Tuesday Seminar on Topology

Seminar information archive ~03/28Next seminarFuture seminars 03/29~

Date, time & place Tuesday 17:00 - 18:30 056Room #056 (Graduate School of Math. Sci. Bldg.)
Organizer(s) KAWAZUMI Nariya, KITAYAMA Takahiro, SAKASAI Takuya

Seminar information archive

2016/11/15

17:00-18:30   Room #056 (Graduate School of Math. Sci. Bldg.)
Takuya Sakasai (The University of Tokyo)
Cohomology of the moduli space of graphs and groups of homology cobordisms of surfaces (JAPANESE)
[ Abstract ]
We construct an abelian quotient of the symplectic derivation Lie algebra of the free Lie algebra generated by the fundamental representation of the symplectic group. It gives an alternative proof of the fact first shown by Bartholdi that the top rational homology group of the moduli space of metric graphs of rank 7 is one dimensional. As an application, we construct a non-trivial abelian quotient of the homology cobordism group of a surface of positive genus. This talk is based on joint works with Shigeyuki Morita, Masaaki Suzuki and Gwénaël Massuyeau.

2016/11/08

17:00-18:30   Room #056 (Graduate School of Math. Sci. Bldg.)
Toshiyuki Akita (Hokkaido University)
Second mod 2 homology of Artin groups (JAPANESE)
[ Abstract ]
After a brief survey on the K($\pi$,1) conjecture and homology of Artin groups, I will introduce our recent result: we determined second mod 2 homology of arbitrary Artin groups without assuming the K($\pi$,1)-conjecture. The key ingredients are Hopf's formula and a result of Howlett on Schur multipliers of Coxeter groups. This is a joint work with Ye Liu.

2016/11/01

17:00-18:30   Room #056 (Graduate School of Math. Sci. Bldg.)
Takahiro Oba (Tokyo Institute of Technology)
Higher-dimensional contact manifolds with infinitely many Stein fillings (JAPANESE)
[ Abstract ]
A Stein fillings of a given contact manifold is a Stein domain whose boundary is contactomorphic to the given contact manifold.
Open books, Lefschetz fibrations, and mapping class groups of their fibers in particular help us to produce various contact manifolds and their Stein fillings. However, little is known about mapping class groups of higher-dimensional manifolds. This is one of the reasons that it was unknown whether there is a contact manifold of dimension > 3 with infinitely many Stein fillings. In this talk, I will choose a certain symplectic manifold as fibers of open books and Lefschetz fibrations and by using them, construct an infinite family of higher-dimensional contact manifolds with infinitely many Stein fillings.

2016/10/18

17:30-18:30   Room #056 (Graduate School of Math. Sci. Bldg.)
Yoshitake Hashimoto (Tokyo City University)
Conformal field theory for extended W-algebras (JAPANESE)
[ Abstract ]
This talk is based on a joint work with A. Tsuchiya (Kavli IPMU) and T. Matsumoto (Nagoya Univ). In 2006 Feigin-Gainutdinov-Semikhatov-Tipunin introduced vertex operator algebras M called extended W-algebras. Tsuchiya-Wood developed representation theory of M by the method of
"infinitesimal deformation of parameter" and Jack symmetric polynomials.

In this talk I will discuss the following subjects:
1. "factorization" in conformal field theory,
2. tensor structure of the category of M-modules and "module-bimodule correspondence".

2016/10/11

17:00-18:30   Room #056 (Graduate School of Math. Sci. Bldg.)
Nariya Kawazumi (The University of Tokyo)
The Kashiwara-Vergne problem and the Goldman-Turaev Lie bialgebra in genus zero (JAPANESE)
[ Abstract ]
In view of results of Goldman and Turaev, the free vector space over the free loops on an oriented surface has a natural Lie bialgebra structure. The Goldman bracket has a formal description by using a special (or symplectic) expansion of the fundamental group of the surface. It is natural to ask for a formal description of the Turaev cobracket. We will show how to obtain a formal description of the Goldman-Turaev Lie bialgebra for genus 0 using a solution of the Kashiwara-Vergne problem. A similar description was recently obtained by Massuyeau using the Kontsevich integral. Moreover we propose a generalization of the Kashiwara-Vergne problem in the context of the Goldman-Turaev Lie bialgebra. This talk is based on a joint work with A. Alekseev, Y. Kuno and F. Naef.

