本文印刷
全画面プリント
トポロジー火曜セミナー
過去の記録 ～07/26｜次回の予定｜今後の予定 07/27～
| 開催情報 | 火曜日 17:00～18:30 数理科学研究科棟(駒場) 056号室 |
|---|---|
| 担当者 | 河澄 響矢, 北山 貴裕, 逆井卓也 |
| セミナーURL | http://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index.html |
過去の記録
2014年07月22日(火)
16:30-18:00 数理科学研究科棟(駒場) 056号室
Tea: 16:00 - 16:30 コモンルーム
Jesse Wolfson 氏 (Northwestern University)
The Index Map and Reciprocity Laws for Contou-Carrere Symbols (ENGLISH)
Tea: 16:00 - 16:30 コモンルーム
Jesse Wolfson 氏 (Northwestern University)
The Index Map and Reciprocity Laws for Contou-Carrere Symbols (ENGLISH)
[ 講演概要 ]
In the 1960s, Atiyah and Janich constructed the families index as a natural map from the space of Fredholm operators to the classifying space of topological K-theory, and showed it to be an equivalence. In joint work with Oliver Braunling and Michael Groechenig, we construct an analogous index map in algebraic K-theory. Building on recent work of Sho Saito, we show this provides an analogue of Atiyah and Janich's equivalence. More significantly, the index map allows us to relate the Contou-Carrere symbol, a local analytic invariant of schemes, to algebraic K-theory. Using this, we provide new proofs of reciprocity laws for Contou-Carrere symbols in dimension 1 (first established by Anderson--Pablos Romo) and 2 (established recently by Osipov--Zhu). We extend these reciprocity laws to all dimensions.
In the 1960s, Atiyah and Janich constructed the families index as a natural map from the space of Fredholm operators to the classifying space of topological K-theory, and showed it to be an equivalence. In joint work with Oliver Braunling and Michael Groechenig, we construct an analogous index map in algebraic K-theory. Building on recent work of Sho Saito, we show this provides an analogue of Atiyah and Janich's equivalence. More significantly, the index map allows us to relate the Contou-Carrere symbol, a local analytic invariant of schemes, to algebraic K-theory. Using this, we provide new proofs of reciprocity laws for Contou-Carrere symbols in dimension 1 (first established by Anderson--Pablos Romo) and 2 (established recently by Osipov--Zhu). We extend these reciprocity laws to all dimensions.
2014年07月08日(火)
16:30-18:00 数理科学研究科棟(駒場) 056号室
Tea: 16:00 - 16:30 コモンルーム
Ingrid Irmer 氏 (JSPS, 東京大学大学院数理科学研究科)
The Johnson homomorphism and a family of curve graphs (ENGLISH)
Tea: 16:00 - 16:30 コモンルーム
Ingrid Irmer 氏 (JSPS, 東京大学大学院数理科学研究科)
The Johnson homomorphism and a family of curve graphs (ENGLISH)
[ 講演概要 ]
Abstract: A family of curve graphs of an oriented surface $S_{g,1}$ will be defined on which there exists a natural orientation, coming from the orientation of subsurfaces. Distances in these graphs represent commutator lengths in $\\pi_{1}(S_{g,1})$. The displacement of vertices in the graphs under the action of the Torelli group is used to give a combinatorial description of the Johnson homomorphism."
Abstract: A family of curve graphs of an oriented surface $S_{g,1}$ will be defined on which there exists a natural orientation, coming from the orientation of subsurfaces. Distances in these graphs represent commutator lengths in $\\pi_{1}(S_{g,1})$. The displacement of vertices in the graphs under the action of the Torelli group is used to give a combinatorial description of the Johnson homomorphism."
2014年07月01日(火)
16:30-18:00 数理科学研究科棟(駒場) 056号室
Tea: 16:00 - 16:30 コモンルーム
今城 洋亮 氏 (Kavli IPMU)
Singularities of special Lagrangian submanifolds (JAPANESE)
Tea: 16:00 - 16:30 コモンルーム
今城 洋亮 氏 (Kavli IPMU)
Singularities of special Lagrangian submanifolds (JAPANESE)
[ 講演概要 ]
There are interesting invariants defined by "counting" geometric
objects, such as instantons in dimension 4 and pseudo-holomorphic curves
in symplectic manifolds. To do the counting in a sensible way, however,
we have to care about singularities of the geometric objects. Special
Lagrangian submanifolds seem very difficult to "count" as their
singularities may be very complicated. I'll talk about simple
singularities for which we can make an analogy with instantons in
dimension 4 and pseudo-holomorphic curves in symplectic manifolds. To do
it I'll use some techniques from geometric measure theory and Lagrangian
Floer theory, and the Floer-theoretic part is a joint work with Dominic
Joyce and Oliveira dos Santos.
