## 過去の記録

#### トポロジー火曜セミナー

17:00-18:30   数理科学研究科棟(駒場) 056号室
Tea: 16:40 -- 17:00 コモンルーム
Jer\^ome Petit 氏 (東京工業大学, JSPS)
Turaev-Viro TQFT splitting.
[ 講演概要 ]
The Turaev-Viro invariant is a 3-manifolds invariant. It is obtained in this way :
1) we use a combinatorial description of 3-manifolds, in this case it is : triangulation / Pachner moves
2) we define a scalar thanks to a categorical data (spherical category) and a topological data (triangulation)
3)we verify that the scalar is invariant under Pachner moves, then we obtain a 3-manifolds invariant.

The Turaev-Viro invariant can also be extended to a TQFT. Roughly speaking a TQFT is a data which assigns a finite dimensional vector space to every closed surface and a linear application to every 3-manifold with boundary.

In this talk, we will give a decomposition of the Turaev-Viro TQFT. More precisely, we decompose it into blocks. These blocks are given by a group associated to the spherical category which was used to construct the Turaev-Viro invariant. We will show that these blocks define a HQFT (roughly speaking a TQFT with an "homotopical data"). This HQFT is obtained from an homotopical invariant, which is the homotopical version of the Turaev-Viro invariant. Moreover this invariant can be used to obtain the homological Turaev-Viro invariant defined by Yetter.

#### Lie群論・表現論セミナー

16:45-18:15   数理科学研究科棟(駒場) 126号室

Lipsman予想の反例と代数多様体の特異点について
[ 講演概要 ]
リー群$G$が多様体$M$に作用しているとき, その商空間$G\\backspace M$のハウスドルフ性は, 不連続群論の研究において重要である. 特に, ベキ零リー群が線型空間にアファインかつ自由に作用するとき, 商位相は常にハウスドルフであるとLipsmanは予想した.
しかし, この予想には反例があり, 商位相は必ずしもハウスドルフでない.
この講演では, この非ハウスドルフ性を可視化'したい. より正確には, $M$への$G$作用から, 自然に代数多様体$V$が定義され, $V$の特異点が商位相の非ハウスドルフ性に対応することを見る.
[ 参考URL ]
http://akagi.ms.u-tokyo.ac.jp/seminar.html

### 2008年05月19日(月)

#### Kavli IPMU Komaba Seminar

17:00-18:30   数理科学研究科棟(駒場) 002号室
Jean-Michel Bismut 氏 (Univ. Paris-Sud, Orsay)
A survey of Quillen metrics

[ 講演概要 ]
In this lecture, I will survey basic results
on Quillen metrics.

Indeed let $X$ be a complex K\\"ahler manifold, and let $E$ be a
holomorphic Hermitian vector bundle on $X$. Let $\\lambda$ be the complex line
which is the determinant of the cohomology of $E$. The Quillen metric
is a metric on the line $\\lambda$, which one obtains using a spectral
invariant of the Hodge Laplacian, the Ray-Singer analytic torsion.

The Quillen metrics have a number of remarkable properties. Among them
the curvature theorem says that when one considers a family of such
$X$, the curvature of the holomorphic Hermitian connection on
$\\lambda$ is given by a formula of Riemann-Roch-Grothendieck type.

I will explain some of the ideas which go into the proof of these
properties, which includes Quillen's superconnections.

#### 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

On the projectively embeddable complex-foliated structures

#### 講演会

16:00-17:30   数理科学研究科棟(駒場) 126号室
Jean-Pierre Puel 氏
(ヴェルサイユ大学 (Universite de Versailles St Quentin)
)
A non standard unique continuation property related to Schiffer conjecture
[ 講演概要 ]
Coming from a control problem for a coupled fluid-structure system, we are confronted to the following problem in dimension 2:
\\Delta^2 w = -\\lambda \\Delta w in \\Omega w = {\\partial w}/{\\partial n} = 0 on \\Gamma {\\partial\\Delta w}/{\\partial n}=0 on \\Gamma_0 \\subset \\Gamma.
The question is : do we have w=0?
There is a counterexample when \\Omega is a disc. The analogous of (local) Schiffer's conjecture is : is the disc the only domain for which we can have a non zero solution?
Notice that the term local means that the additional boundary condition occurs only on a part of the boundary and when this boundary is not analytic, this is a major difference. A sub-conjecture would be : when the boundary is not analytic, do we have w=0?
Here we show that when \\Omega has a corner of angle \\theta_{0} with \\theta_{0} \\neq \\pi, 3\\pi/2 and when $\\Gamma_{0}$ is (locally) one edge of this angle then the only solution is w=0.
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/top/general-access.html