2016/09/27

17:00-18:30   Room #056 (Graduate School of Math. Sci. Bldg.)
Shouta Tounai (The University of Tokyo)
CAT(0) properties for orthoscheme complexes (JAPANESE)
[ Abstract ]
Gromov showed that a cubical complex is locally CAT(0) if and only if the link of every vertex is a flag complex. Brady and MacCammond introduced an orthoscheme complex as a generalization of cubical complexes. It is, however, difficult to tell whether an orthoscheme complex is (locally) CAT(0) or not. In this talk, I will discuss a translation of Gromov's characterization for orthoscheme complexes. As a generalization of Gromov's characterization, I will show that the orthoscheme complex of locally distributive semilattice is CAT(0) if and only if it is a flag semilattice.

2016/07/19

17:00-18:30   Room #056 (Graduate School of Math. Sci. Bldg.)
Yohsuke Watanabe (University of Hawaii)
The geometry of the curve graphs and beyond (JAPANESE)
[ Abstract ]
The curve graphs are locally infinite. However, by using Masur-Minsky's tight geodesics, one could view them as locally finite graphs. Bell-Fujiwara used a special property of tight geodesics and showed that the asymptotic dimension of the curve graphs is finite. In this talk, I will introduce a new class of geodesics which also has the property. If time permits, I will explain how such geodesics can be adapted in Out(F_n) setting.

2016/07/12

17:00-18:30   Room #056 (Graduate School of Math. Sci. Bldg.)
John Parker (Durham University)
Non-arithmetic lattices (ENGLISH)
[ Abstract ]
In this talk I will discuss arithmetic and non-arithmetic lattices and I will give a history of the problem of finding non-arithmetic lattices. I will also briefly describe the construction of new non-arithmetic lattices in SU(2,1) found in my joint workwith Martin Deraux and Julien Paupert.

2016/06/28

17:00-18:30   Room #056 (Graduate School of Math. Sci. Bldg.)
Masato Mimura (Tohoku University)
Strong algebraization of fixed point properties (JAPANESE)
[ Abstract ]
Concerning proofs of fixed point properties, we succeed in removing all forms of "bounded generation" assumptions from previous celebrated strategy of "algebraization" by Y. Shalom ([Publ. IHES, 1999] and [ICM proceedings, 2006]). Our condition is stated as the existence of winning strategies for a certain "Game."

2016/06/21

17:00-18:30   Room #056 (Graduate School of Math. Sci. Bldg.)
Noboru Ito (The University of Tokyo)
Spaces of chord diagrams of spherical curves (JAPANESE)
[ Abstract ]
In this talk, the speaker introduces a framework to obtain (possibly infinitely many) new topological invariants of spherical curves under local homotopy moves (several types of Reidemeister moves). They are defined by chord diagrams, each of which is a configurations of even paired points on a circle. We see that these invariants have useful properties.

2016/06/14

17:00-18:30   Room #056 (Graduate School of Math. Sci. Bldg.)
Naohiko Kasuya (Aoyama Gakuin University)
Non-Kähler complex structures on R^4 (JAPANESE)
[ Abstract ]
We consider the following problem. "Is there any non-Kähler complex structure on R^{2n}?" If n=1, the answer is clearly negative. On the other hand, Calabi and Eckmann constructed non-Kähler complex structures on R^{2n} for n ≥ 3. In this talk, I will construct uncountably many non-Kähler complex structures on R^4, and give the affirmative answer to the case where n=2. For the construction, it is important to understand the genus-one achiral Lefschetz fibration S^4 → S^2 found by Yukio Matsumoto and Kenji Fukaya. This is a joint work with Antonio Jose Di Scala and Daniele Zuddas.