There are interesting invariants defined by "counting" geometric
objects, such as instantons in dimension 4 and pseudo-holomorphic curves
in symplectic manifolds. To do the counting in a sensible way, however,
we have to care about singularities of the geometric objects. Special
Lagrangian submanifolds seem very difficult to "count" as their
singularities may be very complicated. I'll talk about simple
singularities for which we can make an analogy with instantons in
dimension 4 and pseudo-holomorphic curves in symplectic manifolds. To do
it I'll use some techniques from geometric measure theory and Lagrangian
Floer theory, and the Floer-theoretic part is a joint work with Dominic
Joyce and Oliveira dos Santos.
2014年06月24日(火)
17:10-18:10 数理科学研究科棟(駒場) 056号室
Tea: 16:50 - 17:10 コモンルーム
野坂 武史 氏 (九州大学数理学研究院)
On third homologies of quandles and of groups via Inoue-Kabaya map (JAPANESE)
Tea: 16:50 - 17:10 コモンルーム
野坂 武史 氏 (九州大学数理学研究院)
On third homologies of quandles and of groups via Inoue-Kabaya map (JAPANESE)
[ 講演概要 ]
In this talk, we demonstrate certain quandles, which are defined from a
group $G$ and an isomorphism $¥rho:G - G$, and introduce the following
results: First, "Inoue-Kabaya chain map" is formulated as a map from
quandle homology to group homology. For example, with respect to every
Alexander quandle over F_q, the all of Mochizuki 3-cocycle is derived
from some group 3-cocycle, and mostly interpreted by a Massey products.
In addition, for universal centrally extended quandles, the chain map
induces an isomorphism between the 3-rd homologies (up to certain
torsion parts).
In this talk, we demonstrate certain quandles, which are defined from a
group $G$ and an isomorphism $¥rho:G - G$, and introduce the following
results: First, "Inoue-Kabaya chain map" is formulated as a map from
quandle homology to group homology. For example, with respect to every
Alexander quandle over F_q, the all of Mochizuki 3-cocycle is derived
from some group 3-cocycle, and mostly interpreted by a Massey products.
In addition, for universal centrally extended quandles, the chain map
induces an isomorphism between the 3-rd homologies (up to certain
torsion parts).
2014年06月17日(火)
16:30-18:00 数理科学研究科棟(駒場) 002号室
Tea: 16:00 - 16:30 コモンルーム
松田 能文 氏 (青山学院大学)
2次元軌道体群の円周への作用の有界オイラー数 (JAPANESE)
Tea: 16:00 - 16:30 コモンルーム
松田 能文 氏 (青山学院大学)
2次元軌道体群の円周への作用の有界オイラー数 (JAPANESE)
[ 講演概要 ]
Burger,Iozzi,Wienhardは連結かつ向き付けられた有限型の穴あき曲面の基本群
の円周への作用に対して有界オイラー数を定義した.有界オイラー数を含むMilnor-Wood型
の不等式が成立しその最大性はフックス作用を準共役を除いて特徴付ける.被覆を考えること
により有界オイラー数の定義は2次元軌道体群の作用に対して拡張される.Milnor-Wood型の
不等式およびフックス作用の特徴付けはこの場合にも成立する.この講演では,モジュラー群
などのいくつかの2次元軌道体群のフックス作用の持ち上げがいつ有界オイラー数により特徴
づけられるかについて記述する.
Burger,Iozzi,Wienhardは連結かつ向き付けられた有限型の穴あき曲面の基本群
の円周への作用に対して有界オイラー数を定義した.有界オイラー数を含むMilnor-Wood型
の不等式が成立しその最大性はフックス作用を準共役を除いて特徴付ける.被覆を考えること
により有界オイラー数の定義は2次元軌道体群の作用に対して拡張される.Milnor-Wood型の
不等式およびフックス作用の特徴付けはこの場合にも成立する.この講演では,モジュラー群
などのいくつかの2次元軌道体群のフックス作用の持ち上げがいつ有界オイラー数により特徴
づけられるかについて記述する.
