## 過去の記録

#### 作用素環セミナー

16:30-18:00   数理科学研究科棟(駒場) 056号室

Spatial property of the canonical map associated to von Neumann algebras

#### 講演会

10:40-12:10   数理科学研究科棟(駒場) 128号室
Mikael Pichot 氏 (東大数理)
Topics in ergodic theory, von Neumann algebras, and rigidity
[ 講演参考URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/pichot.htm

### 2007年11月21日(水)

#### 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
Christopher Rasmussen 氏 (京都大学数理解析研究所)
Abelian varieties with constrained torsion
[ 講演概要 ]
The pro-$l$ Galois representation attached to the arithmetic fundamental group of a curve $X$ is heavily influenced by the arithmetic of certain classes of its branched covers. It is natural, therefore, to search for and classify these special covers in a meaningful way. When $X$ is the projective line minus three points, one finds that such covers are very scarce. In joint work with Akio Tamagawa, we formulate a conjecture to quanitify this scarcity, and present a proof for the conjecture in the case of genus one curves defined over $\\Q$.

#### 統計数学セミナー

16:20-17:30   数理科学研究科棟(駒場) 122号室

[ 講演概要 ]

[ 講演参考URL ]
https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2007/10.html

### 2007年11月20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

A certain slice of the character variety of a knot group
and the knot contact homology

[ 講演概要 ]
For a knot $K$ in 3-sphere, we can consider representations of
the knot group $G_K$ into $SL(2,\\mathbb{C})$.
Their characters construct an algebraic set.
This is so-called the $SL(2,\\mathbb{C})$-character variety of
$G_K$ and denoted by $X(G_K)$.

In this talk, we introduce a slice (a subset) $S_0(K)$ of $X(G_K)$.
In fact, this slice is closely related to the A-polynomial
and the abelian knot contact homology.
For example, the A-polynomial $A_K(m,l)$ of a knot $K$ is
a two-variable polynomial knot invariant defined by using
the character variety $X(G_K)$.
Then we can show that for any {\\it small knot} $K$, the number of
irreducible components of $S_0(K)$ gives an upper bound of
the maximal degree of the A-polynomial $A_K(m,l)$ in terms of
the variable $l$.
Moreover, for any 2-bridge knot $K$, we can show that
the coordinate ring of $S_0(K)$ is exactly the degree 0
abelian knot contact homology $HC_0^{ab}(K)$.

We will mainly explain these facts.

#### Lie群論・表現論セミナー

16:30-18:00   数理科学研究科棟(駒場) 126号室

Asymptotic cone for semisimple elements and the associated variety of degenerate principal series
[ 講演概要 ]
Let $a$ be a hyperbolic element in a semisimple Lie algebra over the real number field. Let $K$ be the complexification of a maximal compact subgroup of the corresponding real adjoint group. We study the asymptotic cone of the semisimple orbit through $a$ under the adjoint action by $K$. The resulting asymptotic cone is the associated variety of a degenerate principal series representation induced from the parabolic associated to $a$.
[ 講演参考URL ]
https://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html

### 2007年11月19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

### 2007年11月17日(土)

#### 保型形式の整数論月例セミナー

13:30-16:00   数理科学研究科棟(駒場) 123号室

Pullback formula for vector valued Siegel modular forms and its applications

[ 講演概要 ]
$H_n$ を $n$ 次 Siegel 上半空間, $E^n_k$ を次数 $n$, 重さ $k$ のSiegel Eisenstein 級数とする. いま $p$, $q$ を自然数としたとき,$H_p\\times H_q$ は $H_{p+q}$ の中に埋め込むことができる. Garrett は $E^{p+q}_k$ を $H_p\\times H_q$ 上に制限したときに Klingen Eisenstein 級数や Siegel 保型形式の standard $L$ 函数の値などで表示する公式を与へた. この公式は pullback formula とよばれてゐる.
この pullback formula はBoecherer によつて複素パラメータつきの Eisenstein 級数の場合に拡張され, Klingen Eisenstein 級数や standard $L$ 函数についての結果が得られてゐる.

