g}$の部分リー環$\mathfrak{h}$が定まる.本講演ではその逆, すなわち,リー環$\mathfrak{g}$とその部分リー環$\mathfrak{h}$が与えられた とき構造リー環が$\mathfrak{h}$となるリー$\mathfrak{g}$-葉層構造が存在す るかという問題についてて,$\mathfrak{g}$がベキ零リー環の場合に説明をする.

17:30 -- 18:30

石田 智彦 (東京大学大学院数理科学研究科)

Quasi-morphisms on the group of area-preserving diffeomorphisms of the 2-disk

Abstract: Gambaudo and Ghys constructed linearly independent countably many quasi- morphisms on the group of area-preserving diffeomorphisms of the 2-disk from quasi-morphisms on braid groups. In this talk, we will explain that their construction is injective as a homomorphism between vector spaces of quasi-morphisms. If time permits, we introduce an application by Brandenbursky and K\c{e} dra. 


1月22日 -- 056号室, 16:30 -- 18:00

Jarek Kedra (University of Aberdeen)

On the autonomous metric of the area preserving diffeomorphism of the two dimensional disc.

Abstract: Let D be the open unit disc in the Euclidean plane and let G:=Diff(D, area) be the group of smooth compactly supported area-preserving diffeomorphisms of D. A diffeomorphism is called autonomous if it is the time one map of the flow of a time independent vector field. Every diffeomorphism in G is a composition of a number of autonomous diffeomorphisms. The least amount of such diffeomorphisms defines a norm on G. In the talk I will investigate geometric properties of such a norm.
In particular I will construct a bi-Lipschitz embedding of the free abelian group of arbitrary rank to G. I will also show that the space of homogeneous quasi-morphisms vanishing on all autonomous diffeomorphisms in G is infinite dimensional.
This is a joint work with Michael Brandenbursky.


2月19日 -- 056号室, 16:30 -- 18:00

畠中 英里 (東京農工大学)

On the ring of Fricke characters of free groups

Abstract: This is a joint work with Takao Satoh (Tokyo University of Science). We study a descending filtration of the ring of Fricke characters of a free group consisting of ideals on which the automorphism group of the free group naturally acts. Then by using it, we define a descending filtration of the automorphism group of a free group, and investigate a relation between it and the Andreadakis-Johnson filtration.


3月19日 -- 002号室, 16:30 -- 18:00

川室 圭子 (University of Iowa)

Open book foliation and application to contact topology

Abstract: Open book foliation is a generalization of Birman and Menasco's braid foliation. Any 3-manifold admits open book decompositions. Open book foliation is a singular foliation on an embedded surface, and is define by the intersection of a surface and the pages of the open book decomposition. By Giroux's identification of open books and contact structures one can use open book foliation method to study contact structures. In this talk I define the open book foliation and show some applications to contact topology. This is joint work with Tetsuya Ito (University of British Columbia).


過去のプログラム