# 談話会・セミナー

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## 談話会/Colloquium

Title

Is an irng singly generated as an ideal?

Date

2012年2月22日（水）　16:30～17:30 　　 （16:00より105談話室でtea)

Place

(Rm110, Building No.3, Faculty of Science, Kyoto University)

Speaker

Abstract

I will address the problem whether every finitely generated idempotent ideal of a ring is singly generated as an ideal, and discuss its relationship to the Wiegold problem. Joint work with N. Monod and A. Thom.

Comment

### 大談話会

Title

Date

2012年2月15日（水）　14:40～15:40

Place

(Rm110, Building No.3, Faculty of Science, Kyoto University)

Speaker

Abstract

20世紀の関数論の発展に大きな役割を果たしてきた Loewner 微分方程式は、 2000年に至って Oded Schramm によって SLE (stochastic Loewner evolution あるいは Schramm-Loewner evolution)と呼ばれるランダムな曲線の時間発展と しての等角的に不変な確率過程の構成に用いられた。それは統計物理学に関連 する様々な離散確率モデルの連続極限と厳密に同定され、相転移現象等の数学 的理解を深めるのに著しく貢献している。

Comment 15:40-16:30 109号室にてTea Break

### 大談話会

Title

クラスター代数と圏化

Date

2012年2月15日（水）　16:30～17:30

Place

(Rm110, Building No.3, Faculty of Science, Kyoto University)

Speaker

Abstract

2002年にFomin-Zelevinskyによって導入されたクラスター代数は、一見誰にで も分かる簡単な定義を持つにも関わらず、その性質を調べていくうちに、箙の表 現論、タイヒミュラー空間の量子化、Donaldson-Thomas不変量、といった数学の いろいろな分野の研究とつながりを持つことが明らかにされてきた。

Comment 15:40-16:30 109号室にてTea Break

Title

Rigidity of surjective holomorphic maps to projective manifolds

Date

2012年1月26日（木）　16:50～17:50　　（16:20より１階ロビーでtea)

Place

(Rm111, Research Institute for Mathematical Sciences, Kyoto University)

Speaker

Jun-Muk Hwang 氏（Korea Institute for Advanced Study）

Abstract

Generally, surjective holomorphic maps to a projective manifold are rare. We discuss just how rare they are by introducing the notion of target rigidity. It is expected that most projective manifolds are target rigid, in the sense that any family of surjective holomorphic maps to them essentially come from their automorphisms. We will give a survey of recent developments on target rigidity.

Comment

Title

Gorenstain空間におけるループ(余)積の微分捻れ関手による解釈
(Torsion functor description of loop (co)products on Gorenstein spaces)

Date

2012年1月18日（水）　16:30～17:30 　　 （16:00より105談話室でtea)

Place

(Rm110, Building No.3, Faculty of Science, Kyoto University)

Speaker

Abstract

String topology of Chas and Sullivan describes a rich structure in the homology of the free loop space of a closed oriented manifold. The most basic operation is an intersection type product on the shifted homology. The key to defining these operations is to construct wrong way maps on the homology of manifolds. In this talk we will give a brief overview of Gorenstein spaces, which is no longer a manifold in general, and discuss such important maps on the spaces with a remarkable result due to Felix and Thomas. The setting enables us to develop string topology in the derived category of differential graded modules over the singular cochain algebra of a Gorenstein space. In particular, the duals to loop (co)products can be described in terms of differential torsion functors.
This is joint work with Luc Mencihi (Angers University) and Takahito Naito (Shinshu University).

Comment

Title

Existence of outer automorphisms of the Calkin algebra is undecidable

Date

2012年1月11日（水）　16:30～17:30　　（16:00より１階ロビーでtea)

Place

(Rm110, Research Institute for Mathematical Sciences, Kyoto University)

