## 過去の記録

### 2010年10月14日(木)

#### 作用素環セミナー

16:30-18:00   数理科学研究科棟(駒場) 122号室

Nonstandard analysis for operator algebraists (JAPANESE)

### 2010年10月12日(火)

#### トポロジー火曜セミナー

16:30-18:00   数理科学研究科棟(駒場) 056号室
Tea: 16:00 - 16:30 コモンルーム
Andrei Pajitnov 氏 (Univ. de Nantes, 東京大学大学院数理科学研究科)
Asymptotics of Morse numbers of finite coverings of manifolds (ENGLISH)
[ 講演概要 ]
Let X be a closed manifold;
denote by m(X) the Morse number of X
(that is, the minimal number of critical
points of a Morse function on X).
Let Y be a finite covering of X of degree d.

In this survey talk we will address the following question
posed by M. Gromov: What are the asymptotic properties
of m(N) as d goes to infinity?

It turns out that for high-dimensional manifolds with
free abelian fundamental group the asymptotics of
the number m(N)/d is directly related to the Novikov homology
of N. We prove this theorem and discuss related results.

### 2010年10月08日(金)

#### 談話会・数理科学講演会

16:30-17:30   数理科学研究科棟(駒場) 123号室

お茶&Coffee&お菓子: 16:00～16:30 (コモンルーム)。

$3+¥ell$ ($¥ell=1,2,¥ldots$) 個の確定特異点を持つ
Schroedinger (Sturm-Liouville)方程式の解としての例外Jacobi多項式 (JAPANESE)
[ 講演概要 ]
3個(超幾何),4個(Heun)より多くの確定特異点を持つFuchs型微分方程式の大域解は,今までほとんど知られていない.この話では,$3+¥ell$ ($¥ell=1,2,¥ldots$)個の確定特異点を持つSchroedinger (Sturm-Liouville)方程式の解の完全系の具体形を与える.この方程式は,次のようなHamiltonian (Schroedinger作用素)を持つ Darboux-P¥"oschl-Tellerポテンシャル¥[ ¥mathcal{H}=-¥frac{d^2}{dx^2}+¥frac{g(g-1)}{¥sin^2x}+¥frac{h(h-1)} {¥cos^2x} ¥]の変形である.固有関数は例外 Jacobi多項式$¥{P_{¥ell,n}(¥eta)¥}$, $n=0,1,2,¥ldots$, からなり,その次数はdeg($P_{¥ell,n}$)$=n+¥ell$である.従ってBochnerの定理による制約を受けない.合流型の極限から2種類の例外Laguerre多項式,$¥ell=1,2,¥ldots$が得られる. 同様の変形方法によって,例外WilsonおよびAskey-Wilson多項式,$¥ell=1,2,¥ldots$が得られる.

### 2010年10月06日(水)

#### 東京幾何セミナー

14:45-18:00   数理科学研究科棟(駒場) 056号室

「今後の予定」欄には、東工大で行われるセミナーは表��

Handle attaching in wrapped Floer homology and brake orbits in classical Hamiltonian systems (JAPANESE)
[ 講演概要 ]
In this talk, the term "classical Hamiltonian systems" means special types of Hamiltonian systems, which describe solutions of classical equations of motion. The study of periodic solutions of Hamiltonian systems is an interesting problem, and for classical Hamiltonian systems, the following result is known : for any compact and regular energy surface $S$, there exists a brake orbit (a particular type of periodic solutions) on $S$. This result is first proved by S.V.Bolotin in 1978, and it is a special case of the Arnold chord conjecture. In this talk, I will explain that calculations of wrapped Floer homology (which is a variant of Lagrangian Floer homology) give a new proof of the above result.

Mirror Symmetry for Weighted Homogeneous Polynomials (JAPANESE)
[ 講演概要 ]
First we give an overview of the algebraic and the geometric aspects of the mirror symmetry conjecture for weighted homogeneous polynomials. Then we concentrate on polynomials in three variables, and show the existence of full (strongly) exceptional collection of categories of maximally graded matrix factorizations for invertible weighted homogeneous polynomials. We will also explain how the mirror symmetry naturally explains and generalizes the Arnold's strange duality between the 14 exceptional unimodal singularities.