2016/06/07

17:00-18:30   Room #056 (Graduate School of Math. Sci. Bldg.)
Kenta Hayano (Keio University)
Topology of holomorphic Lefschetz pencils on the four-torus (JAPANESE)
[ Abstract ]
In this talk, we will show that two holomorphic Lefschetz pencils on the four-torus are (smoothly) isomorphic if they have the same genus and divisibility. The proof relies on the theory of moduli spaces of polarized abelian surfaces. We will also give vanishing cycles of some holomorphic pencils of the four-torus explicitly. This is joint work with Noriyuki Hamada (The University of Tokyo).

2016/05/31

17:00-18:30   Room #056 (Graduate School of Math. Sci. Bldg.)
Benoît Guerville-Ballé (Tokyo Gakugei University)
A linking invariant for algebraic curves (ENGLISH)
[ Abstract ]
We construct a topological invariant of algebraic plane curves, which is in some sense an adaptation of the linking number of knot theory. As an application, we show that this invariant distinguishes a new Zariski pair of curves (ie a pair of curves having same combinatorics, yet different topology).

2016/05/24

17:00-18:30   Room #056 (Graduate School of Math. Sci. Bldg.)
Kokoro Tanaka (Tokyo Gakugei University)
Independence of Roseman moves for surface-knot diagrams (JAPANESE)
[ Abstract ]
Roseman moves are seven types of local modifications for surface-knot diagrams in 3-space which generate ambient isotopies of surface-knots in 4-space. In this talk, I will discuss independence among the seven Roseman moves. In particular, I will focus on Roseman moves involving triple points and on those involving branch points. The former is joint work with Kanako Oshiro (Sophia University) and Kengo Kawamura (Osaka City University), and the latter is joint work with Masamichi Takase (Seikei University).

2016/05/17

17:00-18:30   Room #056 (Graduate School of Math. Sci. Bldg.)
Hidetoshi Masai (The University of Tokyo)
Some dynamics of random walks on the mapping class groups (JAPANESE)
[ Abstract ]
The dynamics of random walks on the mapping class groups on closed surfaces of genus >1 will be discussed. We define the topological entropy of random walks. Then we prove that the drift with respect to Thurston or Teichmüller metrics and the Lyapunov exponent all coincide with the topological entropy. This is a "random version" of pseudo-Anosov dynamics observed by Thurston and I will begin this talk by recalling the work of Thurston.

2016/05/10

17:00-18:30   Room #056 (Graduate School of Math. Sci. Bldg.)
Yuka Kotorii (The University of Tokyo)
On Milnor's link-homotopy invariants for handlebody-links (JAPANESE)
[ Abstract ]
A handlebody-link is a disjoint union of handlebodies embedded in $S^3$ and HL-homotopy is an equivalence relation on handlebody-links generated by self-crossing changes. A. Mizusawa and R. Nikkuni classified the set of HL-homotopy classes of 2-component handlebody-links completely using the linking numbers for handlebody-links. In this talk, by using Milnor's link-homotopy invariants, we construct an invariant for handlebody-links and give a bijection between the set of HL-homotopy classes of n-component handlebody-links with some assumption and a quotient of the action of the general linear group on a tensor product of modules. This is joint work with Atsuhiko Mizusawa at Waseda University.

2016/04/26

17:00-18:30   Room #056 (Graduate School of Math. Sci. Bldg.)
Jun Ueki (The University of Tokyo)
Arithmetic topology on branched covers of 3-manifolds (JAPANESE)
[ Abstract ]
The analogy between 3-dimensional topology and number theory was first pointed out by Mazur in the 1960s, and it has been studied systematically by Kapranov, Reznikov, Morishita, and others. In their analogies, for example, knots and 3-manifolds correspond to primes and number rings respectively. The study of these analogies is called arithmetic topology now.
In my talk, based on their dictionary of analogies, we study analogues of idelic class field theory, Iwasawa theory, and Galois deformation theory in the context of 3-dimensional topology, and establish various foundational analogies in arithmetic topology.