Speaker

N. Christopher Phillips 氏（京大・数理研 & University of Oregon）

Abstract

Let $H$ be a separable infinite dimensional Hilbert space, for example, the space $l^2$ of all square summable sequences. Let $L (H)$ be the algebra of all continuous linear maps from $H$ to~$H,$ and let $K (H)$ be the closure in $L (H)$ of the set of continuous linear maps which have finite rank. Then $K (H)$ is an ideal in $L (H),$ and we can form the quotient algebra $Q = L (H) / K (H).$ It is called the Calkin algebra, and is an example of a C*-algebra. Question: Does the Calkin algebra have outer automorphisms, that is, automorphisms not of the form $a \mapsto u a u^{-1}$ for suitable $u \in Q$?
It turns out that this question is undecidable in ZFC. If one assumes the Continuum Hypothesis, then outer automorphisms exist. In fact, there are more automorphisms than there are possible choices for~$u.$ (This is joint work with Nik Weaver.) However, Ilijas Farah proved that it is consistent with ZFC that $Q$~has no outer automorphisms.
This talk is intended for a general audience. I will describe some of the background, and give several of the ideas of the proof that the Continuum Hypothesis implies the existence of outer automorphisms of the Calkin algebra.

Comment

Title

Knot theoretic views on homotopy groups

Date

2011年12月14日（水）　16:30～17:30　　（16:00より１階ロビーでtea)

Place

(Rm110, Research Institute for Mathematical Sciences, Kyoto University)

Speaker

Jie Wu 氏（National University of Singapore）

Abstract

In this talk, we will discuss some fundamental connections between knot theory and homotopy groups. The general homotopy groups of spheres can be expressed as certain canonical sub-quotients of link groups. Also a canonical simplicial resolution of a knot group can provide a combinatorial model for the loop space of 3-spheres. These connections seem to address some new questions in knot theory. The talk will aim to general audience.

Comment

Title

(On embedding graphs into hyperbolic space forms)

Date

2011年12月7日（水）　16:30～17:30 　　 （16:00より105談話室でtea)

Place

(Rm110, Building No.3, Faculty of Science, Kyoto University)

Speaker

Abstract

Comment

Title

Parabolic Reduction, Stability and Volumes of Fundamental Domains

Date

2011年11月30日（水）　16:30～17:30　　（16:00より１階ロビーでtea)

Place

(Rm110, Research Institute for Mathematical Sciences, Kyoto University)

Speaker

Lin Weng 氏 （九州大・数理学研究院）

Abstract

In this talk, we expose an intrinsic structure of volumes of fundamental domains for reductive groups G defined over number fields, in terms of parabolic reduction using stability. It claims that:
For any parabolic subgroup P of G, let v_P=prod_M v_M denote the product of v_M, the volumes of the fundamental domains associated to the Levi factors M of P and u_P=prod_M u_M denote the product of u_M, the volumes of moduli spaces of semistable points associated to the Levi factors M of P, then
v_G= sum_P c_Pu_P
and
u_G= sum_P sgn(P) e_Pv_P
with c_P and e_P non-trivial positive rational numbers, where P runs over all standard parabolic subgroups of G.
This pair of relations is found with the help of Arthur's analytic truncation, Lafforgue's arithmetic truncation, and Langlands' theory of Eisenstein series.
A beautiful formula of Kontsevich for SL(n,Z), obtained using Harder-Narasimhan filtrations, one of our starting points, and some examples with lower ranks obtained by 足立憲治 will be given.
[pdf]

Comment

Title

(Quantum Field Theory And Phases Of Calabi-Yau Categories)

Date

2011年11月24日（木）　16:30～17:30　　（16:00より１階ロビーでtea)

Place

(Rm110, Research Institute for Mathematical Sciences, Kyoto University)

Speaker

Abstract

ある種の2次元(2,2)超対称ゲージ理論から(2,2)超共形場の理論の族が得られ、 そのパラメーター空間の様々な領域は様々なカラビ-ヤウ多様体あるいはその非可換版に対応している。 このことと(2,2)超対称性の一般原理を合わせると、 （非可換）カラビ-ヤウ多様体の連接層の導来圏、深谷圏、グロモフ-ウィッテン不変量やその一般化について興味深い結論が導かれる。 一方で、この分野における数学の進展は新たな双対性の発見など場の理論のよ り良い理解につながっている。 この談話会では以上のことについて解説したい。
A certain two dimensional (2,2) supersymmetric gauge theory leads to a family of (2,2) superconformal field theories, and various regions of the parameter space correspond to various Calabi-Yau varieties or non-commutative versions thereof. Combined with general principles of (2,2) supersymmetry, this fact leads to interesting consequences on the derived category of coherent sheaves, Fukaya category and Gromov-Witten invariants or its generalizations of the (non-commutative) Calabi-Yau varieties. On the other hand, progress in mathematical studies in this area leads to better understanding of quantum field theory such as discovery of a new duality. In this talk, I would like to explain these matters.

