2014年10月 -- 2015年3月
[English]
[過去のプログラム]
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 17, 2015
世話係
河野 俊丈
河澄 響矢
逆井 卓也
10月7日 -- 056号室, 16:30 -- 18:00
入江 慶 (京都大学数理解析研究所)
Transversality problems in string topology and de Rham chains
Abstract:
ストリング・トポロジーの出発点は，多様体の自由ループ空間のホモロジーの上に
Batalin-Vilkovisky(BV)代数の構造を発見したChas-Sullivanの仕事である．
この結果を精密化して鎖レベルの構造を定義することは重要な問題であるが，
まだ決定版の解答は得られていない．困難の一つは，
交叉積を鎖レベルで定義する際に現れる，横断正則性の問題である．
講演では，de Rham 鎖というものを用いることでこの困難を回避し，
鎖レベルの構造が部分的に実現できるということを説明したい．
10月21日 -- 056号室, 16:30 -- 18:00
秋田 利之 (北海道大学)
Vanishing theorems for p-local homology of Coxeter groups
and their alternating subgroups
Abstract:
Given a prime number p, we estimate vanishing ranges of
p-local homology groups of Coxeter groups (of possibly infinite
order) and alternating subgroups of finite reflection groups. Our
results generalize those by Nakaoka for symmetric groups and
Kleshchev-Nakano and Burichenko for alternating groups. The key
ingredient is the equivariant homology of Coxeter complexes.
11月4日 -- 056号室, 16:30 -- 18:00
Brian Bowditch (University of Warwick)
The coarse geometry of Teichmüller space.
Abstract:
We describe some results regarding the coarse geometry of the
Teichmüller space
of a compact surface. In particular, we describe when the Teichmüller
space admits quasi-isometric embeddings of euclidean spaces and
half-spaces.
We also give some partial results regarding the quasi-isometric rigidity
of Teichmüller space. These results are based on the fact that Teichmüller
space admits a ternary operation, natural up to bounded distance
which endows it with the structure of a coarse median space.
11月11日 -- 056号室, 16:30 -- 18:00
Kenneth Baker (University of Miami)
Unifying unexpected exceptional Dehn surgeries
Abstract:
This past summer Dunfield-Hoffman-Licata produced examples of
asymmetric, hyperbolic, 1-cusped 3-manifolds with pairs of lens space
Dehn fillings through a search of the extended SnapPea census.
Examinations of these examples with Hoffman and Licata lead us to
coincidences with other work in progress that gives a simple holistic
topological approach towards producing and extending many of these
families. In this talk we'll explicitly describe our construction and
discuss related applications of the technique.
11月18日 -- 056号室, 16:30 -- 18:00
Charles Siegel (Kavli IPMU)
A Modular Operad of Embedded Curves
Abstract:
Modular operads were introduced by Getzler and Kapranov to formalize the structure of gluing maps between moduli of stable marked curves. We present a construction of analogous gluing maps between moduli of pluri-log-canonically embedded marked curves, which fit together to give a modular operad of embedded curves. This is joint work with Satoshi Kondo and Jesse Wolfson.
11月25日 -- 056号室, 16:30 -- 18:00
齋藤 昌彦 (University of South Florida)
Quandle knot invariants and applications
Abstract:
A quandles is an algebraic structure closely related to knots. Homology theories of
quandles have been defined, and their cocycles are used to construct invariants for
classical knots, spatial graphs and knotted surfaces. In this talk, an overview is given
for quandle cocycle invariants and their applications to geometric properties of knots.
The current status of computations, recent developments and open problems will also
be discussed.
12月2日 -- 056号室, 16:30 -- 18:00
窪田 陽介 (東京大学大学院数理科学研究科)
The Atiyah-Segal completion theorem in noncommutative topology
Abstract:
C*環の位相的な性質を扱う"非可換"トポロジーの理論を用
いて，Atiyah-Segal completion theoremに新しい視点を導入する．ここで，R.