Congruences connecting Tate-Shafarevich groups with Hurwitz numbers
[ 講演概要 ]

$h(-p)≡2^{-1}E_{(p-1)/2} mod p$
$h(-p)≡ -2B_{(p+1)/2} mod p$
となり, 右辺の最小の剰余は左辺そのものを与へます. 但し $B_n$ は Bernoulli 数, $E_n$ は Euler 数. この合同式の一般化として, ある種の楕円曲線の Tate-Shafarevich 群の位数の平方根と Hurwitz 数との間の同様な合同式を与へます.

#### 東京無限可積分系セミナー

13:00-16:30   数理科学研究科棟(駒場) 126号室
Gleb Novichkov 氏 (Keio Univ.) 13:00-14:30
Dynamical r-matrices coupled with dual Poisson Lie group
[ 講演概要 ]
The notion dynamical r-matrix coupled with Poisson manifold
is a natural generalization of the notion of the classical
dynamical r-matrix. We will consider special case when
Poisson manifold is a dual Poisson Lie group. We discuss
necessary conditions for the existence dynamical r-matrices
coupled with dual Poisson Lie groups and provide
some examples. We will also discuss some open questions
and possible relations to other subjects.
Vladimir V. Bazhanov 氏 (Australian National Univ.) 15:00-16:30
Yang-Baxter Equation and Quantum Geometry
[ 講演概要 ]
We demonstrate that certain integrable models
of statistical mechanics and quantum field theory
can be interpreted as quantization's of objects
of classical discrete geometry.
The fluctuating variables in these models take continuous
values. The classical geometry corresponds to stationary
configurations in the quasi-classical (or zero-temperature)
limit of the quantum system.
Our main example is the Faddeev-Volkov model which describes
the quantization of the circle patterns and associated with
the Thurston's discrete analogue of the Riemann mapping theorem
(discrete conformal transformations of the 2D plane).
Other examples will be also considered.
Finally we will discuss the geometric origins of integrability
which stem from from the classical results of Lam\\'e,
Darboux and Bianchi in differential geometry.

### 2007年11月15日(木)

#### 作用素環セミナー

16:30-18:00   数理科学研究科棟(駒場) 056号室

Generators of II$_1$ factors (Dykema-Sinclair-Smith-White)の紹介

### 2007年11月14日(水)

#### 統計数学セミナー

16:20-17:30   数理科学研究科棟(駒場) 122号室

Estimation of Distortion Risk Measures
[ 講演概要 ]
By Kusuoka's representation theorem, the class of distortion risk measures with convex distortions coincides with the set of coherent risk measures that are law invariant and comonotonically additive. The class includes the renowned expected shortfall which has many nice features and is of frequent use in practice. To implement the risk management/regulatory procedure using risk measures, it is necessary to estimate the values of such risk measures. For a distortion risk measure, its form suggests a natural estimator which is a simple form of $L$-statistics. We have seen in our previous work that it has nice asymptotic properties with i.i.d.\\ data. After reviewing these results briefly, we investigate the large sample properties of the estimator based on dependent data, especially GARCH sequences, which are often used for modelling financial time series data. Related issues such as semiparametric estimation with the extreme value theory and backtesting are briefly addressed.
[ 講演参考URL ]
https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2007/09.html

### 2007年11月13日(火)

#### 講演会

16:00-17:30   数理科学研究科棟(駒場) 052号室
Jens Starke 氏 (Technical University of Denmark)
Modelling the olfactory system: From receptor neuron dynamics over axonal pathfinding and sorting to spatio-temporal activities in the bulb
[ 講演概要 ]
The olfactory system of e.g. mice serves as important model case for other brain regions. The odor signals are processed from receptor neurons over the glomeruli level to a neural network of mitral and granular cells while various types of nonlinear behaviour can be observed.

(1) Nonlinear dynamics in receptor neurons:
A mathematical model for Ca oscillations in the cilia of olfactory
sensory neurons is suggested and analyzed. The existence of an oscillatory regime based on a Hopf bifurcation is proven using stoichiometric network analysis where the knowledge of exact parameters is not required. Predictions of the model are in quantitative agreement with experiment, both with respect to oscillations and to fast adaptation.