Comment

Title

(On generalization of the non-abelian Lubin-Tate theory to symplectic groups)

Date

2011年11月16日（水）　16:30～17:30　　（16:00より１階ロビーでtea)

Place

(Rm110, Research Institute for Mathematical Sciences, Kyoto University)

Speaker

Abstract

Comment

Title

ホモロジー的ミラー対称性のある変形について
(On some deformation of homological mirror symmetry)

Date

2011年11月2日（水）　16:30～17:30　　（16:00より１階ロビーでtea)

Place

(Rm110, Research Institute for Mathematical Sciences, Kyoto University)

Speaker

Abstract

ミラー対称性予想の解決に向けて,両者の多様体を共通な底空間上の 互いに双対なトーラスファイバー束として記述する Strominger-Yau- Zaslow(SYZ)によるミラー対称性の定式化が有効であると思われる. このSYZトーラスファイバー束として定められるミラー双対な シンプレクティック多様体と複素多様体の組のある変形として, ある葉層構造を持つシンプレクティックトーラスファイバー束と 複素トーラスファイバー束のある非可換変形が得られる. この変形の組がまたミラー双対であると主張するための根拠として, シンプレクティック多様体上の深谷圏と,ミラー双対な複素多様体上 の連接層の導来圏の同値性として定式化されるホモロジー的ミラー 対称性の対応する変形についてお話ししたいと思います. （もともとの変形されていない設定で分かっているレベルで, その変形された圏の組も同値となることがいえる. ）

Comment

Title

リーマンゼータ関数と確率論
(Riemann zeta function and probability theory)

Date

2011年10月26日（水）　16:30～17:30 　　 （16:00より105談話室でtea)

Place

(Rm110, Building No.3, Faculty of Science, Kyoto University)

Speaker

Abstract

リーマンゼータ関数の特殊値（特にバーゼル問題$\zeta(2)=\pi^2/6$)を 初等確率論の手法で求める。2つの独立なコーシー分布の商、逆正弦分布 の商、指数分布の商、ウィグナー半円分布の商のすべてでバーゼル問題、 リーマンゼータ関数に関するオイラー公式が導き出せる。また、ルジャン ドル展開の手法でもバーゼル問題が解けることや、チェビシェフ多項式と の関連なども論じる。

Comment

Title

Special Legendrian submanifolds in toric Sasaki-Einstein manifolds

Date

2011年10月19日（水）　16:30～17:30 　　 （16:00より105談話室でtea)

Place

(Rm110, Building No.3, Faculty of Science, Kyoto University)

Speaker

Abstract

Comment

Title

New results in Free Probability theory and applications to Quantum Information theory

Date

2011年10月12日（水）　16:30～17:30 　　 （16:00より105談話室でtea)

Place

(Rm110, Building No.3, Faculty of Science, Kyoto University)

Speaker

Benoît Collins 氏 （University of Ottawa）

Abstract

Motivated by Operator Algebraic questions, Voiculescu introduced Free Probability in the early eighties. Ten years later, he discovered that Free Probability explains some behaviours of eigenvalues of Random Matrices in the limit of large dimension.
In this talk we will first describe new convergence results for norms for random matrices with unitary invariance, hereby solving conjectures by Pisier and Haagerup. Then, we will describe some applications to Quantum Information theory.
This talk is based on results obtained through collaborations with Belinschi, Nechita, Fukuda and Male.

