Seminar information archive

Seminar information archive ~02/06Today's seminar 02/07 | Future seminars 02/08~


Lie Groups and Representation Theory

16:30-18:00   Room #126 (Graduate School of Math. Sci. Bldg.)
示野 信一 (岡山理科大)
Matrix valued commuting differential operators with B2 symmetry
[ Abstract ]
B2 型のWeyl群の作用による対称性を持つ2次正方行列値の2階の可換な微分作用素を構成した。
作用素は Iida (Publ. Res. Inst. Math. Sci. Kyoto Univ. 32 (1996)) により計算された Sp(2,R)/U(2) の等質ベクトル束上の不変微分作用素の動径成分を特別な場合として含み、係数は楕円関数を用いて表される。
講演では、群の場合、可換な作用素の構成、spin Calogero-Sutherland 模型との関係について述べる。
[ Reference URL ]

Tuesday Seminar on Topology

16:30-18:00   Room #056 (Graduate School of Math. Sci. Bldg.)
山口 祥司 (東京大学大学院数理科学研究科)
On the geometry of certain slices of the character variety of a knot group
[ Abstract ]
joint work with Fumikazu Nagasato (Meijo University)
This talk is concerned with certain subsets in the character variety of a knot group.
These subsets are called '"slices", which are defined as a level set of a regular function associated to a meridian of a knot.
They are related to character varieties for branched covers along the knot.
Some investigations indicate that an equivariant theory for a knot is connected to a theory for branched covers via slices, for example, the equivariant signature of a knot and the equivariant Casson invariant.
In this talk, we will construct a map from slices into the character varieties for branched covers and investigate the properties.
In particular, we focus on slices called "trace-free", which are used to define the Casson-Lin invariant, and the relation to the character variety for two--fold branched cover.


Seminar on Geometric Complex Analysis

10:30-12:00   Room #128 (Graduate School of Math. Sci. Bldg.)
本多 宣博 (東工大理工)
A new series of compact minitwistor spaces and Moishezon twistor spaces over them

Kavli IPMU Komaba Seminar

17:00-18:30   Room #002 (Graduate School of Math. Sci. Bldg.)
Shinobu Hikami (The University of Tokyo)
Intersection theory from duality and replica
[ Abstract ]
Kontsevich's work on Airy matrix integrals has led to explicit results for the
intersection numbers of the moduli space of curves. In this article we show that a duality between k-point functions on N by N matrices and N-point functions of k by k matrices, plus the replica method, familiar in the theory of disordered systems, allows one to recover Kontsevich's results on the intersection numbers, and to generalize them to other models. This provides an alternative and simple way to compute intersection numbers with one marked point, and leads also to some new results. This is a joint work with E. Brezin (Comm.Math. Phys. in press, arXiv:0708.2210).


Operator Algebra Seminars

16:30-18:00   Room #056 (Graduate School of Math. Sci. Bldg.)
Rolf Dyre Svegstrup (東大数理)
2D models in AQFT from wedge algebras


Lie Groups and Representation Theory

16:30-18:00   Room #126 (Graduate School of Math. Sci. Bldg.)
笹木集夢 (早稲田大学)
Visible actions on multiplicity-free spaces
[ Abstract ]
The holomorphic action of a Lie group G on a complex manifold D is called strongly visible if there exist a real submanifold S such that D':=G・S is open in D and an anti-holomorphic diffeomorphism σ which is an identity map on S and preserves each G-orbit in D'.
In this talk, we treat the case where D is a multiplicity-free space V of a connected complex reductive Lie group G(C), and show that the action of a compact real form of G(C) on V is strongly visible.
[ Reference URL ]


Seminar on Geometric Complex Analysis

10:30-12:00   Room #128 (Graduate School of Math. Sci. Bldg.)
下村 俊 (慶大理工)


Monthly Seminar on Arithmetic of Automorphic Forms

13:30-16:00   Room #123 (Graduate School of Math. Sci. Bldg.)
Raimandus Vidunas
) 13:30-14:30
Identities between Appell's and univariate hyeprgeometric functions

[ Abstract ]
We look for univariate specializations of Appell'd bivariante hypergeometric functions that can be expressed in terms of univaraite ${}_{i+1} F_{i} ~(i=1,2,3)$ HGF's. The method is identifying cases when the partial differential equations for Appell's functions imply hypegeometric ordinary differential equations for their univariate specializations. In general, ordinary differential equations for univariate specializations of Apell's functions have order at moast 4.
示野 信一 (岡山理科大学理学部) 14:45-15:45
Whittaker functions with one-dimensional $K$-type on a semisimple Lie group of Hermitian type
[ Abstract ]
橋爪(Hiroshima J. Math. 12(1982))が与えたクラス1 Whittaker関数の表示式のHermitian対称空間上の1次元$K$-typeに付随したWhittaker関数への拡張を与える。またHeckeman-Opdamの超幾何関数の極限として、クラス1または1次元$K$-type を持つWhittaker関数が得られることを調べる。後者は石井-織田-平野(Math. Proc. Cambridge Philos. Soc. 41 (2006))の類似であり、一部は大島利雄氏との共同研究である。



16:30-17:30   Room #123 (Graduate School of Math. Sci. Bldg.)
Jean-Michel Bismut (Univ. Paris-Sud, Orsay)
Functional integration and index theory

[ Abstract ]
The heat equation proof of the Atiyah-Singer index theorem involves a local `fantastic cancellation' mechanism, which has long been unexplained conceptually.