2016/04/19

17:00-18:30   Room #056 (Graduate School of Math. Sci. Bldg.)
Błażej Szepietowski (Gdansk University)
Topological rigidity of finite cyclic group actions on compact surfaces (ENGLISH)
[ Abstract ]
Two actions of a group on a surface are called topologically equivalent if they are conjugate by a homeomorphism of the surface. I will describe a method of enumeration (and classification) of topological equivalence classes of actions of a finite group on a compact surface, based on the combinatorial theory of noneuclidean crystallographic groups (NEC groups in short) and a relationship between the outer automorphism group of an NEC group and certain mapping class group. By this method we study topological equivalence of actions of a finite cyclic group on a compact surface, in the situation where the order of the group is large relative to the genus of the surface.

2016/04/12

17:00-18:30   Room #056 (Graduate School of Math. Sci. Bldg.)
Aniceto Murillo (Universidad de Malaga)
Homotopy theory of differential graded Lie algebras (ENGLISH)
[ Abstract ]
Having as motivation the Deligne's principle by which every deformation functor is governed by a differential graded Lie algebra, we build a homotopy theory for these algebras which extend the classical Quillen approach and let us model any (non necessarily 1-connected nor path connected) complex. This is joint work with Urtzi Buijs, Yves Félix and Daniel Tanré.

2016/04/05

17:00-18:30   Room #056 (Graduate School of Math. Sci. Bldg.)
Takahiro Kitayama (The University of Tokyo)
Torsion invariants and representation varieties for non-positively curved cube complexes (JAPANESE)
[ Abstract ]
Applications of torsion invariants and representation varieties have been extensively studied for 3-manifolds. Twisted Alexander polynomials are known to detect the Thurston norm and fiberedness of a 3-manifold. Ideal points of character varieties are known to detect essential surfaces in a 3-manifold in a certain extension of Culler-Shalen theory. In view of cubulation of 3-manifolds one can expect that these results naturally extend to a wider framework and, in particular, the case of virtually special cube complexes. We formulate and discuss such analogous questions for non-positively curved cube complexes.

2016/02/16

17:00-18:30   Room #056 (Graduate School of Math. Sci. Bldg.)
Luc Menichi (University of Angers)
String Topology, Euler Class and TNCZ free loop fibrations (ENGLISH)
[ Abstract ]
Let $M$ be a connected, closed oriented manifold.
Chas and Sullivan have defined a loop product and a loop coproduct on
$H_*(LM;¥mathbb{F})$, the homology of the
free loops on $M$ with coefficients in the field $¥mathbb{F}$.
By studying this loop coproduct, I will show that if the free loop
fibration
$¥Omega M¥buildrel{i}¥over¥hookrightarrow
LM¥buildrel{ev}¥over¥twoheadrightarrow M$
is homologically trivial, i.e. $i^*:H^*(LM;¥mathbb{F})¥twoheadrightarrow
H^*(¥Omega M;¥mathbb{F})$ is onto,
then the Euler characteristic of $M$ is divisible by the characteristic
of the field $¥mathbb{F}$
(or $M$ is a point).

2016/01/19

15:00-16:00   Room #056 (Graduate School of Math. Sci. Bldg.)
Hikaru Yamamoto (The University of Tokyo)
Ricci-mean curvature flows in gradient shrinking Ricci solitons (JAPANESE)
[ Abstract ]
A Ricci-mean curvature flow is a coupled parabolic PDE system of a mean
curvature flow and a Ricci flow.
In this talk, we consider a Ricci-mean curvature flow in a gradient
shrinking Ricci soliton, and give a generalization of a well-known result
of Huisken which states that if a mean curvature flow in a Euclidean space
develops a singularity of type I, then its parabolic rescaling near the singular
point converges to a self-shrinker.