MeyerとR. Nestらによって発展したKasparov categoryの三角圏としてのホモロ
ジー代数が中心的な役割を果たす．また，これは系として同変Kホモロジーや捩
れK理論に対するAtiyah-Segal型のcompletion theoremを含む．これは荒野悠輝
氏との共同研究である．
12月9日 -- 056号室, 16:30 -- 18:00
藤原 耕二 (京都大学大学院理学研究科)
Stable commutator length on mapping class groups
Abstract:
Let MCG(S) be the mapping class group of a closed orientable surface S.
We give a precise condition (in terms of the Nielsen-Thurston
decomposition) when an element
in MCG(S) has positive stable commutator length.
Stable commutator length tends to be positive if there is "negative
curvature".
The proofs use our earlier construction in the paper "Constructing group
actions on quasi-trees and applications to mapping class groups" of
group actions on quasi-trees.
This is a joint work with Bestvina and Bromberg.
12月16日 -- 056号室, 17:10 -- 18:10
岩瀬 則夫 (九州大学)
Differential forms in diffeological spaces
Abstract:
The idea of a space with smooth structure is first introduced by K. T. Chen in his study of a loop space to employ the idea of iterated path integrals.
Following the pattern established by Chen, J. M. Souriau introduced his version of a space with smooth structure which is now called diffeology and become one of the most exciting topics in Algebraic Topology. Following Souriau, P. I.-Zenmour presented de Rham theory associated to a diffeology of a space. However, if one tries to show a version of de Rham theorem for a general diffeological space, he must encounter a difficulty to show the existence of a partition of unity and thus the exactness of the Mayer-Vietoris sequence. To resolve such difficulties, we introduce a new definition of differential forms.
1月13日 -- 056号室, 16:30 -- 18:00
吉田 建一 (東京大学大学院数理科学研究科)
Stable presentation length of 3-manifold groups
Abstract:
We will introduce the stable presentation length
of a finitely presented group, which is defined
by stabilizing the presentation length for the
finite index subgroups. The stable presentation
length of the fundamental group of a 3-manifold
is an analogue of the simplicial volume and the
stable complexity introduced by Francaviglia,
Frigerio and Martelli. We will explain some
similarities of stable presentation length with
simplicial volume and stable complexity.
1月20日 -- 056号室, 16:30 -- 17:30
吉安 徹 (東京大学大学院数理科学研究科)
On Lagrangian caps and their applications
Abstract:
In 2013, Y. Eliashberg and E. Murphy established the h-principle for
exact Lagrangian embeddings with a concave Legendrian boundary. In this
talk, I will explain a modification of their h-principle and show
applications to Lagrangian submanifolds in the complex projective spaces.
3月10日 -- 056号室, 16:30 -- 18:00
Andrei Pajitnov (Université de Nantes)
Arnold conjecture, Floer homology,
and augmentation ideals of finite groups.
Abstract:
Let H be a generic time-dependent 1-periodic
Hamiltonian on a closed weakly monotone
symplectic manifold M. We construct a refined version
of the Floer chain complex associated to (M,H),
and use it to obtain new lower bounds for the number P(H)
of the 1-periodic orbits of the corresponding hamiltonian
vector field. We prove in particular that
if the fundamental group of M is finite
and solvable or simple, then P(H)
is not less than the minimal number
of generators of the fundamental group.
This is joint work with Kaoru Ono.
3月24日 -- 056号室, 17:00 -- 18:30
Mina Aganagic (University of California, Berkeley)
Knots and Mirror Symmetry
Abstract:
I will describe two conjectures relating knot theory and mirror symmetry. One can associate, to every knot K, one a Calabi-Yau manifold Y(K), which depends on the homotopy type of the knot only. The first conjecture is that Y(K) arises by a generalization of SYZ mirror symmetry, as mirror to the conifold, O(-1)+O(-1)->P^1. The second conjecture is that topological string provides a quantization of Y(K) which leads to quantum HOMFLY invariants of the knot. The conjectures are based on joint work with C. Vafa and also with T.Ekholm, L. Ng.