# Studio Phones Seminar

Studio Phones Seminar continues as Kobe Studio Seminar from April 2013. Please refer to Kobe Studio Seminar for Mathematics.

## Schedule of talks and past topics:

### Past seminars

date:
2013/02/21 15:10 - 16:40
room:
A739
title:
Chinese Mathematics in Qin and Han periods
speaker:
Makoto Tamura(Osaka Sangyo University)
abstract:

Zhangjiashan Han bamboo book "Suanshu-shu" and Qin bamboo book "Shu" housed at Yuelu Academy are mathematical books in ancient China, whose texts and photographs were published several years ago.

Our procedure was to decipher again the letters from the photographs with the following investigation from mathematical and historical viewpoints. In this talk, the contents of two books will be introduced briefly and some issues will be compared with those of "The Nine Chapters on the Mathematical Art."

date:
2012/09/27 1600-1800
room:
A750
title:
Heegaard splitting of distance exactly $n$ for each non-negative integer $n$
speaker:
Tsuyoshi Kobayashi (Nara Women's University) (joint work with Ayako Ido and Yeonhee Jang)
abstract:

Hempel introduced the concept of distance of Heegaard splitting by using curve complex, and showed that there exist Heegaard splittings of closed orientable 3-manifolds with distance $>n$ for any integer $n$. In this talk, we construct pairs of curves with distance exactly $n$ for any integer $n$, and we show that there exist Heegaard splittings of 3-manifolds with distance exactly $n$.

date:
2012/07/16 1000-1100
room:
A739
title:
Dimensions of triangulated categories with respect to subcategories
speaker:
Tokuji Araya(Tokuyama College of Technology)
abstract:

We will introduce the concept of the dimension of a triangulated category with respect to a fixed full subcategory. For the bounded derived category of an abelian category, upper bounds of the dimension with respect to a contravariantly finite subcategory and a resolving subcategory are given. Our methods not only recover some known results on the dimensions of derived categories in the sense of Rouquier, but also apply to various commutative and non-commutative noetherian rings.

date:
2012/07/16 1110-1210
room:
A739
title:
Bar-Natan's cobordism category of Khovanov-Rozansky homology
speaker:
Yasuyoshi Yonezawa(Nagoya University)
abstract:

Khovanov defined a bi-graded link homology whose Euler characteristic is Jones polynomial. Subsequently, Bar-Natan defined a cobordism category associated to Khovanov homology and showed a chain complex of cobordisms is a link invariant up to homotopy equivalence. In this talk, I'll introduce a cobordism category associated to Khovanov-Rozansky homology (a triple graded homology whose Euler characteristic is a specialized HOMFLY polynomial). If I have a time, I'll explain a relation of the cobordism category, a homotopy category of matrix factorizations and a category of Soergel bimodules.

date:
2012/07/16 1320-1430
room:
A739
title:
Silting mutation in triangulated categories
speaker:
Osamu Iyama(Nagoya University)
abstract:

Silting objects appeared in work of Keller-Vossieck on quiver representations. Following I.-Aihara (JLMS 2012), Koenig-Yang (arXiv:1203.5657) and Adachi-I.-Reiten, I will explain mutation theory of silting objects in triangulated categories as well as their relationship with t-structures and co-t-structures.

date:
2012/07/16 1450-1600
room:
A739
title:
Selfinjective quivers with potentials and derived equivalences
speaker:
Yuya Mizuno(Nagoya University)
abstract:

It is known that there is only trivial tilting module over selfinjective algebra. Hence it is difficult to give a derived equivalent algebra explicitly for selfinjective algebra. In this talk, I will explain some connections between selfinjective quivers with potentials and derived equivalences, and provide a derived equivalence class algebras.

date:
2012/07/16 1620-1730
room:
A739
title:
Derived Categories and Stability Conditions in Arithmetic Geometry
speaker:
Hiroki Minamide(Kobe University)
abstract:

I will start with a survay of well known properties of derived categories in algebraic geometry and Bridgeland's stability conditions. I also explain a Huybrechts' excellent article (arXiv:1009.4371). If we have enough time, I shall refer to relations with structures of Chow groups and some categorical problems in arithmetic geometry.

date:
2012/06/12 1300-1500
room:
A752
title:
Top cell attaching map in 3-cell complex
speaker:
Toshiyuki Miyauchi(Fukuoka University)
abstract:

I. M. James introduce the characteristic of a CW-complex $S^q\cup e^n\cup e^{q+n}$. This is a relation between the homotopy class of the attaching map of $e^{q+n}$ and the ring structure of the singular cohomology. For a CW-complex $S^q\cup e^n\cup e^{q+n+k}$, we consider a relation between the homotopy class of the attaching map of $e^{q+n+k}$ and the ring structure of a generalized cohomology.

date:
2012/06/11 1300-1500
room:
B103
title:
Unstable homotopy group
speaker:
Toshiyuki Miyauchi(Fukuoka University)
abstract:

I will give a brief description of unstable homotopy groups of CW-complexes. Specially, for a CW-complex X and its subcomplex A, I will talk about methods of calculation of homotopy groups of X using by homotopy groups of A, relative homotopy groups of (X,A) and the CW-structure of the homotopy fiber of a pinching map A to a point in X.

articles and slides (license is CC-BY-NC):
Miyauchi20120611.pdf
date:
2012/06/06 1000-1200, 1400-1800
room:
A748
title:
Categoricity
speaker:
Kota Takeuchi (Tsukuba University)
abstract:

We first introduce logical structures and discuss basic properties. Then we prove that strongly minimal structures are uncountably categorical. Specific examples of this result are "Vector spaces with fixed base field are isomorphic if and only if they have the same dimension defined by the linear dependence." and "Algebraically closed fields with characteristic p are isomorphic if and only if they have the same dimension defined by the algebraic dependence." This fact is a very simple version of Morley's categoricity theorem which is one of the most important classical result in model theory.

date:
2012/05/16 1250-1400
room:
B103
title:
Local fields and its arithmetic Part 2.
speaker:
Kazuma Shimomoto(Kansai University)
abstract:

I will talk about an elementary proof of (local) Kronecker-Weber theorem. Other topics will include local class field theory and its applications.

reference:
• J.-P. Serre, Local fields, Springer
• J. Neukirch, Algebraic number theory, Springer
date:
2012/05/16 1430-1530
room:
B103
title:
Bridgeland's stability conditions and it's wall-crossing.
speaker:
Hiroki Minamide(Kobe University)
abstract:

In this talk we shall survey recent progress on the Bridgeland's stability conditions and it's wall-crossing. The material covered in this talk is based almost entirely on the two celebrated articles by T. Bridgeland. We shall treat special objects the bounded derived category of coherent sheaves on smooth projective curves and K3/abelian surfaces. If there is enough time, I will also explain some results on relations classical stability and Bridgeland's stability.

date:
2012/05/16 1540-1610
room:
B103
title:
Local Bertini theorem and the Iwasawa's main conjecture
speaker:
Kazuma Shimomoto(Kansai University)
abstract:

This is a report on joint work with T. Ochiai (Osaka University) on the relation between the characteristic ideal arising from Hida deformation and the 2-variable p-adic L-function.

date:
2012/02/23 1000-1130
room:
A739
title:
Cellular and stellar stratified spaces
speaker:
Dai Tamaki(shinshu University)
abstract:

The speaker recently introduced a generalization and a refinement of cell complexes, called cellular stratified spaces, which allow us to extend techniques used by combinatorialists to study posets and simplicial complexes to much more general structures such as topological categories. This talk is an exposition of cellular stratified spaces and related structures. We mainly focus on motivations and (possible) applications.

date:
2012/02/22 1600-1730
room:
A739
title:
Simplicial and cellular structures in algebraic topology
speaker:
Dai Tamaki(shinshu University)
abstract:

