[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 May 14, 2012
世話係
河野俊丈
河澄響矢
4月10日 -- 056号室, 16:30 -- 18:00
逆井 卓也 (東京大学大学院数理科学研究科)
On homology of symplectic derivation Lie algebras of
the free associative algebra and the free Lie algebra
Abstract:
We discuss homology of symplectic derivation Lie algebras of
the free associative algebra and the free Lie algebra
with particular stress on their abelianizations (degree 1 part).
Then, by using a theorem of Kontsevich,
we give some applications to rational cohomology of the moduli spaces of
Riemann surfaces and metric graphs.
This is a joint work with Shigeyuki Morita and Masaaki Suzuki.
4月17日 -- 056号室, 16:30 -- 18:00
Eriko Hironaka (Florida State University)
Pseudo-Anosov mapping classes with small dilatation
Abstract:
A mapping class is a homeomorphism of an oriented surface
to itself modulo isotopy. It is pseudo-Anosov if the lengths of essential
simple closed curves under iterations of the map have exponential growth
rate. The growth rate, an algebraic integer of degree bounded with
respect to the topology of the surface, is called the dilatation of the
mapping class. In this talk we will discuss the minimization problem
for dilatations of pseudo-Anosov mapping classes, and give two general
constructions of pseudo-Anosov mapping classes with small dilatation.
4月24日 -- 056号室, 16:30 -- 18:00
Dylan Thurston (Columbia University)
Combinatorial Heegaard Floer homology
Abstract:
Heegaard Floer homology is a powerful invariant of 3- and 4-manifolds.
In 4 dimensions, Heegaard Floer homology (together with the
Seiberg-Witten and Donaldson equations, which are conjecturally
equivalent), provides essentially the only technique for
distinguishing smooth 4-manifolds. In 3 dimensions, it provides much
geometric information, like the simplest representatives of a given
homology class.
In this talk we will focus on recent progress in making Heegaard Floer
homology more computable, including a complete algorithm for computing
it for knots.
5月1日 -- 056号室, 16:30 -- 18:00
糟谷 久矢 (東京大学大学院数理科学研究科)
Minimal models, formality and hard Lefschetz property of
solvmanifolds with local systems
Abstract:
For a simply connected solvable Lie group G with a
cocompact discrete subgroup {\Gamma}, we consider the space of
differential forms on the solvmanifold G/{\Gamma} with values in certain
flat bundle so that this space has a structure of a differential graded
algebra(DGA). We construct Sullivan's minimal model of this DGA. This
result is an extension of Nomizu's theorem for ordinary coefficients in
the nilpotent case. By using this result, we refine Hasegawa's result of
formality of nilmanifolds and Benson-Gordon's result of hard Lefschetz
properties of nilmanifolds.
5月8日 -- 056号室, 16:30 -- 18:00
石部 正 (東京大学大学院数理科学研究科, 日本学術振興会)
Infinite examples of non-Garside monoids having fundamental elements
Abstract:
The Garside group, as a generalization of Artin groups,
is defined as the group of fractions of a Garside monoid.
To understand the elliptic Artin groups, which are the fundamental
groups of the complement of discriminant divisors of the semi-versal
deformation of the simply elliptic singularities E_6~, E_7~ and E_8~,
we need to consider another generalization of Artin groups.
In this talk, we will study the presentations of fundamental groups
of the complement of complexified real affine line arrangements
and consider the associated monoids.
It turns out that, in some cases, they are not Garside monoids.
Nevertheless, we will show that they satisfy the cancellation condition
and carry certain particular elements similar to the fundamental elements
in Artin monoids.
As a result, we will show that the word problem can be solved
and the center of them are determined.
5月22日 -- 056号室, 17:10 -- 18:10
入谷 寛 (京都大学)
Gamma Integral Structure in Gromov-Witten theory
Abstract:
The quantum cohomology of a symplectic
manifold undelies a certain integral local system
defined by the Gamma characteristic class.
This local system originates from the natural integral
local sysmem on the B-side under mirror symmetry.
In this talk, I will explain its relationships to the problem
of analytic continuation of Gromov-Witten theoy (potentials),
including crepant resolution conjecture, LG/CY correspondence,
modularity in higher genus theory.
5月29日 -- 056号室, 16:30 -- 18:00
中村 伊南沙 (学習院大学, 日本学術振興会)
Triple linking numbers and triple point numbers
of torus-covering $T^2$-links
Abstract:
The triple linking number of an oriented surface link was defined as an
analogical notion of the linking number of a classical link. A
torus-covering $T^2$-link $\mathcal{S}_m(a,b)$ is a surface link in the
form of an unbranched covering over the standard torus, determined from
two commutative $m$-braids $a$ and $b$.
In this talk, we consider $\mathcal{S}_m(a,b)$ when $a$, $b$ are pure
$m$-braids ($m \geq 3$), which is a surface link with $m$-components. We
present the triple linking number of $\mathcal{S}_m(a,b)$ by using the
linking numbers of the closures of $a$ and $b$. This gives a lower bound
of the triple point number. In some cases, we can determine the triple
point numbers, each of which is a multiple of four.
6月5日 -- 056号室, 16:30 -- 18:00
久野 雄介 (津田塾大学)
A generalization of Dehn twists
Abstract:
We introduce a generalization
of Dehn twists for loops which are not
necessarily simple loops on an oriented surface.
Our generalization is an element of a certain
enlargement of the mapping class group of the surface.
A natural question is whether a generalized Dehn twist is
in the mapping class group. We show some results related to this question.
This talk is partially based on a joint work
with Nariya Kawazumi (Univ. Tokyo).
6月12日 -- 056号室, 16:30 -- 18:00
野坂 武史 (京都大学 数理解析研究所, 日本学術振興会)
Topological interpretation of the quandle cocycle invariants of links
Abstract:
Carter et al. introduced many quandle cocycle invariants
combinatorially constructed from link-diagrams. For connected quandles of
finite order, we give a topological meaning of the invariants, without
some torsion parts. Precisely, this invariant equals a sum of "knot
colouring polynomial" and of a Z-equivariant part of the Dijkgraaf-Witten
invariant. Moreover, our approach involves applications to compute "good"
torsion subgroups of the 3-rd quandle homologies and the 2-nd homotopy
groups of rack spaces.
7月17日 -- 056号室, 16:30 -- 18:00
岡 睦雄 (東京理科大学)
Contact structure of mixed links
Abstract:
A strongly non-degenerate mixed function has a Milnor open book
structures on a sufficiently small sphere. We introduce the notion of
a holomorphic-like mixed function
and we will show that a link defined by such a mixed function has a
canonical contact structure.
Then we will show that this contact structure for a certain
holomorphic-like mixed function
is carried by the Milnor open book.
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