2014年06月10日(火)
16:30-18:00 数理科学研究科棟(駒場) 056号室
Tea: 16:00 - 16:30 コモンルーム
小鳥居 祐香 氏 (東京大学大学院数理科学研究科)
On relation between the Milnor's $¥mu$-invariant and HOMFLYPT
polynomial (JAPANESE)
Tea: 16:00 - 16:30 コモンルーム
小鳥居 祐香 氏 (東京大学大学院数理科学研究科)
On relation between the Milnor's $¥mu$-invariant and HOMFLYPT
polynomial (JAPANESE)
[ 講演概要 ]
Milnor introduced a family of invariants for ordered oriented link,
called $¥bar{¥mu}$-invariants. Polyak showed a relation between the $¥
bar{¥mu}$-invariant of length 3 sequence and Conway polynomial.
Moreover, Habegger-Lin showed that Milnor's invariants are invariants of
string link, called $¥mu$-invariants. We show that any $¥mu$-invariant
of length $¥leq k$ can be represented as a combination of HOMFLYPT
polynomials if all $¥mu$-invariant of length $¥leq k-2$ vanish.
This result is an extension of Polyak's result.
Milnor introduced a family of invariants for ordered oriented link,
called $¥bar{¥mu}$-invariants. Polyak showed a relation between the $¥
bar{¥mu}$-invariant of length 3 sequence and Conway polynomial.
Moreover, Habegger-Lin showed that Milnor's invariants are invariants of
string link, called $¥mu$-invariants. We show that any $¥mu$-invariant
of length $¥leq k$ can be represented as a combination of HOMFLYPT
polynomials if all $¥mu$-invariant of length $¥leq k-2$ vanish.
This result is an extension of Polyak's result.
2014年06月03日(火)
16:30-18:00 数理科学研究科棟(駒場) 056号室
Tea: 16:00 - 16:30 コモンルーム
高倉 樹 氏 (中央大学・理工学部)
Vector partition functions and the topology of multiple weight varieties
(JAPANESE)
Tea: 16:00 - 16:30 コモンルーム
高倉 樹 氏 (中央大学・理工学部)
Vector partition functions and the topology of multiple weight varieties
(JAPANESE)
[ 講演概要 ]
A multiple weight variety is a symplectic quotient of a direct product
of several coadjoint orbits of a compact Lie group $G$, with respect to
the diagonal action of the maximal torus. Its geometry and topology are
closely related to the combinatorics concerned with the weight space
decomposition of a tensor product of irreducible representations of $G$.
For example, when considering the Riemann-Roch index, we are naturally
lead to the study of vector partition functions with multiplicities.
In this talk, we discuss some formulas for vector partition functions,
especially a generalization of the formula of Brion-Vergne. Then, by
using
them, we investigate the structure of the cohomology of certain multiple
weight varieties of type $A$ in detail.
A multiple weight variety is a symplectic quotient of a direct product
of several coadjoint orbits of a compact Lie group $G$, with respect to
the diagonal action of the maximal torus. Its geometry and topology are
closely related to the combinatorics concerned with the weight space
decomposition of a tensor product of irreducible representations of $G$.
For example, when considering the Riemann-Roch index, we are naturally
lead to the study of vector partition functions with multiplicities.
In this talk, we discuss some formulas for vector partition functions,
especially a generalization of the formula of Brion-Vergne. Then, by
using
them, we investigate the structure of the cohomology of certain multiple
weight varieties of type $A$ in detail.
2014年05月27日(火)
16:30-18:00 数理科学研究科棟(駒場) 056号室
Tea: 16:00 - 16:30 コモンルーム
藤川 英華 氏 (千葉大学大学院理学研究科)
The Teichmuller space and the stable quasiconformal mapping class group for a Riemann surface of infinite type (JAPANESE)
Tea: 16:00 - 16:30 コモンルーム
藤川 英華 氏 (千葉大学大学院理学研究科)
The Teichmuller space and the stable quasiconformal mapping class group for a Riemann surface of infinite type (JAPANESE)
[ 講演概要 ]
We explain recent developments of the theory of infinite dimensional Teichmuller space. In particular, we observe the dynamics of the orbits by the action of the stable quasiconformal mapping class group on the Teichmuller space and consider the relationship with the asymptotic Teichmuller space. We also introduce the generalized fixed point theorem and the Nielsen realization theorem. Furthermore, we investigate the moduli space of Riemann surface of infinite type.
We explain recent developments of the theory of infinite dimensional Teichmuller space. In particular, we observe the dynamics of the orbits by the action of the stable quasiconformal mapping class group on the Teichmuller space and consider the relationship with the asymptotic Teichmuller space. We also introduce the generalized fixed point theorem and the Nielsen realization theorem. Furthermore, we investigate the moduli space of Riemann surface of infinite type.