### 2008年05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
Mikael Pichot 氏 (東大数理)
Property RD and CAT(0) geometry

#### 応用解析セミナー

16:00-17:30   数理科学研究科棟(駒場) 002号室

( Stability and uniqueness for surfaces with constant anisotropic mean curvature)
[ 講演概要 ]

を保つ変分に対する非等方的表面エネルギーの臨界点を非等方的平均曲率一定曲

あるときをいう.したがって,エネルギー極小解は安定である.

### 2008年05月13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
Tamas Kalman 氏 (東京大学大学院数理科学研究科, JSPS)
The problem of maximum Thurston--Bennequin number for knots
[ 講演概要 ]
Legendrian submanifolds of contact 3-manifolds are
one-dimensional, just like knots. This `coincidence'' gives rise to an
interesting and expanding intersection of contact and symplectic geometry
on the one hand and classical knot theory on the other. As an
illustration, we will survey recent results on maximizing the
Thurston--Bennequin number (which is a measure of the twisting of the
contact structure along a Legendrian) within a smooth knot type. In
particular, we will show how Kauffman's state circles can be used to solve
the maximization problem for so-called +adequate (among them, alternating

#### 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
Andr\'e Martinez 氏 (ボローニャ大学)
Resonances for non-analytic potentials (joint work with T. Ramond and J. Sj\\"ostrand)

#### 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 endomorphisms of the Weyl algebra
[ 講演概要 ]
Noncommutative geometry has revived the interest in the Weyl algebras, which are basic building blocks of quantum field theories.
The Weyl algebra $A_n(\\C)$ is an associative algebra over $\\C$ generated by $p_i, q_i$ ($i=1,\\cdots,n$) with relations $[p_i, q_j]=\\delta_{ij}$. Every endomorphism of $A_n$ is injective since $A_n$ is simple.
Dixmier (1968) initiated a systematic study of the Weyl algebra $A_1$ and posed the following problem: Is every endomorphism of $A_1$ an automorphism?
We give an affirmative answer to this conjecture.
[ 参考URL ]
http://akagi.ms.u-tokyo.ac.jp/seminar.html

### 2008年05月12日(月)

#### Kavli IPMU Komaba Seminar

17:00-18:30   数理科学研究科棟(駒場) 002号室
Jean-Michel Bismut 氏 (Univ. Paris-Sud, Orsay)
The hypoelliptic Laplacian
[ 講演概要 ]
Let $X$ be a compact Riemannian manifold. The Laplace Beltrami
operator $-\\Delta^{X}$, or more generally the Hodge Laplacian
$\\square^{X}$, is an elliptic second order self adjoint operator on $X$.

We will explain the construction of a deformation of the elliptic
Laplacian to a family of hypoelliptic operators acting on the total
space of the cotangent bundle $\\mathcal{X}$. These operators depend
on a parameter $b>0$, and interpolate between the Hodge Laplacian
(the limit as $b\\to 0$) and the geodesic flow (the limit as $b\\to + \\infty$).
Actually, the deformed Laplacian is associated with an exotic Hodge
theory on the total space of the cotangent bundle, in which the
standard $L_{2}$ scalar product on forms is replaced by a
symmetric bilinear form of signature $\\left( \\infty, \\infty \\right)$.

This deformation can be understood as a version of the Witten
deformation on the loop space associated with the energy functional.
From a probabilistic point of view, the deformed Laplacian
corresponds to a Langevin process.

The above considerations can also be used in complex geometry, in
which the Dolbeault cohomology is considered instead of the Rham cohomology.

Results obtained with Gilles Lebeau on the analysis of the
hypoelliptic Laplacian will also be presented, as well as
applications to analytic torsion.