We review simplicial and cellular structures used in algebraic topology, such as simplicial complexes, cell complexes, simplicial sets, simplicial spaces, $\Delta$-sets, and cosimplicial spaces, from a historical perspective. Simplicial complexes played a fundamental role when Poincare tried to define homology. Cell complexes and CW complexes were introduced by Whitehead and form basic building blocks of classical algebraic topology. In modern algebraic topology, model categories equipped with simplicial or cellular structures are basic objects of study. Simplicial sets also provide a foundation of $(\infty,1)$-categories, from which Lurie developed derived algebraic geometry and extended topological quantum field theories. If time allows, we might be able to discuss these recent developments.

articles and slides (license is CC-BY-NC):
abstract_dai_tamaki.pdf
date:
2012/02/10 1000-1200, 1400-1800
place and room:
Studio Phones Room301B
title:
Higher-order generalization of Fukaya's Morse homotopy invariant of 3-manifolds
speaker:
abstract:

We give a higher order generalization of Fukaya's Morse homotopy theoretic approach to 2-loop Chern--Simons perturbation theory. In this talk, we construct a sequence of invariants of homology 3-spheres with values in a space of trivalent graphs (Jacobi diagrams) by using Morse homotopy theory.

date:
2012/02/09 1500-1600
room:
A739
title:
Morse theory and invariants of manifolds
speaker:
abstract:

The diffeomorphism type of a differentiable manifold can be studied by considering some smooth function on the manifold (Morse theory). I will review the basics of Morse theory and some related topics.

date:
2012/02/09 1610-1730
room:
A739
title:
Higher-order generalization of Fukaya's Morse homotopy invariant of 3-manifolds
speaker:
abstract:

We give a higher order generalization of Fukaya's Morse homotopy theoretic approach to 2-loop Chern--Simons perturbation theory. In this talk, we construct a sequence of invariants of homology 3-spheres with values in a space of trivalent graphs (Jacobi diagrams) by using Morse homotopy theory.

date:
2012/01/05 1000-1130
room:
A739
title:
An Introduction to Model Theory
speaker:
Kota Takeuchi (University of Tsukuba)
abstract:

This talk will be a brief introduction to the Model Theory. We will discuss a model theoretic viewpoint over mathematics and, especially, algebra.This talk assumes no prior knowledge of logic.

date:
2012/01/05 1230-1400
room:
A739
title:
Topology of hyperplane arrangements
speaker:
Masahiko Yoshinaga (Kyoto University)
abstract:

I will survey several results concerning topology of hyperplane arrangements with focus on the fundamental group. (Kew words: homotopy type, K(\pi, 1) space, minimality, fundamental group.)

date:
2012/01/04 1500-1700
room:
A739
title:
Definable Morse functions in a real closed field
speaker:
Tomohiro Kawakami (Wakayama University)
abstract:

Let $X$ be a definably compact definable $C^r$ manifold and $2 \le r <\infty$. Then the set of definable Morse functions $Def_{Morse}^r(X)$ is open and dense in the set $Def^r(X)$ of definable $C^r$ functions on $X$ with respect to the definable $C2$ topology.

date:
2011/11/09 1700-1800
room:
A739
title:
Toric degenerations of integrable systems on Grassmannians
speaker:
Yuichi Nohara (Kagawa University)
abstract:

An integrable system on a symplectic manifold of dimension 2n is an n-tuple of independent functions which are mutually Poisson commutative. Moment maps of torus actions on toric varieties are typical example of integrable systems. I would like to talk about integrable systems on the Grassmannians of two-planes, and their deformations into toric moment maps. We also discuss a relation to bending Hamiltonians on the moduli space of polygons in the Euclidean three-space. This is a joint work with K. Ueda.