2014年05月20日(火)
16:30-18:00 数理科学研究科棟(駒場) 056号室
Tea: 16:00 - 16:30 コモンルーム
黒木 慎太郎 氏 (東京大学大学院数理科学研究科)
An application of torus graphs to characterize torus manifolds
with extended actions (JAPANESE)
Tea: 16:00 - 16:30 コモンルーム
黒木 慎太郎 氏 (東京大学大学院数理科学研究科)
An application of torus graphs to characterize torus manifolds
with extended actions (JAPANESE)
[ 講演概要 ]
A torus manifold is a compact, oriented 2n-dimensional T^n-
manifolds with fixed points. This notion is introduced by Hattori and
Masuda as a topological generalization of toric manifolds. For a given
torus manifold, we can define a labelled graph called a torus graph (
this may be regarded as a generalization of some class of GKM graphs).
It is known that the equivariant cohomology ring of some nice class of
torus manifolds can be computed by using a combinatorial data of torus
graphs. In this talk, we study which torus action of torus manifolds can
be extended to a non-abelian compact connected Lie group. To do this, we
introduce root systems of (abstract) torus graphs and characterize
extended actions of torus manifolds. This is a joint work with Mikiya
Masuda.
A torus manifold is a compact, oriented 2n-dimensional T^n-
manifolds with fixed points. This notion is introduced by Hattori and
Masuda as a topological generalization of toric manifolds. For a given
torus manifold, we can define a labelled graph called a torus graph (
this may be regarded as a generalization of some class of GKM graphs).
It is known that the equivariant cohomology ring of some nice class of
torus manifolds can be computed by using a combinatorial data of torus
graphs. In this talk, we study which torus action of torus manifolds can
be extended to a non-abelian compact connected Lie group. To do this, we
introduce root systems of (abstract) torus graphs and characterize
extended actions of torus manifolds. This is a joint work with Mikiya
Masuda.
2014年05月13日(火)
16:30-18:00 数理科学研究科棟(駒場) 056号室
Tea: 16:00 - 16:30 コモンルーム
足助 太郎 氏 (東京大学大学院数理科学研究科)
Transverse projective structures of foliations and deformations of the Godbillon-Vey class (JAPANESE)
Tea: 16:00 - 16:30 コモンルーム
足助 太郎 氏 (東京大学大学院数理科学研究科)
Transverse projective structures of foliations and deformations of the Godbillon-Vey class (JAPANESE)
[ 講演概要 ]
Given a smooth family of foliations, we can define the derivative of the Godbillon-Vey class
with respect to the family. The derivative is known to be represented in terms of the projective
Schwarzians of holonomy maps. In this talk, we will study transverse projective structures
and connections, and show that the derivative is in fact determined by the projective structure
and the family.
Given a smooth family of foliations, we can define the derivative of the Godbillon-Vey class
with respect to the family. The derivative is known to be represented in terms of the projective
Schwarzians of holonomy maps. In this talk, we will study transverse projective structures
and connections, and show that the derivative is in fact determined by the projective structure
and the family.
2014年04月15日(火)
16:30-18:00 数理科学研究科棟(駒場) 056号室
Tea: 16:00 - 16:30 コモンルーム
内藤 貴仁 氏 (東京大学大学院数理科学研究科)
On the rational string operations of classifying spaces and the
Hochschild cohomology (JAPANESE)
Tea: 16:00 - 16:30 コモンルーム
内藤 貴仁 氏 (東京大学大学院数理科学研究科)
On the rational string operations of classifying spaces and the
Hochschild cohomology (JAPANESE)
[ 講演概要 ]
Chataur and Menichi initiated the theory of string topology of
classifying spaces.
In particular, the cohomology of the free loop space of a classifying
space is endowed with a product
called the dual loop coproduct. In this talk, I will discuss the
algebraic structure and relate the rational dual loop coproduct to the
cup product on the Hochschild cohomology via the Van den Bergh isomorphism.
Chataur and Menichi initiated the theory of string topology of
classifying spaces.
In particular, the cohomology of the free loop space of a classifying
space is endowed with a product
called the dual loop coproduct. In this talk, I will discuss the
algebraic structure and relate the rational dual loop coproduct to the
cup product on the Hochschild cohomology via the Van den Bergh isomorphism.