#### 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

### 2008年05月08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

Non-separable UHF algebras

### 2008年05月07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

(東京大学大学院数理科学研究科)
On the connected components of moduli spaces of finite flat models

### 2008年05月01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
Rune Johansen 氏 (Copenhagen 大学)
On the structure of graph algebras of presentations of a sofic shift

### 2008年04月30日(水)

#### 東京幾何セミナー

14:40-18:00   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��

Morse theory for abelian hyperkahler quotients
[ 講演概要 ]
Kirwan はモーメント写像のノルムの2乗を Morse 関数として Morse 理論を展開することにより,シンプレクティック商のトポロジーを研究した.本講演では,これらの理論をトーラスによるハイパーケーラー商に拡張する.ハイパーケーラーモーメント写像のノルムの2乗はプロパーな関数でないが,ある場合には Morse 理論が展開できることを示す.さらに,Morse 理論が展開できる場合には,シンプレクティック商の場合より組織的に Betti 数やコホモロジー環が決定できることを示す.

ラグランジュはめ込みのフレアー理論について
[ 講演概要 ]

#### 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

Iwasawa theory of totally real fields for certain non-commutative $p$-extensions
[ 講演概要 ]
Recently, Kazuya Kato has proven the non-commutative Iwasawa main
conjecture (in the sense of Coates, Fukaya, Kato, Sujatha and Venjakob) for
non-commutative Galois extensions of "Heisenberg type" of totally real fields,
using integral logarithmic homomorphisms. In this talk, we apply Kato's method
to certain non-commutative $p$-extensions which are more complicated than those
of Heisenberg type, and prove the main conjecture for them.

### 2008年04月24日(木)

#### 応用解析セミナー

16:00-17:30   数理科学研究科棟(駒場) 002号室

[ 講演概要 ]

#### 統計数学セミナー

16:20-17:30   数理科学研究科棟(駒場) 126号室

[ 講演概要 ]

・判別問題(特にクラス数が3以上の多値判別問題)
・誤り訂正符号
・ゲーム理論
・最適化理論(線形計画法、2次錐計画法)
・ネットワークフロー理論
・フォン=ノイマンのミニマックス定理
などが挙げられると思います。
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2008/01.html

#### Kavli IPMU Komaba Seminar

17:00-18:30   数理科学研究科棟(駒場) 056号室
Motohico Mulase 氏 (University of California, Davis)
Recursion relations in intersection theory on the moduli spaces of Riemann surfaces
[ 講演概要 ]
In this talk I will give a survey of recent developments in the intersection theory of tautological classes on the moduli spaces of stable algebraic curves. The emphasis is placed on explaining where the Virasoro constraint conditions are originated. Recently several authors have encountered the same combinatorial recursion relation from completely different contexts, that eventually leads to the Virasoro constraint. This mysterious structure of the theory will be surveyed.

### 2008年04月22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
Sergey Yuzvinsky 氏 (University of Oregon)
Special fibers of pencils of hypersurfaces
[ 講演概要 ]
We consider pencils of hypersurfaces of degree $d>1$ in the complex
$n$-dimensional projective space subject to the condition that the
generic fiber is irreducible. We study the set of completely reducible
fibers, i.e., the unions of hyperplanes. The first surprinsing result is
that the cardinality of thie set has very strict uniformed upper bound
(not depending on $d$ or $n$). The other one gives a characterization
of this set in terms of either topology of its complement or combinatorics
of hyperplanes. We also include into consideration more general special
fibers are iimportant for characteristic varieties of the hyperplane
complements.

### 2008年04月21日(月)

#### 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

Scorza quartics of trigonal spin curves and their varieties of power sums
[ 講演概要 ]
Our fundamental result is the construction of new subvarieties in the varieties of power sums for the Scorza quartic of any general pairs of trigonal curves and non-effective theta characteristics. This is a generalization of Mukai's description of smooth prime Fano threefolds of genus twelve as the varieties of power sums for plane quartics. Among other applications, we give an affirmative answer to the conjecture of Dolgachev and Kanev on the existence of the Scorza quartic for any general pairs of curves and non-effective theta characteristics.

#### 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

Ambient realization of conformal jets and deformation complex

### 2008年04月17日(木)

#### 統計数学セミナー

16:20-17:30   数理科学研究科棟(駒場) 126号室

[ 講演概要 ]

[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2008/00.html

#### 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

On a class of II$_1$ factors with at most one Cartan subalgebra II