(2) Sorting by self-organization:
A many particle model with attracting and repulsive interactions is proposed which is able to reproduce the experimental findings of sorting and convergence during axonal pathfinding in the olfactory system. Many axon species, each represented by a huge number of axons, are spatially disordered at the beginning of their growth at the receptor neurons and converge by a self-organized process to a sorted state, i.e. axons of the same receptor type converge to a common position. Under certain model assumptions, it can be proved that the interacting many-particle system of different particle types converges to a sorted state.

(3) Spatio-temporal pattern formation in the olfactory bulb:
Odors evoke a variety of stimulus specific spatio-temporal patterns on the levels of glomeruli and neural network of mitral and granular cells in the olfactory bulb which can be measured in vivo using Ca and voltage sensitive dyes for optical imaging. A spatial independent component analysis of this high-resolution imaging data was used to identify and separate different neuronal populations based on their stimulus specific spatio-temporal activation. Equation-free techniques were used to obtain bifurcation diagramms for the network activity. First, contrast enhancement between several spatially close activations depending on the network topology and second, hysteres effects in recognition of differences between similar odorants depending on the concentration ratios of odorant mixtures.

This is in parts joint work with P. Borowski, M. Eiswirth, C. Ellsaesser, A. Grinvald, N. Hummel, S. Kokkendorff, D. Omer, J. Reidl, H. Spors, J. Strotmann, M. Zapotocky.

### 2007年11月12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

### 2007年11月09日(金)

#### 談話会・数理科学講演会

16:40-17:40   数理科学研究科棟(駒場) 123号室
お茶&Coffee&お菓子: 16:10～16:40(コモンルーム)

[ 講演概要 ]
70年代にRayとSingerは位相幾何学におけるReidemeister捩率の解析的類似を考察し,解析的捩率と呼ばれるスペクトル不変量を導入した. de Rham複体とDolbeault複体に対応して, 解析的捩率には実解析的捩率と正則解析的捩率の二種類の理論があり,80年代から現在に至るBismutの研究により両理論は長足の発展を遂げた.

### 2007年11月08日(木)

#### 代数幾何学セミナー

16:30-18:00   数理科学研究科棟(駒場) 118号室
Alexandru DIMCA 氏 (Univ Nice )
New restrictions on the fundamental groups of complex algebraic varieties
[ 講演概要 ]
My talk will be based on joint work with S. Papadima (Bucarest, Romania) and A. Suciu (Boston, USA). First I will recall the basic facts on characteristic varieties $V_k(M)$ associated to rank one local systems on a complex algebraic variety $M$ which are due to Beauville, Simpson and Arapura. Then I will introduce the resonance varities $R_k(M)$, which may be related to the Isotropic Subspace Theorems by Catanese and Bauer. One of the main new results is that for a class of algebraic varieties (the 1-formal ones), the two types of varieties $V_k(M)$ and $R_k(M)$ are strongly related. Applications to right angle Artin groups, Bestvina-Brady groups and to a conjecture by Kollar will be discussed in the end.

#### 応用解析セミナー

16:00-17:30   数理科学研究科棟(駒場) 126号室

[ 講演概要 ]
This talk is based on the joint work with Kotaro Morimoto (Tokyo Metropolitan University).

We are concerned with stationary solutions to the following reaction diffusion system which is called the Gierer-Meinhardt system with saturation.
$A_t=\\epsilon^2 \\Delta A-A+A^2/(H(1+kA^2), A>0,$
$\\tau H_t=D\\Delta H-H+A2, H>0,$
where $\\epsilon >0$, $\\tau \\geq 0$, $k>0$.
The unknowns $A$ and $H$ represent the concentrations of the activator and the inhibitor. Here $\\Omega$ is a bounded smooth domain in $R^N$ and we consider homogeneous Neumann boundary conditions. When $\\Omega$ is an $x_N$-axially symmetric domain and $2\\leq N\\leq 5$, for sufficiently small $\\epsilon>0$ and large $D>0$, we construct a multi-peak stationary solution peaked at arbitrarily chosen intersections of $x^N$-axis and $\\partial \\Omega$, under the condition that $k\\epsilon^{-2N}$ converges to some $k_0\\in[0,\\infty)$ as $\\epsilon \\to 0$.