2014年04月08日(火)
16:30-18:00 数理科学研究科棟(駒場) 056号室
Tea: 16:00 - 16:30 コモンルーム
正井 秀俊 氏 (東京大学大学院数理科学研究科)
On the number of commensurable fibrations on a hyperbolic 3-manifold. (JAPANESE)
Tea: 16:00 - 16:30 コモンルーム
正井 秀俊 氏 (東京大学大学院数理科学研究科)
On the number of commensurable fibrations on a hyperbolic 3-manifold. (JAPANESE)
[ 講演概要 ]
By work of Thurston, it is known that if a hyperbolic fibred
$3$-manifold $M$ has Betti number greater than 1, then
$M$ admits infinitely many distinct fibrations.
For any fibration $\\omega$ on a hyperbolic $3$-manifold $M$,
the number of fibrations on $M$ that are commensurable in the sense of
Calegari-Sun-Wang to $\\omega$ is known to be finite.
In this talk, we prove that the number can be arbitrarily large.
By work of Thurston, it is known that if a hyperbolic fibred
$3$-manifold $M$ has Betti number greater than 1, then
$M$ admits infinitely many distinct fibrations.
For any fibration $\\omega$ on a hyperbolic $3$-manifold $M$,
the number of fibrations on $M$ that are commensurable in the sense of
Calegari-Sun-Wang to $\\omega$ is known to be finite.
In this talk, we prove that the number can be arbitrarily large.
2014年01月21日(火)
16:30-17:30 数理科学研究科棟(駒場) 056号室
Tea: 16:00 - 16:30 コモンルーム
粕谷 直彦 氏 (東京大学大学院数理科学研究科)
On contact submanifolds of the odd dimensional Euclidean space (JAPANESE)
Tea: 16:00 - 16:30 コモンルーム
粕谷 直彦 氏 (東京大学大学院数理科学研究科)
On contact submanifolds of the odd dimensional Euclidean space (JAPANESE)
[ 講演概要 ]
We prove that the Chern class of a closed contact manifold is an
obstruction for codimension two contact embeddings in the odd
dimensional Euclidean space.
By Gromov's h-principle,
for any closed contact $3$-manifold with trivial first Chern class,
there is a contact structure on $\\mathbb{R}^5$ which admits a contact
embedding.
We prove that the Chern class of a closed contact manifold is an
obstruction for codimension two contact embeddings in the odd
dimensional Euclidean space.
By Gromov's h-principle,
for any closed contact $3$-manifold with trivial first Chern class,
there is a contact structure on $\\mathbb{R}^5$ which admits a contact
embedding.
2014年01月21日(火)
17:30-18:30 数理科学研究科棟(駒場) 056号室
李 暁龍 氏 (東京大学大学院数理科学研究科)
ホモクリニック類における弱固有値:小さい角度を持つサドルからの摂動 (ENGLISH)
李 暁龍 氏 (東京大学大学院数理科学研究科)
ホモクリニック類における弱固有値:小さい角度を持つサドルからの摂動 (ENGLISH)
[ 講演概要 ]
For 3-dimensional homoclinic classes of saddles with index 2, a
new sufficient condition for creating weak contracting eigenvalues is
provided. Our perturbation makes use of small angles between stable and
unstable subspaces of saddles. In particular, by recovering the unstable
eigenvector, we can designate that the newly created weak eigenvalue is
contracting. As applications, we obtain C^1-generic non-trivial index-
intervals of homoclinic classes and the C^1-approximation of robust
heterodimensional cycles. In particular, this sufficient condition is
satisfied by a substantial class of saddles with homoclinic tangencies.
For 3-dimensional homoclinic classes of saddles with index 2, a
new sufficient condition for creating weak contracting eigenvalues is
provided. Our perturbation makes use of small angles between stable and
unstable subspaces of saddles. In particular, by recovering the unstable
eigenvector, we can designate that the newly created weak eigenvalue is
contracting. As applications, we obtain C^1-generic non-trivial index-
intervals of homoclinic classes and the C^1-approximation of robust
heterodimensional cycles. In particular, this sufficient condition is
satisfied by a substantial class of saddles with homoclinic tangencies.
2014年01月14日(火)
17:00-18:00 数理科学研究科棟(駒場) 056号室
Tea: 16:30 - 17:00 コモンルーム
Rinat Kashaev 氏 (University of Geneva)
State-integral partition functions on shaped triangulations (ENGLISH)
Tea: 16:30 - 17:00 コモンルーム
Rinat Kashaev 氏 (University of Geneva)
State-integral partition functions on shaped triangulations (ENGLISH)
[ 講演概要 ]
Quantum Teichm\\"uller theory can be promoted to a
generalized TQFT within the combinatorial framework of shaped
triangulations with the tetrahedral weight functions given in
terms of the Weil-Gelfand-Zak transformation of Faddeev.FN"s
quantum dilogarithm. By using simple examples, I will
illustrate the connection of this theory with the hyperbolic
geometry in three dimensions.
