## 過去の記録

#### 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

Characterization of some smooth vectors for irreducible representations of exponential solvable Lie groups
[ 講演参考URL ]
http://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html

### 2007年12月10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

#### Kavli IPMU Komaba Seminar

17:00-18:30   数理科学研究科棟(駒場) 002号室
Dmitry Kaledin 氏 (Steklov Institute and The University of Tokyo)
Deligne conjecture and the Drinfeld double.
[ 講演概要 ]
Deligne conjecture describes the structure which exists on
the Hochschild cohomology $HH(A)$ of an associative algebra
$A$. Several proofs exists, but they all combinatorial to a certain
extent. I will present another proof which is more categorical in
nature (in particular, the input data are not the algebra $A$, but
rather, the tensor category of $A$-bimodules). Combinatorics is
still there, but now it looks more natural -- in particular, the
action of the Gerstenhaber operad, which is know to consist of
homology of pure braid groups, is induced by the action of the braid
groups themselves on the so-called "Drinfeld double" of the category
$A$-bimod.

If time permits, I will also discuss what additional structures
appear in the Calabi-Yau case, and what one needs to impose to
insure Hodge-to-de Rham degeneration.

### 2007年12月06日(木)

#### 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 ]
http://www.ms.u-tokyo.ac.jp/~yasuyuki/pichot.htm

#### 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 ]
この講演では,藤田型の半線形放物型偏微分方程式に関する M. Fila, J. King, P. Polacik, M. Winkler らとの共同研究による成果についてその概要を紹介する.全空間上の藤田型方程式については,これまで様々な挙動を示す時間大域解の存在が示されている.そこで大域解の時間的挙動と初期値の空間的挙動の関係を詳細に調べることにより,大域解をいくつかに分類し,その挙動がそれぞれ異なるメカニズムに支配されていることを明らかにする.時間が許せば,最近の進展や関連する話題についても触れる予定である.

### 2007年12月05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

Classification of two dimensional trianguline representations of p-adic fields
[ 講演概要 ]
Trianguline representation is a class of p-adic Galois representations of p-adic fields. This was defined by P.Colmez by using ($\\varphi, \\Gamma$)-modules over Robba ring. In his study of p-adic local Langlands correspondence of GL_2(Q_p), he completely classified two dimensional trianguline representations of Q_p. On the other hand, L.Berger recently defined the category of B-pairs and established the equivalence between the category of B-pairs and the category of ($\\varphi,\\Gamma$)-modules over Robba ring. In this talk, we extend the Colmez's result by using B-pairs. We completely classify two dimensional trianguline representations of K for any finite extension of Q_p. We also talk about a relation between two dimensional trianguline representations and principal series or special series of GL_2(K).

#### 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

A Decision-Theoretic Approach to Estimation from Wishart matrices on Symmetric Cones
[ 講演概要 ]
James and Stein(1961) have considered the problem of estimating the mean matrix of Wishart distributions under so-called Stein's loss function and obtained a minimax estimator with a constant risk. Later Stein(1977) has given an unbiased risk estimate for a class of orthogonally invariant estimators, from which he obtained orthogonally invariant minimax estimators which are uniformly better than the best triangular-invariant estimator in James and Stein(1961). The works mentioned above lead to the following natural question: Is it possible for any estimators to improve upon the maximum likelihood estimator for the mean matrix of the complex or quaternion Wishart distributions? This talk shows that we can obtain improved estimators for the mean matrix under these models in a unified manner. The method involves an abstract theory of finite-dimensional Euclidean simple Jordan algebra
[ 講演参考URL ]
http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2007/11.html

### 2007年12月04日(火)

#### 諸分野のための数学研究会

15:00-17:15   数理科学研究科棟(駒場) 122号室
Pavel Krejci 氏 (Weierstrass Institute for Applied Analysis and Stochastics) 15:00-16:00
Quasilinear hyperbolic equations with hysteresis
[ 講演概要 ]
We consider a wave propagation problem in a rate independent elastoplastic material described by a counterclockwise convex hysteresis operator. Unlike in viscoelasticity, the speed of propagation is bounded above by the speed of the corresponding elastic waves. The smoothening dissipative effect is due to the convexity of the hysteresis branches. We present some recent results on the long time behavior of solutions under various boundary conditions, including the stability of time periodic solutions under periodic forcing.
[ 講演参考URL ]
http://coe.math.sci.hokudai.ac.jp/sympo/various/index.html
Victor Isakov 氏 (Wichita State University) 16:15-17:15
Carleman estimates for second order operators with two large parameters
[ 講演概要 ]
We obtain new Carleman type estimates for general second order linear partial differential operators. These estimates hold for the weight functions under pseudoconvexity conditions relating the operator and weight function. We discuss these conditions. We give applications to uniqueness and stability of the continuation and inverse problems for elasticity system with residual stress without smallness assumptions on residual stress. This is a joint work with Nanhee Kim.
[ 講演参考URL ]
http://coe.math.sci.hokudai.ac.jp/sympo/various/index.html