#### 代数学コロキウム

16:30-17:30   数理科学研究科棟(駒場) 117号室
いつもと教室が異なりますのでご注意ください
Hélène Esnault 氏 (Universität Duisburg-Essen)
Finite group actions on the affine space (ENGLISH)
[ 講演概要 ]
If $G$ is a finite $\\ell$-group acting on an affine space $\\A^n$ over a
finite field $K$ of cardinality prime to $\\ell$, Serre shows that there
exists a rational fixed point. We generalize this to the case where $K$ is a
henselian discretely valued field of characteristic zero with algebraically
closed residue field and with residue characteristic different from $\\ell$.
We also treat the case where the residue field is finite of cardinality $q$
such that $\\ell$ divides $q-1$. To this aim, we study group actions on weak
N\\'eron models.
(Joint work with Johannes Nicaise)

#### 統計数学セミナー

15:00-16:10   数理科学研究科棟(駒場) 000号室

Elasticnet型正則化を持つMultiple Kernel Learningについて (JAPANESE)
[ 講演概要 ]
Mutiple Kernel Learning (MKL) はGroup Lassoをカーネル法へ拡張した手法であり,

カーネルを学習する方法である.凸最適化で解ける点と多くのカーネルの結合係数
を0にさせるスパース性を有するという利点がある.しかし最近になって,一様重みで

スさ」が画像認識などの応用で良い性能を示すことが実験的に示されている.本発表
ではその「中間的なスパースさ」を実現する方法としてelasticnet型正則化を持つ
MKLを扱い,その効率的な計算アルゴリズムや,漸近的な収束性能について議論する.

[ 講演参考URL ]
https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2010/05.html

### 2010年10月04日(月)

#### 複素解析幾何セミナー

10:30-12:00   数理科学研究科棟(駒場) 128号室

The canonical coordinates associated to homogeneous Kaehler metrics on a homogeneous bounded domain (JAPANESE)
[ 講演概要 ]
For a real analytic Kaehler manifold, one can define a canonical coordinate, called the Bochner coordinate, around each point. In this talk, we show that the canonical cooredinate is globally defined for a bounded homogeneous domain with a homogeneous Kaehler manifold, which is not necessarily the Bergman metric.
Then we obtain a standard realization of the homogeneous domain associated to the homogeneous metric.

### 2010年09月28日(火)

#### 解析学火曜セミナー

16:30-18:00   数理科学研究科棟(駒場) 128号室
Pavel Exner 氏 (Czech Academy of Sciences)
Some spectral and resonance properties of quantum graphs (ENGLISH)
[ 講演概要 ]
In this talk I will discuss three new results about Schr¨odinger operators
on metric graphs obtained in collaboration with Jiri Lipovskyand Brian Davies.
The first one is related to invalidity of the uniform continuation principle for such
operators. One manifestation of this fact are embedded eigenvalues due to
rational relations of graph edge lengths. This effect is non-generic and we show
how geometric perturbations turn these embedded eigenvalues into resonances.
Then second problem is related to high-energy behavior of resonances: we extend
a recent result of Davies and Pushnitski to graphs with general vertex couplings
and find conditions under which the asymptotics does not have Weyl character.
Finally, the last question addressed here concerns the absolutely continuous spectrum
of radial-tree graphs. In a similar vein, we generalize a recent result by Breuer and
Frank that in case of the free (or Kirhhoff) coupling the ac spectrum is absent
provided the edge length are increasing without a bound along the tree.
We show that the result remains valid for a large class of vertex couplings,
but on the other hand, there are nontrivial couplings leading to an ac spectrum.