## Original Studio Phones seminars:

date:
2011/08/23 1030-1130
room:
StudioPhones Room301B
title:
On ring theoretic invariants of quasi-isometry
speaker:
Hokuto Morishima (Osaka University)
abstract:

We consider a certain ring for a finitely generated group, and introduce the results about correspondence of the ring and the quasi-isometric geometry of the finitely generated group.

date:
2011/08/23 1300-1400
room:
StudioPhones Room301B
title:
On pre-computable category
speaker:
Yusuke Kiriu (Studio Phones)
abstract:

This talk is a brief survey of pre-computable category, especially, for topological objects, invariant functions, and algebraic structures. On the background of our research, we are studying computer sciences, logics and linguistics. I also talk about some details of pre-computable category within the context of 2 and 3 dimensional computer graphics and general graphics.

date:
2011/08/23 1410-1800
room:
StudioPhones Room301B
title:
Introduction to Schubert calculus
speaker:
Shizuo Kaji (Yamaguchi University)
abstract:

"How many lines are there in the three space which meet all the four given lines ?" In 19th century, H.Schubert considered this problem in an insightful but not rigorous way. He invented a symbolic "calculation'' for the conditions on lines as follows: [intersecting a given line]^{\cap 4} =   [lying on a given line] \cup [lying on a given line], and obtained the answer two. In fact, the "algebra'' of the conditions on lines is isomorphic to the ring of the symmetric polynomials called Schur polynomials. D.Hilbert asked for a rigorous foundation for the above calculus as the 15th problem in his 1900 lecture and now Schubert’s quiz can be rephrased in terms of cohomology, or equivalently, intersection theory of a Grassmaniann manifold. In this talk, I will briefly review the basics of Schubert calculus with a focus on the correspondence of several algebras occurring in this subject including the above one.

date:
2011/03/08 1500-1800
room:
StudioPhones Room301B
title:
Vertex operator algebras and characters of their modules
speaker:
Yusuke Arike (Osaka University)
abstract:

I will explain about Zhu's modular invariance property of characters of modules for rational vertex operator algebras.

date:
2010/07/29 1300-1700
room:
StudioPhones Room301B
title:
On the tetrahedral number of hyperbolic manifolds of bounded volume
speaker:
Yo'av Rieck (University of Arkansas) after Jorgensen and Thurston, joint with Tsuyoshi Kobayashi
abstract:

In the 70's, Jorgensen and Thruston proved that for any V>0 there exists a finite collection of manifolds X_1,...,X_n so that any complete hyperbolic 3-manifold of volume at most V is obtained by filling some X_i.  A well-know "folk theorem" of Thruston says that there exists a constant K so that X_i can be triangulated using at most KV tetrahedra. We will first motivate this theorem by describing two applications. The purpose of this talk is providing a proof of Thurston's theorem. The proof follows an outline that appeared in the litrature, but as remarked by Benedetti and Petronio, it requirs control over the intersection between the Voronoi cells and the thin and thick parts of the manifolds (the terms will be explained in the talk).  We will show how we control these intersections. Most of the work is elementary and done in hyperbolic 3-space. I will make an effort to make it accessible to students familiar with the upper half space model.

date:
2010/03/15 1300-1700
room:
StudioPhones Room301B
title:
On a variation of the Gordian complex
speaker:
In Dae Jong (Osaka City University)
abstract:

This is a joint work with Kazuhiro Ichihara. We will introduce simplicial complexes by using various invariants and local moves on knots, which give generalizations of the Gordian complex defined by Hirasawa and Uchida. In this talk, we will study simplicial complexes defined by using the Alexander-Conway polynomial and the crossing change or the Delta-move. We will show that these simplicial complexes are Gromov hyperbolic.

date:
2010/02/17 1300-1500
room:
StudioPhones Room301B
title:
On roots of Dehn twists
speaker:
Naoyuki Monden (Osaka University)
abstract:

Margalit and Schleimer constructed nontrivial roots of the Dehn twist about a nonseparating curve.We prove that the conjugacy classes of roots of the Dehn twist about a nonseparating curve correspond to the conjugacy classes of periodic maps with certain conditions.Furthermore, we give data set which determine the conjugacy class of a root. As a consequence, we can find the minimum degree and the maximum degree, and show that the degree must be odd. Also, we give Dehn twist expression of the root of degree 3

date:
2010/02/17 1500-1830
room:
StudioPhones Room301B
title:
Handle decompositions of knot complements
speaker:
Tsubasa Ichikawa (Osaka University)
abstract:

Every smooth compact n-manifold is decomposed into some copies of n-disks (= handles) according to certain rules. I would like to introduce handle decompositions of manifolds (especially knot complements) and demonstrate how to draw them.

date:
2010/02/13 1000-1130
room:
StudioPhones Room301B
title:
Quandles and related topics
speaker:
Yuichi Kabaya (Osaka City University Advanced Mathematical Institute (OCAMI))
abstract:

Quandle is an algebraic structure which was introduced by David Joyce in 1982, motivated by knot theory and conjugation of a group. In this talk I will introduce several aspects of quandles and related topics; quandle homology and relation with group homology, rack space, (twisted) Alexander polynomial, etc.

date:
2010/02/13 1300-1730
room:
StudioPhones Room301B
title:
Iwasawa theory and characteristic invariants
speaker:
Kazuma Shimomoto Joint with T.Ochiai (Osaka University)
abstract:

In recent years, several people have suggested the various kinds of Iwasawa Main Conjecture formulated in the language used in their own field of study. In this talk, I begin with a brief review on classical Iwasawa theory, including the classical Main Conjecture. Then I move on to the p-adic modular forms, L-functions, and the Main Conjecture. The main theme of this talk is to discuss Bertini-type theorem and characteristic invariants which also serve as strategic tools to study similar invariants in toplogy and algebra.

date:
2010/02/10 0930-1130
room:
StudioPhones Room301B
title:
Application of Length of Quandle 3-Cocycle to Surface-Knot Theory
speaker:
Shin Satoh (Kobe University)
abstract:

The homology and cohomology theory of a quandle is useful to study knotted surfaces in 4-space. We define the length of a 3-cocycle of a quandle equipped with a quandle-set, and calculate the lengths of some 3-cocycles. We give lower bounds of the triple point number of a surface-knot by the length of a quandle 3-cocycle.

date:
2010/02/10 1300-1730
room:
StudioPhones Room301B
title:
On quandle homology groups of Alexander quandles of prime order
speaker:
Takefumi Nosaka (RIMS, Kyoto University)
abstract:

Our result is to determine all quandle homology groups of Alexander quandle of prime order. The proof is obtained from the calculations of quandle 'co'homology group with the generators (cocycles) by means of calculus over positive characteristic, which is inspired by T.Mochizuki's computations of third degree cocycles.  This talk outlines the proof, and our goal is to illustate why 'the higher degree cocycles are constructed from lower degree ones, and linear independently generate the quandle cohomology group'.

date:
2009/12/30 1000-1300
room:
StudioPhones Room301B
title:
Similarity between Alexander-Fox Theory and Iwasawa Theory
speaker:
Teruhisa Kadokami (Dalian University of technology)
abstract:

I explain about similarity between Alexander-Fox Theory from Knot Theory, and Iwasawa Theory from Number Theory.

date:
2009/12/30 1430-1630
room:
StudioPhones Room301B
title:
On F-coherent rings
speaker:
Kazuma Shimomoto
abstract:

I will talk about a new class of Noetherian rings defined by the Frobenius map and discuss its basic properties. The talk will also focus on some open questions.

date:
2009/12/30 1430-1730
room:
StudioPhones Room301B
title:
Bertini type theorem and Iwasawa Main Conjecture
speaker:
Kazuma Shimomoto Joint with T.Ochiai (Osaka University)
abstract:

Iwasawa Main Conjecture (IMC) in two variables was proposed by several people and proved by K.Rubin in the classical case.  More recently, T.Ochiai formulated IMC over some type of deformation spaces and he proved it in the case when the deformation space is the Iwasawa algebra.His idea is to take sufficiently many hypersurfaces and analyze the problem on them.I will talk about the so-called Bertini type theorem to generalize IMC to more general deformation spaces.