Quantum Teichm\\"uller theory can be promoted to a
generalized TQFT within the combinatorial framework of shaped
triangulations with the tetrahedral weight functions given in
terms of the Weil-Gelfand-Zak transformation of Faddeev.FN"s
quantum dilogarithm. By using simple examples, I will
illustrate the connection of this theory with the hyperbolic
geometry in three dimensions.
2013年12月24日(火)
16:30-18:00 数理科学研究科棟(駒場) 056号室
Tea: 16:00 - 16:30 コモンルーム
Tirasan Khandhawit 氏 (Kavli IPMU)
Stable homotopy type for monopole Floer homology (ENGLISH)
Tea: 16:00 - 16:30 コモンルーム
Tirasan Khandhawit 氏 (Kavli IPMU)
Stable homotopy type for monopole Floer homology (ENGLISH)
[ 講演概要 ]
In this talk, I will try to give an overview of the
construction of stable homotopy type for monopole Floer homology. The
construction associates a stable homotopy object to 3-manifolds, which
will recover the Floer groups by appropriate homology theory. The main
ingredients are finite dimensional approximation technique and Conley
index theory. In addition, I will demonstrate construction for certain
3-manifolds such as the 3-torus.
In this talk, I will try to give an overview of the
construction of stable homotopy type for monopole Floer homology. The
construction associates a stable homotopy object to 3-manifolds, which
will recover the Floer groups by appropriate homology theory. The main
ingredients are finite dimensional approximation technique and Conley
index theory. In addition, I will demonstrate construction for certain
3-manifolds such as the 3-torus.
2013年12月17日(火)
16:30-18:00 数理科学研究科棟(駒場) 056号室
Tea: 16:00 - 16:30 コモンルーム
中村 伊南沙 氏 (東京大学大学院数理科学研究科)
Satellites of an oriented surface link and their local moves (JAPANESE)
Tea: 16:00 - 16:30 コモンルーム
中村 伊南沙 氏 (東京大学大学院数理科学研究科)
Satellites of an oriented surface link and their local moves (JAPANESE)
[ 講演概要 ]
For an oriented surface link $F$ in $\\mathbb{R}^4$,
we consider a satellite construction of a surface link, called a
2-dimensional braid over $F$, which is in the form of a covering over
$F$. We introduce the notion of an $m$-chart on a surface diagram
$p(F)\\subset \\mathbb{R}^3$ of $F$, which is a finite graph on $p(F)$
satisfying certain conditions and is an extended notion of an
$m$-chart on a 2-disk presenting a surface braid.
A 2-dimensional braid over $F$ is presented by an $m$-chart on $p(F)$.
It is known that two surface links are equivalent if and only if their
surface diagrams are related by a finite sequence of ambient isotopies
of $\\mathbb{R}^3$ and local moves called Roseman moves.
We show that Roseman moves for surface diagrams with $m$-charts can be
well-defined. Further, we give some applications.
For an oriented surface link $F$ in $\\mathbb{R}^4$,
we consider a satellite construction of a surface link, called a
2-dimensional braid over $F$, which is in the form of a covering over
$F$. We introduce the notion of an $m$-chart on a surface diagram
$p(F)\\subset \\mathbb{R}^3$ of $F$, which is a finite graph on $p(F)$
satisfying certain conditions and is an extended notion of an
$m$-chart on a 2-disk presenting a surface braid.
A 2-dimensional braid over $F$ is presented by an $m$-chart on $p(F)$.
It is known that two surface links are equivalent if and only if their
surface diagrams are related by a finite sequence of ambient isotopies
of $\\mathbb{R}^3$ and local moves called Roseman moves.
We show that Roseman moves for surface diagrams with $m$-charts can be
well-defined. Further, we give some applications.
2013年12月10日(火)
16:30-18:00 数理科学研究科棟(駒場) 056号室
Tea: 16:00 - 16:30 コモンルーム
丹下 基生 氏 (筑波大学)
Corks, plugs, and local moves of 4-manifolds. (JAPANESE)
Tea: 16:00 - 16:30 コモンルーム
丹下 基生 氏 (筑波大学)
Corks, plugs, and local moves of 4-manifolds. (JAPANESE)
[ 講演概要 ]
Akbulut and Yasui defined cork, and plug
to produce many exotic pairs.
In this talk, we introduce a plug
with respect to Fintushel-Stern's knot surgery
or more 4-dimensional local moves and
and argue by using Heegaard Fleor theory.