### 2010年09月14日(火)

#### 東京無限可積分系セミナー

10:30-14:00   数理科学研究科棟(駒場) 117号室

AGT予想とrecursion formula (JAPANESE)

BelavinのR行列の3角極限に対する反射方程式の解の分類 (JAPANESE)

### 2010年09月13日(月)

#### 東京無限可積分系セミナー

10:30-15:30   数理科学研究科棟(駒場) 117号室

$C^¥vee C$型DAHAの多項式表現と境界付きqKZ方程式について (JAPANESE)
[ 講演概要 ]
まずC-check-C型ダブルアフィンヘッケ代数と
その多項式表現について基本的な事柄を復習する.

CFT , モノドロミー保存変形, Nekrasov関数 (JAPANESE)
[ 講演概要 ]

(Alday-Gaiotto-Tachikawa予想)に関して, 微分方程式
(特に
モノドロミー保存変形)の観点から紹介する.

Twisted de Rham theory---resonances and the non-resonance (JAPANESE)

### 2010年09月12日(日)

#### 東京無限可積分系セミナー

10:30-17:00   数理科学研究科棟(駒場) 117号室

マクドナルド多項式のベキ根における分解公式 (JAPANESE)
[ 講演概要 ]
We consider a combinatorial property of Macdonald polynomials at roots
of unity.
If we made some plethystic substitution to the variables,
Macdonald polynomials are subjected to a certain decomposition rule
when a parameter is specialized at roots of unity.
We review the result and give an outline of the proof.
This talk is based on a joint work with F. Descouens.

W代数と対称多項式 (JAPANESE)
[ 講演概要 ]
It is well known that we have the factorization property of the Macdonald polynomials under the principal specialization $x=(1,t,t^2,t^3,¥cdots)$. We try to better understand this situation in terms of the Ding-Iohara algebra or the deformend $W$-algebra. Some conjectures are presented in the case of $N$-fold tensor representation of the Fock modules.

Quantizing the difference Painlev¥'e VI equation (JAPANESE)
[ 講演概要 ]
I will review two constructions for quantum (=non-commutative) version of
q-difference Painleve VI equation.

1の巾根でのMacdonald多項式の分解公式の組合せ論的証明について (JAPANESE)
[ 講演概要 ]
The subject of this talk is a factorization formula for the special
values of modied Macdonald polynomials at roots of unity.
We give a combinatorial proof of the formula, via a result by
Haglund--Haiman--Leohr, for some special classes of partitions,
including two column partitions.
(This talk is based on a joint work with F. Descouens and H. Morita.)

### 2010年09月11日(土)

#### 東京無限可積分系セミナー

13:00-17:00   数理科学研究科棟(駒場) 117号室

$BC_n$型$q$-超幾何関数の三項間隣接関係式とその応用 (JAPANESE)
[ 講演概要 ]
この講演における$BC_n$型$q$-超幾何関数とは、
ガウスの超幾何関数の積分表示のある種の$q$-類似であり、

この$q$-超幾何級数に含まれるパラメータの個数が6+1個の場合に、
ある対称多項式の族を定義すると(ここではBC型補間多項式と呼ぶ)、
ガウスの超幾何関数の隣接関係式に類似の三項間関係式が

この$q$-超幾何級数が満たすランクn+1の一階連立$q$-差分方程式系を

Gustafson の$q$-積分の無限積表示の別証明が得られるので、
それも紹介したい。

TBA (JAPANESE)

AGT予想と幾何工学 (JAPANESE)
[ 講演概要 ]

えられている
AGT予想について議論する。

その結果、局所Calabi-Yau多様体上のcurve countingから、

る。

### 2010年09月09日(木)

#### 講演会

16:30-18:00   数理科学研究科棟(駒場) 126号室
Bernhard Mühlherr 氏 (Justus-Liebig-Universität Gießen)
Mini-course on Buildings (3/3) (ENGLISH)
[ 講演概要 ]
The goal of this course is to provide an overview on the theory of buildings which was developed by Jacques Tits.

The third lecture will be then devoted to classification results,
mainly the classification of spherical buildings. However, I will try to say some words on the classification of affine buildings and twin buildings as well.