Comment

Title

(A new variational approach for a singularly perturbed nonlinear Schrödinger equation)

Date

2011年10月5日（水）　16:30～17:30 　　 （16:00より105談話室でtea)

Place

(Rm110, Building No.3, Faculty of Science, Kyoto University)

Speaker

Abstract

Comment

Title

Amazonランキングの謎を解く
(The Amazon mystery)

Date

2011年7月20日（水）　16:30～17:30 　　 （16:00より105談話室でtea)

Place

Rm110, Department of Mathematics Graduate School of Science, Kyoto University

Speaker

Abstract

この研究は，オンライン書店の本のランキングの時間変化の理解 という現実への応用から始まった．約５年の研究の過程を追う形 で，何を解決するためにどう考えたか，に力点を置いて話し，そ れによって，現実の新しい現象に数学を適用する研究スタイルの 例を提示したい．

Comment

Title

The Dynamical Degree of a Mapping

Date

2011年7月13日（水）　16:30～17:30 　　 （16:00より105談話室でtea)

Place

Rm110, Department of Mathematics Graduate School of Science, Kyoto University

Speaker

Eric Bedford 氏　（Indiana University）

Abstract

We consider polynomial or rational mappings of complex $k$-dimensional space, which are mappings of the form $f=(f_1,\dots,f_k)$ with the coordinate functions polynomial orrational. Our interest is to study properties of these mappings under iteration: $f^n=f\circ \cdots\circ f$. The main invariant for such problems is the dynamical degree, which we will define and show how it is computed in certain cases.

Comment

Title

(A view of mirror quintic 3-folds through log mixed Hodge theory)

Date

2011年7月6日（水）　16:30～17:30 　　 （16:00より105談話室でtea)

Place

Rm110, Department of Mathematics Graduate School of Science, Kyoto University

Speaker

Abstract

As a joint work of Kazuya Kato, Chikara Nakayama, and Usui, various partial compactifications of a classifying space D of mixed Hodge structures were constructed, and their relation was described as a fundamental diagram. We will observe mirror quintic 3-folds in this framework. The following were known:
- A large complex structure limit point is a boundary point of a toroidal partial compactification of a quotient of D.
- The canonical coordinate is a cusp form at this boundary point.
- Generic global Torelli theorem holds.
The fundamental diagram itself seems to be more closely related with mirror symmetry.

Comment

Title

Old and recent topics on the subject of resolution of singularities

Date

2011年6月29日（水）　16:30～17:30 （16:00より１階ロビーでtea)

Place

Speaker

Kenji Matsuki 氏　（京大・数理研 & Purdue University）

Abstract

Comment

Title

(Topology of line arrangements)

Date

2011年6月22日（水）　16:30～17:30　　（16:00より１階ロビーでtea)

Place

Speaker

Abstract

Comment

Title

Date

2011年6月15日（水）　16:30～17:30 　　 （16:00より105談話室でtea)

Place

Speaker

Abstract

Mazur-Tate-Teitelbaumはpで通常還元(または分裂乗法的還元) を持つ有理数体上の楕円曲線に対してBSD予想のp進類似を定式 化した.講演ではできるだけ基本的な事項の復習から始め, 現時点 でこの予想に関して知られている結果を紹介したい.もし時間に 余裕があれば総実代数体上の楕円曲線の場合への一般化について 現在行っている研究を報告したいと思う.

Comment

Title

Toward birational classification of three dimensional algebraic varieties

Date

2011年6月8日（水）　16:30～17:30　　（16:00より１階ロビーでtea)

Place

Speaker

Jungkai Chen氏（京大・数理研 & Taiwan National University）

Abstract

The major goals of birational geometry are to find a good model inside a birational equivalency class and to study the geometry of such a model. Therefore, it consists of two major parts: the minimal model program and the geometry of minimal models and Mori fiber spaces.
The purpose of this talk is to give a brief introduction and survey of my recent work with Meng Chen and Christopher Hacon on the birational geometry of threefolds.