date:
2009/12/05 1000-1800
room:
2nd Floor, Lecture Room, Kanazawa University Satellite Plaza
title:
Godel's incompleteness theorem and its application
speaker:
Shunsuke Yatabe (National Institute of Advanced Industrial Science and Technology)
abstract:

In this talk, we introduce an overview of a proof of Godel's incompleteness theorem. First we see the details of arithmetization of natural number theory, then we see how Godel sentence is constructed. Then we see the arithmetical hierarchy and its "circular structure" in Global sense. If we have enough time, we also try to see some facts about non-standard model of Arithmetic.

date:
2009/10/08 1300-1800
room:
StudioPhones Room301B
title:
An Application of Category Theory to Systems Biology
speaker:
Taichi Haruna (Kobe University/JST)
abstract:

We propose a new data analytical tool for directed networks by using category theory. We develop a category theoretical treatment of directed networks in order to obtain functional networks for real networks. By applying our method to concrete data on real information processing biological networks, we find a distinguishing global structure of functional networks. We discuss a possibility of a new hypothesis on network motifs based on our theory and data analysis. We also present a glimpse of calculations when our method is thought of an abstract graph transformation.

date:
2009/10/14 1000-1200
room:
StudioPhones Room301B
title:
Cohen-Macaulay modules over Gorenstein rings
speaker:
Tokuji Araya (Nara University of Education)
abstract:

Gorenstein rings have nice homological properties to investigate the category of finitely generated modules. In this talk, I will give some basic properties of Cohen-Macaulay modules over Gorenstein rings.

date:
2009/10/14 1500-1700
room:
StudioPhones Room301B
title:
Cohen-Macaulay modules over Gorenstein rings
speaker:
Tokuji Araya (Nara University of Education)
abstract:

Gorenstein rings have nice homological properties to investigate the category of finitely generated modules. In this talk, I will give some basic properties of Cohen-Macaulay modules over Gorenstein rings.

date:
2009/09/27 1000-1300
room:
StudioPhones Room301B
title:
Basics of plane curves
speaker:
Hisanori Ohashi (RIMS, Kyoto University)
abstract:

I will give an introduction to algebraic geometry. We will see several aspects of algebraic curves, being as conscious to the general theory as possible. If time permits, I will explain the Mathieu group, the first generation of the Happy Family of finite simple sporadic groups.

date:
2009/09/27 1400-1600
room:
StudioPhones Room301B
title:
Geometry of second order PDE
speaker:
abstract:

This is an introduction to exterior differential systems. I will talk the classical theory given by E.Cartan.

date:
2009/09/27 1600-1800
room:
StudioPhones Room301B
title:
Symbolic Manipulation for pure functions
speaker:
Yusuke Kiriu (Studio Phones)(Joint with T.Sakasai)
abstract:

Beginning with a short introduction to symbolic and numeric computation, we discuss interaction between computer science and low-dimensional topology, especially, algorithms and programming paradigms. In this talk, we give an extension language designed specifically to symbolic manipulaton of pure functions by using low-level structures of Mathematica .

date:
2009/09/25 1830-2000
room:
StudioPhones Room301B
title:
Kirby's theorem
speaker:
abstract:

Using Cerf theory Kirby proved that two framed links represent diffeomorphic closed 3-manifolds if and only if they are related to each other by a sequence of "Kirby moves" on framed links. A rough sketch of Kirby's proof is explained along his original paper.

date:
2009/08/22 1000-1500
room:
StudioPhones Room301B
title:
Towards on analogy of Dehn surgery in number theory
speaker:
Yasushi Mizusawa (Nagoya Institute of Technology)
abstract:

Based on the analogy between Galois groups and Knot groups, we discuss on analogy of the theory of Dehn suregery for knots.