This is Part 3 of a 3-part lecture.

### 2010年09月06日(月)

#### 代数幾何学セミナー

16:40-18:10   数理科学研究科棟(駒場) 126号室
Prof. Remke Kloosterman 氏 (Humboldt University, Berlin)
Non-reduced components of the Noether-Lefschetz locus (ENGLISH)
[ 講演概要 ]
Let $M_d$ be the moduli space of complex smooth degree $d$ surfaces in $\\mathbb{P}3$. Let $NL_d \\subset M_d$ be the subset corresponding to surfaces with Picard number at least 2. It is known that $NL_r$ is Zariski-constructable, and each irreducible component of $NL_r$ has a natural scheme structure. In this talk we describe the largest non-reduced components of $NL_r$. This extends work of Maclean and Otwinowska.
This is joint work with my PhD student Ananyo Dan.

### 2010年09月04日(土)

#### 講演会

09:30-11:00   数理科学研究科棟(駒場) 126号室
Bernhard Mühlherr 氏 (Justus-Liebig-Universität Gießen)
Mini-course on Buildings (1/3) (ENGLISH)
[ 講演概要 ]
The goal of this course is to provide an overview on the theory of buildings which was developed by Jacques Tits.

In my first lecture I will begin by introducing generalized polygons, namely rank two spherical buildings, and discussing several aspects of them which will be generalized later, and then move on to defining Coxeter complexes and giving the classical definition of buildings as simplicial complexes. I will try to include as many examples as possible.

This is Part 1 of a 3-part lecture. The second lecture will follow after a ten-minute break.

#### 講演会

11:10-12:40   数理科学研究科棟(駒場) 126号室
Bernhard Mühlherr 氏 (Justus-Liebig-Universität Gießen)
Mini-course on Buildings (2/3) (ENGLISH)
[ 講演概要 ]
The goal of this course is to provide an overview on the theory of buildings which was developed by Jacques Tits.

In my second lecture I will start with chamber systems and coset
geometries, introducing some special properties of chamber systems in order to give another definition of a building. This definition is less standard but it will give some results on presentations of groups acting on buildings for free. In particular it will enable me to present a sketch of a proof of the Curtis-Tits theorem for Chevalley groups and to formulate Tits' extension theorem.

This is Part 2 of a 3-part lecture. Part 1 takes place ealier on the same day. Part 3 will take place on Thursday, September 9.

### 2010年09月03日(金)

#### 講演会

14:30-15:30   数理科学研究科棟(駒場) 370号室
Luc Robbiano 氏 (University of Versailles)
Carleman estimates and boundary problems. (JAPANESE)
[ 講演概要 ]
In this presentation, based on joint works with Jerome LeRousseau and Matthieu Leautaud, we consider boundary problems for elliptic/parabolic operators. We prove Carleman estimates in such cases. One of the interest for such an estimate is the implied controllability of (semi-linear) heat equations.

One of the main aspects of the proof is a microlocal decomposition separating high and low tangential frequencies.

If time permits, we will present how such an approach can be used to prove Carleman estimates in the case of non smooth coefficients at an interface, possibly with an additional diffusion process along the interface.

### 2010年09月01日(水)

#### Lie群論・表現論セミナー

16:30-18:00   数理科学研究科棟(駒場) 002号室
いつもと場所が違います
Bernhard M\"uhlherr 氏 (Justus-Liebig-Universit\"at Giessen)
Groups of Kac-Moody type (ENGLISH)
[ 講演概要 ]
Groups of Kac-Moody type are natural generalizations of Kac-Moody groups over fields in the sense that they have an RGD-system. This is a system of subgroups indexed by the roots of a root system and satisfying certain commutation relations.
Roughly speaking, there is a one-to-one correspondence between groups of Kac-Moody type and Moufang twin buildings. This correspondence was used in the last decade to prove several group theoretic results on RGD-systems and in particular on Kac-
Moody groups over fields.

