Tuesday Seminar on Topology (October, 2012 -- March, 2013)
[Japanese]
[Past Programs]
16:30 -- 18:00 Graduate School of Mathematical Sciences,
The University of Tokyo
Tea: 16:00 -- 16:30 Common Room
Last updated March 1, 2013
Information :@
Toshitake Kohno
Nariya Kawazumi
October 2 -- Room 056, 16:30 -- 18:00
Akito Futaki (The University of Tokyo)
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.
October 9 -- Room 056, 16:30 -- 18:00
Michihiko Fujii (Kyoto University)
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.
October 16 -- Room 056, 17:10 -- 18:10
Ken-Ichi Yoshikawa (Kyoto University)
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.
October 23 -- Room 056, 16:30 -- 18:00
Nariya Kawazumi (The University of Tokyo)
A geometric approach to the Johnson homomorphisms
Abstract:
We re-construct the Johnson homomorphisms as an embeddig of the Torelli
group
into the completed Goldman-Turaev Lie bialgebra. Then the image is
included in the
kernel of the Turaev cobracket. In the case where the boundary is
connected,
the Turaev cobracket clarifies a geometric meaning of the Morita traces.
Time permitting, we also discuss the case of holed discs.
This talk is based on a joint work with Yusuke Kuno (Tsuda College).
October 30 -- Room 126, 16:30 -- 18:00
Koya Shimokawa (Saitama University)
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.
November 6 -- Room 056, 16:30 -- 18:00
Furusho Hidekazu (Nagoya University)
Galois action on knots
Abstract:
I will explain a motivic structure on knots.
Then I will explain that the absolute Galois group of
the rational number field acts non-trivially
on 'the space of knots' in a non-trivial way.
November 13 -- Room 056, 16:30 -- 18:00
Takahiro Kitayama (RIMS, Kyoto UniversityCJSPS 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).
November 20 -- Room 056, 16:30 -- 18:00
Kentaro Nagao (Nagoya University)
3 dimensional hyperbolic geometry and cluster algebras
Abstract:
The cluster algebra was discovered by Fomin-Zelevinsky in 2000.
Recently, the structures of cluster algebras are recovered in
many areas including the theory of quantum groups, low
dimensional topology, discrete integrable systems, Donaldson-Thomas
theory, and string theory and there is dynamic development in the
research on these subjects. In this talk I introduce a relation between
3 dimensional hyperbolic geometry and cluster algebras motivated
by some duality in string theory.
November 27 -- Room 056, 16:30 -- 18:00
Hiraku Nozawa (JSPS-IHES fellow)
On a finite aspect of characteristic classes of foliations
Abstract:
Characteristic classes of foliations are not bounded due to Thurston.
In this talk, we will explain finiteness of characteristic classes for
foliations with certain transverse structures (e.g. transverse
conformally flat structure) and its relation to unboundedness and
rigidity of foliations.
(This talk is based on a joint work with Jesús Antonio
Álvarez López at University of Santiago de Compostela,
which is available as arXiv:1205.3375.)
December 4 -- Room 056, 16:30 -- 18:00
Yoshitake Hashimoto (Tokyo City University)
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.
December 11 -- Room 056, 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.
January 21 (Monday) -- Room 002
16:30 -- 17:30
Naoki Kato (The University of Tokyo)
Lie foliations transversely modeled on nilpotent Lie
algebras
Abstract:
To each Lie $\mathfrak{g}$-foliation, there is an associated subalgebra
$\mathfrak{h}$ of $\mathfrak{g}$ with the foliation, which is called the
structure Lie algabra. In this talk, we will explain the inverse problem,
that is, which pair $(\mathfrak{g},\mathfrak{h})$ can be realized as a
Lie $\mathfrak{g}$-foliation with the structure Lie algabra $\mathfrak{h}
$, under the assumption that $\mathfrak{g}$ is nilpotent.
17:30 -- 18:30
Tomohiko Ishida (The University of Tokyo)
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.@
January 22 -- Room 056, 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.
February 19 -- Room 056, 16:30 -- 18:00
Eri Hatakenaka (Tokyo University of Agriculture and Technology)
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.
March 19 -- Room 002, 16:30 -- 18:00
Keiko Kawamuro (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).