#### 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

Morse theory for abelian hyperkahler quotients

[ 講演概要 ]
In 1980's Kirwan computed Betti numbers of symplectic quotients by using Morse theory. In this talk, we develop this method to hyperkahler quotients by abelian Lie groups. In this method, many computations are much more simplified in the case of hyperkahler quotients than the case of symplectic quotients. As a result we compute not only the Betti numbers, but also the cohomology rings of abelian hyperkahler quotients.

### 2007年12月03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29日(木)

#### 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 ]
http://www.ms.u-tokyo.ac.jp/~yasuyuki/pichot.htm

### 2007年11月27日(火)

#### 代数幾何学セミナー

16:30-18:00   数理科学研究科棟(駒場) 122号室
Alexander Kuznetsov 氏 (Steklov Inst)
Categorical resolutions of singularities
[ 講演概要 ]
I will give a definition of a categorical resolution of singularities and explain how such resolutions can be constructed.

#### 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

Heaviside's theory of signal transmission on submarine cables

#### 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 quandle cocycle invariant for handlebody-links

[ 講演概要 ]
[joint work with Masahide Iwakiri (Osaka City University)]
A handlebody-link is a disjoint union of circles and a
finite trivalent graph embedded in a closed 3-manifold.
We consider it up to isotopies and IH-moves.
Then it represents an ambient isotopy class of
handlebodies embedded in the closed 3-manifold.
In this talk, I explain how a quandle cocycle invariant

### 2007年11月26日(月)

#### Kavli IPMU Komaba Seminar

17:00-18:30   数理科学研究科棟(駒場) 002号室
Mich\"ael Pevzner 氏 (Universit\'e de Reims and the University of Tokyo)
Kontsevich quantization of Poisson manifolds and Duflo isomorphism.
[ 講演概要 ]
Abstract: Since the fundamental results by Chevalley, Harish-Chandra and Dixmier one knows that the set of invariant polynomials on the dual of a Lie algebra of a particular type (solvable, simple or nilpotent) is isomorphic, as an algebra, to the center of the enveloping algebra. This fact was generalized to an arbitrary finite-dimensional real Lie algebra by M. Duflo in late 1970's. His proof was based on the Kirillov's orbits method that parametrizes infinitesimal characters of unitary irreducible representations of the corresponding Lie group in terms of co-adjoint orbits.

The Kontsevich' Formality theorem implies not only the existence of the Duflo map but shows that it is canonical. We shall describe this construction and indicate how does this construction extend to the whole Poisson cohomology of an arbitrary finite-dimensional real Lie algebra.

#### 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

Analysis related to probability theory based on p-adic hierarchical structure

### 2007年11月22日(木)

#### 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

Critical frequencyをもつ非線形シュレディンガー方程式のマルチピーク解
[ 講演概要 ]

$$-\\epsilon2 \\Delta u +V(x)u= u^p, u>0 \\ \\hbox{in} \\R^N, u\\in H1(\\R^N)$$
において、$\\epsilon \\to 0$ としたときに V(x) の k個の極小点にピークが集中していくマルチピーク解 $u_\\epsilon$ について考える。
ここで、p はsuperlinear, subcriticalの条件を満たし, ポテンシャル関数 V(x) は非負の有界な関数で $\\liminf_{|x|\\to \\infty}V(x)>0$ を満たすとする。

もし V(x) の各極小点に集中するピークがあるとしたら、そのピークの形状や大きさはその極小値が正であるか、0であるかによって大きく異なることが知られている。
この講演では V(x) の各極小値が正であるか 0 であるかにかかわらず、各 k個の極小点にピークが集中するマルチピーク解 $u_\\epsilon$ を構成する。

#### 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 ]
http://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 ]
http://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 ]
http://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.