In my talk I will explain RGD-systems and how they provide twin
buildings in a natural way. I will then present some of the group theoretic applications mentioned above and describe how twin buildings are used as a main tool in their proof.

#### 博士論文発表会

16:30-17:45   数理科学研究科棟(駒場) 123号室

On the moduli spaces of finite flat models of Galois representations （Galois表現の有限平坦モデルのモジュライ空間について） (JAPANESE)

### 2010年08月06日(金)

#### 講演会

15:30-17:45   数理科学研究科棟(駒場) 370号室
Leevan Ling 氏 (Hong Kong Baptist University) 15:30-16:30
A Spectral Method for Space--
Time Fractional Diffusion Equation (ENGLISH)
Mourad Choulli 氏 (University of Metz) 16:45-17:45
A multidimensional Borg-Levinson theorem (ENGLISH)

#### GCOEセミナー

15:00-16:30   数理科学研究科棟(駒場) 122号室
Matthieu Alfaro 氏 (University Montpellier 2)
Motion by mean curvature and Allen-Cahn equations (ENGLISH)
[ 講演概要 ]
After introducing the classical and the generalized motion by mean curvature, we give some connections with the singular limit of Allen-Cahn equations in both framework. New results and estimates shall be provided.

### 2010年08月05日(木)

#### 講演会

16:30-17:30   数理科学研究科棟(駒場) 370号室
Yongzhi Steve Xu 氏 (University of Louisville, USA)
Radiation Conditions for Wave in Stratified Medium and Related Inverse
Problems (ENGLISH)

#### 講演会

16:30-17:30   数理科学研究科棟(駒場) 370号室
Yongzhi Steve Xu 氏 (University of Louisville, USA)
Radiation Conditions for Wave in Stratified Medium and Related Inverse Problems (ENGLISH)

### 2010年07月30日(金)

#### GCOEセミナー

16:30-17:30   数理科学研究科棟(駒場) 370号室
Oleg Emanouilov 氏 (Colorado State University)
Global uniqueness in determining a coefficient by boundary data on small subboundaries (ENGLISH)
[ 講演概要 ]
We consider the Dirichlet problem for the stationary two-dimensional Schroedinger equation. We discuss an inverse boundary value problem of determining the potential from a pair of all Dirichlet data supported in a subboundary S+ and all the corresponding Neumann data taken only on a subboundary S-. In the case where S+ = S- are the whole boundary, the data are the classical Dirichlet to Neumann map and there are many uniqueness results, while in the case where S+=S- is an arbitrary subboundary, Imanuvilov-Uhlmann-Yamamoto (2010) proves the uniqueness. In this talk, for the case where S+ and S- are not same, we prove the global uniqueness for this inverse problem under a condition only on the locations of S+, S-. We note that within the condition, S+ and S- can be arbitrarily small. The key of the proof is the construction of suitable complex geometrical optics solutions by a Carleman estimate with singular weight function.

### 2010年07月29日(木)

#### 代数幾何学セミナー

14:30-16:00   数理科学研究科棟(駒場) 126号室
いつもと曜日・時間帯が異なります。ご注意ください。

Homological Mirror Symmetry for 2-dimensional toric Fano stacks (JAPANESE)
[ 講演概要 ]
Homological Mirror Symmetry (HMS for short) is a conjectural
duality between complex and symplectic geometry, originally proposed
for mirror pairs of Calabi-Yau manifolds and later extended to
Fano/Landau-Ginzburg mirrors (both due to Kontsevich, 1994 and 1998).

We explain how HMS is established in the case of 2-dimensional smooth
toric Fano stack X as an equivalence between the derived category of X
and the derived directed Fukaya category of its mirror Lefschetz
fibration W. This is related to Kontsevich-Soibelman's construction of
3d CY category from the quiver with potential.

We also obtain a local mirror extension following Seidel's suspension
theorem, that is, the local HMS for the canonical bundle K_X and the
double suspension W+uv. This talk is joint with Kazushi Ueda (Osaka
U.).