date:
2009/08/19 1300-1500
room:
StudioPhones Room301B
title:
Everywhere integral sections of elliptic surfaces
speaker:
Hisanori Ohashi (RIMS, Kyoto University)
abstract:

integral points of elliptic curves have long history in number theory and algebraic geometry. In this talk I will introduce the analogue of integral points in the elliptic surface case, originally defined by T. Shioda. To do so, I will explain elliptic surfaces, their Mordell-Weil lattices, related sphere packings, lattice theory and group theory. The purpose is to overview the subject.

date:
2009/08/17 1500-1800
room:
StudioPhones Room301B
title:
Lefschetz fibrations and Teichmuller spaces
speaker:
Hiroshige Shiga (Tokyo Institute of Technology)
abstract:

We discuss interaction  between Teichmuller spaces and hoomorphic Lefschetz fibrations.

date:
2009/08/17 1230-1730
room:
StudioPhones Room301B
title:
Invariants and constructions of Lefschetz fibrations
speaker:
Hisaaki Endo (Osaka University)
abstract:

Beginning with a short introduction to 4-manifolds, we discuss various properties of Lefschetz fibrations, especially, signature of Lefschetz fibrations and substitution technique for positive relations.

date:
2009/08/16 1000-1200
room:
StudioPhones Room301B
title:
Lens spaces and some invariants
speaker:
Motoo Tange (RIMS, Kyoto University)
abstract:

The speaker shall define 3-dimensional lens spaces in some ways and shall compute various topological invariants. We will consider whether we can investigate the Dehn surgery problem from the values.

date:
2009/08/16 1300-1730
room:
StudioPhones Room301B
title:
Lens spaces and some invariants
speaker:
Motoo Tange (RIMS, Kyoto University)
abstract:

The speaker shall define 3-dimensional lens spaces in some ways and shall compute various topological invariants. We will consider whether we can investigate the Dehn surgery problem from the values.

date:
2009/07/25 1000-1200
room:
StudioPhones Room301B
title:
Standard models of Train tracks
speaker:
Hideki Miyachi (Osaka University)
abstract:

In this talk, we will survey properties of the standard models of train tracks.

date:
2009/07/18 1300-1730
room:
StudioPhones Room301B
title:
Dualizing complex of the Stanley ring associated with a simplicial poset
speaker:
Kohji Yanagawa (Kansai University)
abstract:

In 1991, R. Stanley assigned a commutative ring $A_P$ to a finite simplicial poset $P$ for a combinatorial purpose. Recently, M. Masuda et al. studied $A_P$ as the equivariant cohomology ring of a torus manifold. In this talk, we give a concise description of the dualizing complex of $A_P$, and show an application.

date:
2009/05/30 1030-1130
room:
StudioPhones Room301B
title:
Schubert calculus and combinatorics of words
speaker:
Hiroshi Naruse (Okayama University)
abstract:

In this talk I will explain how combinatorics of words can be used in Schubert calculus, i.e. reducing the problem to calculate topological invariants for Schubert varieties in terms of subword combinatorics of Coxeter groups. There are recurrence relations for canonical classes and structure constants, and explicit formulas for the solutions are given for some special cases.

date:
2009/05/30 1300-1800
room:
StudioPhones Room301B
title:
How to overcome Russell paradox (within fuzzy logic)
speaker:
Shunsuke Yatabe (National Institute of Advanced Industrial Science and Technology)
abstract:

It is well known that Russell paradox shows that the naive set theory implies a contradiction within classical logic. However, in 1970's, it turned out that the theory is consistent within many non-classical logics. In this talk, we introduce the case of fuzzy logic. One of the most interesting aspect of such set theory is that it forgives the very strong form of circular definitions. However this makes difficult to construct its models. In this talk we briefly introduce about them.

date:
2009/02/23 1500-1800
room:
StudioPhones Room301B
title:
Geometric method on Virtual Knot Theory
speaker:
Teruhisa Kadokami (Dalian University of technology)
abstract:

A virtual link is an extended concept of a link in S^3 which can be realized as a diagram on S^2 by introducing virtual crossings. Geometrically, a virtual link can be considered as a link in the product space of an oriented closed surface and the closed interval. So we can study virtual links geometrically. I will introduce some geometric methods of Virtual Knot Theory.

date:
2009/02/20 1600-2030
room:
StudioPhones Room301B
title:
Teichmueller spaces and Banach spaces in the Teichmueller theory 1
speaker:
Hideki Miyachi (Osaka University)
abstract:

In this talk, I give a brief introduction of the Teichmueller theory. Especially, we will discuss the complex analytic structure of the Teichmueller space.

date:
2009/02/21 1000-1600
room:
StudioPhones Room301B
title:
Teichmueller spaces and Banach spaces in the Teichmueller theory 1
speaker:
Hideki Miyachi (Osaka University)
abstract:

In this talk, I give a brief introduction of the Teichmueller theory. Especially, we will discuss the complex analytic structure of the Teichmueller space.

date:
2009/02/21 1600-1830
room:
StudioPhones Room301B
title:
When is a Ford-like polygon non-generic?
speaker:
Akira Ushijima (Kanazawa University)
abstract:

The detail of the proof that Ford-like polygons for a given Fuchsian group are generic for almost all points will be discussed in this talk.

date:
2009/02/22 1000-1200
room:
StudioPhones Room301B
title:
Limit sets of Kleinian groups
speaker:
Kentaro Ito (Nagoya University)
abstract:

I will explain some basic properties of limit sets of Kleinian groups.

date:
2009/02/20 1300-1800
room:
StudioPhones Room301B
title:
Wrokshop
speaker:
Yusuke Kiriu(Studio Phones)
abstract:

date:
2009/02/19 1400-1800
room:
StudioPhones Room301B
title:
Toric degenerations of Gerfand-Cetlin systems and their applications
speaker:
Yuichi Nohara (Tohoku University)
abstract:

The Gelfand-Cetlin system is a completely integrable system       on a flag manifold of type A, whose moment polytope is known       as the Gelfand-Cetlin polytope.       We show that the Gelfand-Cetlin system can be deformed into       a moment map on a toric variety corresponding to the       Gelfand-Cetlin polytope.       We also discuss an application to disk counting problem.

date:
room:
StudioPhones Room301B
title:
Sutured Floer homology and its application
speaker:
Motoo Tange (RIMS, Kyoto University)
abstract:

Juhasz has defined sutured Floer homologies for sutured manifolds. We will talk about its definition, calculation, and applications.

date:
2009/01/16 1300-1600
room:
StudioPhones Room301B
title:
Foliations on 3-dimesional manifolds
speaker:
Hiroko Murai (Tokyo Denki University)
abstract:

For a given knot K in the 3-sphere , D. Gabai has given a method for constructing a taut finite depth foliations on the exterior of such that the minimal genus Seifert surface for K is a leaf of the foliation and the restriction of the foliation to the boundary is a foliation by circles. In this talk, we apply the method to 5_2 knot and see the behavior of leaves of the foliation.

date:
2008/12/13 1130-1300
room:
StudioPhones Room301B
title:
Quandle and hyperbolic volume
speaker:
Ayumu Inoue (Tokyo Institute of Technology)
abstract:

In this talk, we will show that the hyperbolic volume of a hyperbolic knot is a quandle cocycle invariant.   Further we will show that it completely determines invertibility and positive/negative amphicheirality of hyperbolic knots.

date:
2008/12/13 1430-1700
room:
StudioPhones Room301B
title:
Quandle and hyperbolic volume
speaker:
Ayumu Inoue (Tokyo Institute of Technology)
abstract:

In this talk, we will show that the hyperbolic volume of a hyperbolic knot is a quandle cocycle invariant.   Further we will show that it completely determines invertibility and positive/negative amphicheirality of hyperbolic knots.