Akbulut and Yasui defined cork, and plug
to produce many exotic pairs.
In this talk, we introduce a plug
with respect to Fintushel-Stern's knot surgery
or more 4-dimensional local moves and
and argue by using Heegaard Fleor theory.
2013年12月03日(火)
17:00-18:00 数理科学研究科棟(駒場) 056号室
Tea: 16:30 - 17:00 コモンルーム
Bruno Martelli 氏 (Univ. di Pisa)
Hyperbolic four-manifolds with one cusp (cancelled) (JAPANESE)
Tea: 16:30 - 17:00 コモンルーム
Bruno Martelli 氏 (Univ. di Pisa)
Hyperbolic four-manifolds with one cusp (cancelled) (JAPANESE)
[ 講演概要 ]
(joint work with A. Kolpakov)
We introduce a simple algorithm which transforms every
four-dimensional cubulation into a cusped finite-volume hyperbolic
four-manifold. Combinatorially distinct cubulations give rise to
topologically distinct manifolds. Using this algorithm we construct
the first examples of finite-volume hyperbolic four-manifolds with one
cusp. More generally, we show that the number of k-cusped hyperbolic
four-manifolds with volume smaller than V grows like C^{V log V} for
any fixed k. As a corollary, we deduce that the 3-torus bounds
geometrically a hyperbolic manifold.
(joint work with A. Kolpakov)
We introduce a simple algorithm which transforms every
four-dimensional cubulation into a cusped finite-volume hyperbolic
four-manifold. Combinatorially distinct cubulations give rise to
topologically distinct manifolds. Using this algorithm we construct
the first examples of finite-volume hyperbolic four-manifolds with one
cusp. More generally, we show that the number of k-cusped hyperbolic
four-manifolds with volume smaller than V grows like C^{V log V} for
any fixed k. As a corollary, we deduce that the 3-torus bounds
geometrically a hyperbolic manifold.
2013年11月26日(火)
16:30-18:00 数理科学研究科棟(駒場) 056号室
Tea: 16:00 - 16:30 コモンルーム
徳永 浩雄 氏 (首都大学東京)
有理楕円曲面とあるline-conic arrangements (JAPANESE)
Tea: 16:00 - 16:30 コモンルーム
徳永 浩雄 氏 (首都大学東京)
有理楕円曲面とあるline-conic arrangements (JAPANESE)
[ 講演概要 ]
Sは有理楕円曲面とする.Sの生成ファイバーは
1変数有理函数体上の楕円曲線であり,楕円曲線の
群構造を利用してSの切断C_1からS上の曲線
C_2を構成することできる.本講演では,このアイ
デアに基づいて得られるある7次のline-conic
arrangementsについて解説する.
Sは有理楕円曲面とする.Sの生成ファイバーは
1変数有理函数体上の楕円曲線であり,楕円曲線の
群構造を利用してSの切断C_1からS上の曲線
C_2を構成することできる.本講演では,このアイ
デアに基づいて得られるある7次のline-conic
arrangementsについて解説する.
2013年11月19日(火)
16:30-18:00 数理科学研究科棟(駒場) 056号室
Tea: 16:00 - 16:30 コモンルーム
児玉 大樹 氏 (東京大学大学院数理科学研究科)
測度論的基本領域を持つ円周上の極小微分同相写像 (JAPANESE)
Tea: 16:00 - 16:30 コモンルーム
児玉 大樹 氏 (東京大学大学院数理科学研究科)
測度論的基本領域を持つ円周上の極小微分同相写像 (JAPANESE)
[ 講演概要 ]
任意の無理数αに対して、ルベーグ測度について基本領域を持つ
円周上の極小微分同相写像で回転数がαとなるものを構成した。
これは松元重則氏(日本大学)との共同研究である。
任意の無理数αに対して、ルベーグ測度について基本領域を持つ
円周上の極小微分同相写像で回転数がαとなるものを構成した。
これは松元重則氏(日本大学)との共同研究である。
2013年11月12日(火)
16:30-18:00 数理科学研究科棟(駒場) 056号室
Tea: 16:00 - 16:30 コモンルーム
Alexander Voronov 氏 (University of Minnesota)
The Batalin-Vilkovisky Formalism and Cohomology of Moduli Spaces (ENGLISH)
Tea: 16:00 - 16:30 コモンルーム
Alexander Voronov 氏 (University of Minnesota)
The Batalin-Vilkovisky Formalism and Cohomology of Moduli Spaces (ENGLISH)
[ 講演概要 ]
We use the Batalin-Vilkovisky formalism to give a new proof of Costello's theorem on the existence and uniqueness of solution to the Quantum Master Equation. We also make a physically motivated conjecture on the rational homology of moduli spaces. This is a joint work with Domenico D'Alessandro.