In my talk, I will explain related results comparing the differences between the case $k=0$ and $k>0$, the basic strategy of the proof of our results with some details, and open questions.

### 2007年11月07日(水)

#### 統計数学セミナー

16:20-17:30   数理科学研究科棟(駒場) 122号室

ハプロタイプ関連解析:EMアルゴリズムによるアプローチ
[ 講演概要 ]

[ 講演参考URL ]
https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2007/08.html

### 2007年11月06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

Thustion's inequality and open book foliations
[ 講演概要 ]
We will study codimension 1 foliations on 3-manifolds.
Thurston's inequality, which implies convexity of the foliation in
some sense, folds for Reebless foliations [Th]. We will discuss
whether the inequality holds or not for open book foliations.
[Th] W. Thurston: Norm on the homology of 3-manifolds, Memoirs of the
AMS, 339 (1986), 99--130.

#### Lie群論・表現論セミナー

15:00-16:30   数理科学研究科棟(駒場) 126号室
Michaël Pevzner 氏 (Université de Reims and University of Tokyo)
Quantization of symmetric spaces and representation. IV
[ 講演参考URL ]
https://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html

#### Lie群論・表現論セミナー

16:30-18:00   数理科学研究科棟(駒場) 126号室

Multiplicity-free decompositions of the minimal representation of the indefinite orthogonal group
[ 講演参考URL ]
https://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html

### 2007年11月01日(木)

#### Lie群論・表現論セミナー

16:30-18:00   数理科学研究科棟(駒場) 052号室
Michaël Pevzner 氏 (Université de Reims and University of Tokyo)
Quantization of symmetric spaces and representation. III
[ 講演概要 ]
Kontsevich's formality theorem and applications in Representation theory.

We shall first give an explicit construction of an associative star-product on an arbitrary smooth finite-dimensional Poisson manifold.

As application, we will consider in details the crucial example of the dual of a finite-dimensional Lie algebra and will sketch a generalization of the Duflo isomorphism describing the set of infinitesimal characters of irreducible unitary representations of the corresponding Lie group.
[ 講演参考URL ]
https://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html

### 2007年10月31日(水)

#### 統計数学セミナー

16:20-17:30   数理科学研究科棟(駒場) 122号室

[ 講演概要 ]

[ 講演参考URL ]
https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2007/07.html

#### 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
Pierre Colmez 氏 (Ecole Polytechnique)
On the p-adic local Langlands correspondance for GL2(Qp)

### 2007年10月30日(火)

#### Lie群論・表現論セミナー

16:30-18:00   数理科学研究科棟(駒場) 126号室

On Weyl groups for parabolic subalgebras
[ 講演概要 ]
Let ${\\mathfrak g}$ be a complex semisimple Lie algebra.
We call a parabolic subalgebra ${\\mathfrak p}$ of ${\\mathfrak g}$
normal, if any parabolic subalgebra which has a common Levi part with ${\\mathfrak p}$
is conjugate to ${\\mathfrak p}$ under an inner automorphism of ${\\mathfrak g}$.
For a normal parabolic subalgebra, we have a good notion of the restricted root system
or the little Weyl group. We have a comparison result on the Bruhat order on the Weyl group for
${\\mathfrak g}$ and the little Weyl group.
We also apply this result to the existence problem of the homomorphisms between scalar generalized Verma modules.
[ 講演参考URL ]
https://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html

#### Lie群論・表現論セミナー

15:00-16:30   数理科学研究科棟(駒場) 126号室
Michaël Pevzner 氏 (Université de Reims and University of Tokyo)
Quantization of symmetric spaces and representation. II
[ 講演概要 ]
Back to Mathematics. Two methods of quantization.