2016/01/12

16:30-18:30   Room #056 (Graduate School of Math. Sci. Bldg.)
Morimichi Kawasaki (The University of Tokyo) 16:30-17:30
Heavy subsets and non-contractible trajectories (JAPANESE)
[ Abstract ]
For a compact set Y of an open symplectic manifold $(N,¥omega)$ and a free
homotopy class $¥alpha¥in [S^1,N]$, Biran, Polterovich and Salamon
defined the relative symplectic capacity $C_{BPS}(N,Y;¥alpha)$ which
measures the existence of non-contractible 1-periodic trajectories of
Hamiltonian isotopies.

On the hand, Entov and Polterovich defined heaviness for closed subsets
of a symplectic manifold by using spectral invarinats of the Hamiltonian
Floer theory on contractible trajectories.
Heavy subsets are known to be non-displaceable.

In this talk, we prove the finiteness of $C(M,X,¥alpha)$ (i.e. the
existence of non-contractible 1-periodic trajectories under some setting)
by using heaviness.
Ryo Furukawa (The University of Tokyo) 17:30-18:30
On codimension two contact embeddings in the standard spheres (JAPANESE)
[ Abstract ]
In this talk we consider codimension two contact
embedding problem by using higher dimensional braids.
First, we focus on embeddings of contact $3$-manifolds to the standard $
S^5$ and give some results, for example, any contact structure on $S^3$
can embed so that it is smoothly isotopic to the standard embedding.
These are joint work with John Etnyre. Second, we consider the relative
Euler number of codimension two contact submanifolds and its Seifert
hypersurfaces which is a generalization of the self-linking number of
transverse knots in contact $3$-manifolds. We give a way to calculate
the relative Euler number of certain contact submanifolds obtained by
braids and as an application we give examples of embeddings of one
contact manifold which are isotopic as smooth embeddings but not
isotopic as contact embeddings in higher dimension.

2015/12/15

17:00-18:30   Room #056 (Graduate School of Math. Sci. Bldg.)
Constantin Teleman (University of California, Berkeley)
The Curved Cartan Complex (ENGLISH)
[ Abstract ]
The Cartan model computes the equivariant cohomology of a smooth manifold X with
differentiable action of a compact Lie group G, from the invariant polynomial
functions on the Lie algebra with values in differential forms and a deformation
of the de Rham differential. Before extracting invariants, the Cartan differential
does not square to zero and is apparently meaningless. Unrecognised was the fact
that the full complex is a curved algebra, computing the quotient by G of the
algebra of differential forms on X. This generates, for example, a gauged version of
string topology. Another instance of the construction, applied to deformation
quantisation of symplectic manifolds, gives the BRST construction of the symplectic
quotient. Finally, the theory for a X point with an additional quadratic curving
computes the representation category of the compact group G, and this generalises
to the loop group of G and even to real semi-simple groups.

2015/12/08

17:00-18:30   Room #056 (Graduate School of Math. Sci. Bldg.)
Yuichi Yamada (The Univ. of Electro-Comm.)
Lens space surgery and Kirby calculus of 4-manifolds (JAPANESE)
[ Abstract ]
The problem asking "Which knot yields a lens space by Dehn surgery" is
called "lens space surgery". Berge's list ('90) is believed to be the
complete list, but it is still unproved, even after some progress by
Heegaard Floer Homology.
This problem seems to enter a new aspect: study using 4-manifolds, lens
space surgery from lens spaces, checking hyperbolicity by computer.

In the talk, we review the structure of Berge's list and talk on our
study on pairs of distinct knots but yield same lens spaces, and
4-maniolds constructed from such pairs. This is joint work with Motoo
Tange (Tsukuba University).

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