We use the Batalin-Vilkovisky formalism to give a new proof of Costello's theorem on the existence and uniqueness of solution to the Quantum Master Equation. We also make a physically motivated conjecture on the rational homology of moduli spaces. This is a joint work with Domenico D'Alessandro.
2013年11月05日(火)
16:30-18:00 数理科学研究科棟(駒場) 123号室
Tea: 16:00 - 16:30 コモンルーム
Carlos Moraga Ferrandiz 氏 (東京大学大学院数理科学研究科, 日本学術振興会)
The isotopy problem of non-singular closed 1-forms. (ENGLISH)
Tea: 16:00 - 16:30 コモンルーム
Carlos Moraga Ferrandiz 氏 (東京大学大学院数理科学研究科, 日本学術振興会)
The isotopy problem of non-singular closed 1-forms. (ENGLISH)
[ 講演概要 ]
Given alpha_0, alpha_1 two cohomologous non-singular closed 1-forms of a compact manifold M, are they always isotopic? We expect a negative answer to this question, at least in high dimensions by the work of Laudenbach, as well as an obstruction living in the algebraic K-theory of the Novikov ring associated to the underlying cohomology class.
A similar problem for functions N x [0,1] --> [0,1] without critical points was treated by Hatcher and Wagoner in the 70s.
The first goal of this talk is to explain how we can carry a part of the strategy of Hatcher and Wagoner into the context of closed 1-forms and to indicate the main difficulties that appear by doing so. The second goal is to show the techniques to treat this difficulties and the progress in defining the expected obstruction.
Given alpha_0, alpha_1 two cohomologous non-singular closed 1-forms of a compact manifold M, are they always isotopic? We expect a negative answer to this question, at least in high dimensions by the work of Laudenbach, as well as an obstruction living in the algebraic K-theory of the Novikov ring associated to the underlying cohomology class.
A similar problem for functions N x [0,1] --> [0,1] without critical points was treated by Hatcher and Wagoner in the 70s.
The first goal of this talk is to explain how we can carry a part of the strategy of Hatcher and Wagoner into the context of closed 1-forms and to indicate the main difficulties that appear by doing so. The second goal is to show the techniques to treat this difficulties and the progress in defining the expected obstruction.
2013年10月29日(火)
16:30-18:00 数理科学研究科棟(駒場) 056号室
Tea: 16:00 - 16:30 コモンルーム
Daniel Matei 氏 (IMAR, Bucharest)
Fundamental groups of algebraic varieties (ENGLISH)
Tea: 16:00 - 16:30 コモンルーム
Daniel Matei 氏 (IMAR, Bucharest)
Fundamental groups of algebraic varieties (ENGLISH)
[ 講演概要 ]
We discuss restrictions imposed by the complex
structure on fundamental groups of quasi-projective
algebraic varieties with mild singularities.
We investigate quasi-projectivity of various geometric
classes of finitely presented groups.
We discuss restrictions imposed by the complex
structure on fundamental groups of quasi-projective
algebraic varieties with mild singularities.
We investigate quasi-projectivity of various geometric
classes of finitely presented groups.
2013年10月22日(火)
16:30-18:00 数理科学研究科棟(駒場) 056号室
Tea: 16:00 - 16:30 コモンルーム
井上 玲 氏 (千葉大学)
Cluster algebra and complex volume of knots (JAPANESE)
Tea: 16:00 - 16:30 コモンルーム
井上 玲 氏 (千葉大学)
Cluster algebra and complex volume of knots (JAPANESE)
[ 講演概要 ]
The cluster algebra was introduced by Fomin and Zelevinsky around
2000. The characteristic operation in the algebra called `mutation' is
related to various notions in mathematics and mathematical physics. In
this talk I review a basics of the cluster algebra, and introduce its
application to study the complex volume of knot complements in S^3.
Here a mutation corresponds to an ideal tetrahedron.
This talk is based on joint work with Kazuhiro Hikami (Kyushu University).
The cluster algebra was introduced by Fomin and Zelevinsky around
2000. The characteristic operation in the algebra called `mutation' is
related to various notions in mathematics and mathematical physics. In
this talk I review a basics of the cluster algebra, and introduce its
application to study the complex volume of knot complements in S^3.
Here a mutation corresponds to an ideal tetrahedron.
This talk is based on joint work with Kazuhiro Hikami (Kyushu University).