Comment

Title

マルコフ過程の周遊理論とその応用
(Excursion theory of Markov processes and its applications)

Date

2011年6月1日（水）　16:30～17:30 　　 （16:00より105談話室でtea)

Place

Speaker

Abstract

Comment

Title

Coalgebra, its Logic, and some of its Mathematical Environments

Date

2011年5月25日（水）　16:30～17:30　　（16:00より１階ロビーでtea)

Place

Speaker

Yde Venema氏（京大・数理研 & University of Amsterdam）

Abstract

Computers and other electronic equipment are becoming more and prominent, both in our daily life, and in society as a whole. When we are confronted with undesired or incomprehensible behavior of for instance our mobile phone, we will naively start reasoning about the system, modelling it as a state-based evolving system, that we can only observe as a black box. Clearly, when it comes to specifying and reasoning about the behavior of critical software systems, a sophisticated mathematical theory is needed.
The theory of coalgebra, which has emerged from theoretical computer science in the last two decades, provides a general, mathematical framework for reasoning about such state-based evolving systems. It combines mathematical simplicity with wide applicability, due to its categorical foundations: many features such as input/output, nondeterminism, probability, and interaction can be encoded in the coalgebraic type which formally is a functor over Set (or some other base category). Coalgebra allows us to give precise mathematical definitions of notions such as behavior or observational equivalence of systems. Logic naturally enters the picture since we want to specify and reason about behavior in a formal way.
In the talk, we will give a very informal introduction and motivation of coalgebra and coalgebraic logic. We then briefly explain the dualities between algebra and coalgebra, and discuss the principle of coinduction. In the second part of the talk we describe some of the mathematical environments of the theory, and sketch how ideas from coalgebraic logic can be used to generalize results in topology (the Vietoris construction) and automata theory (Rabin's Theorem).

Comment

### 大談話会

Title

Continuous solutions of linear equations

Date

2011年5月18日（水）　14:40～15:40

Place

Speaker

János Kollár氏 (Princeton University)

Abstract

Consider a system of linear equations $A\cdot y=b$ where the entries of $A$ and of $b$ are themselves continuous functions on ${\mathbb R}^n$. Our aim is to decide whether the system has a solution where the entries of $y$ are also continuous functions on ${\mathbb R}^n$.
We pay special attention to the case when the entries of $A$ are polynomials but $b$ and $y$ are only continuous. (Joint work with Charles Fefferman.)

Comment 15:40-16:30 110号室にてTea Break

### 大談話会

Title

(On generalizations of the Shimura-Taniyama conjecture)

Date

2011年5月18日（水）　16:30～17:30

Place

Speaker

Abstract

Comment 15:40-16:30 110号室にてTea Break

Title

アフィンヘッケ環のLascoux-Leclerc-Thibon-Ariki理論について
(Affine Hecke algebras and Lascoux-Leclerc-Thibon-Ariki theory)

Date

2011年5月11日（水）　16:30～17:30 　　 （16:00より105談話室でtea)

Place

Speaker

Abstract

Comment

Title

A bound for the 2-edge-connected subgraph problem

Date

2011年4月27日（水）　16:30～17:30 　　 （16:00より１階ロビーでtea)

Place

Speaker

Ramamoorthi Ravi氏　（京大・数理研 & Tepper School of Business, Carnegie Mellon University）

Abstract

The minimum-cost traveling salesperson problem (TSP) that asks for a shortest Hamiltonian circuit is perhaps the most studied problem in combinatorial optimization. Since it is NP-complete, finding good approximation algorithms is an important area of study. A longstanding open problem in this direction concerns the metric version where the costs obey the triangle inequality. In this case, it has been widely conjectured that a shortest Hamilton circuit has cost at most four-thirds the value of the subtour linear programming (LP) relaxation. In the metric case, this LP relaxation coincides with the LP relaxation for finding a minimum-cost two-edge-connected subgraph.
The simplest fractional solutions to the subtour LP relaxation are half integral solutions where every edge variable is a multiple of half. We show that the minimum cost of a 2-edge-connected subgraph is at most four-thirds that of the minimum cost half-integral solution of the subtour relaxation, lending support to the conjecture.
This talk describes joint work with Robert Carr from Sandia National Laboratories.

Comment

Title

(Small points and canonical measures from the nonarchimedean viewpoint)

Date

2011年4月20日（水）　16:30～17:30 　　 （16:00より105談話室でtea)

Place

Speaker

Abstract

Comment

Title

ランダム媒質中の対称マルコフ連鎖の挙動とそのスケール極限
(Behavior of symmetric Markov chains on random media and their scaling limits)

Date

2011年4月13日（水）　16:30～17:30 　　 （16:00より１階ロビーでtea)

Place

Speaker

Abstract

Comment

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