In this lecture, I will show how the supersymmetric formalism introduced by physicists has ultimately led to a new understanding of this cancellation mechanism. Ideas of Witten and Atiyah relating the index theorem to the localization formulas of Duistermaat-Heckman in equivariant cohomology have ultimately led to a renewed understanding of the cancellation mechanism as being of geometric nature (albeit in infinite dimensions). The key fact is that when interpreting the heat equation method for the proof of the index theorem, integrals of measures on the loop space of the given manifold, which one obtains via Ito stochastic calculus, should be properly interpreted as integrals of differential forms on the loop space.

I will then explain how this new understanding of the local index theorem has naturally led to a better understanding of spectral invariants, and often to the proof of certain key properties.


Applied Analysis

16:00-17:30   Room #002 (Graduate School of Math. Sci. Bldg.)
森 洋一朗 (University of British Columbia)
[ Abstract ]

電気生理学が対象とするのは細胞および組織レベルでの電気活動であり,これは神経・心・内分泌機能の根幹をなすものである.Hodgkin とHuxley の有名な仕事を契機として,この方面の研究は数理生理学に格好の題材を提供し続けてきた.本講演では,まず電気生理の基礎概念を紹介した後,イオン動態と細胞膜の3次元形状の効果を取り入れたモデルについて解説し,その心臓生理学への応用について語る.さらに時間が許せば,私が今興味を持っている細胞極性の生成,細胞の動きなどの話題についても紹介したい.

Seminar on Probability and Statistics

16:20-17:30   Room #126 (Graduate School of Math. Sci. Bldg.)
逸見 昌之 (統計数理研究所)
[ Abstract ]
メタアナリシスとは、目的を同じくする複数の研究から得られる統計的結果を統合し、より強い統計的 エビデンスを得るための統計解析のことで、近年特に、医学・健康科学の分野において盛んに行われて いる。しかしながら、メタアナリシスのために行われる研究結果の選択過程は、必ずしも無作為(ランダ ム)であるとは限らない。例えば、統計的に有意でない結果は有意である結果に比べて公表(出版)されに くいので、公表されている結果だけでメタアナリシスを行うと統合結果も有意になる、ということがしば しば起こる。研究結果を選択する過程で入り込むバイアスの原因はこの他にもいろいろあり得るが、この 問題は一般に「出版バイアス(publication bias)」の問題と呼ばれている。出版バイアスを調整するた めによく使われる一つの方法は、研究結果の選択のされ方を統計的にモデリングすることであるが、そ のためには研究の選択過程に対して、データそのものからは検証できない強い仮定が必要である。その ため、その仮定がデータ以外の背景情報から強く支持されないと、間違った結論を導く可能性がある。 そこで本講演では、できるだけ多くの場合に許容されるような弱い仮定の下で、(メタアナリシスの結 果としての)信頼区間やP-値の最悪評価を行い、それらにもとづいて最終的な統計的有意性の判断を行 う方法を提案する。この信頼区間やP-値の最悪評価は、選択されなかった研究の数という未知数にも 依存しているので一意には決まらないが、この値を現実的に可能性のある範囲で振らせることによって、 どの辺で統計的有意性に関する結論が変化するかを知ることができる。その意味で、提案する方法は感 度解析法となっている。この方法論は、選択関数の作るある関数空間上の最適化問題の結果にもとづい ているが、今回はその数理的部分についてもできる限り詳しくお話しする予定である。
[ Reference URL ]


Mathematical Finance

17:30-19:00   Room #128 (Graduate School of Math. Sci. Bldg.)
尾張 圭太 (一橋大)
Robust Exponential Hedging and Indifference Valuation


Tuesday Seminar of Analysis

16:30-18:00   Room #128 (Graduate School of Math. Sci. Bldg.)
Vania Sordoni (ボローニャ大学)
Wave operators for diatomic molecules

Tuesday Seminar on Topology

17:00-18:30   Room #056 (Graduate School of Math. Sci. Bldg.)
Jer\^ome Petit (東京工業大学, JSPS)
Turaev-Viro TQFT splitting.
[ Abstract ]
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 Groups and Representation Theory

16:45-18:15   Room #126 (Graduate School of Math. Sci. Bldg.)
吉野太郎 (東京工業大学)
[ Abstract ]
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.
[ Reference URL ]


Kavli IPMU Komaba Seminar

17:00-18:30   Room #002 (Graduate School of Math. Sci. Bldg.)
Jean-Michel Bismut (Univ. Paris-Sud, Orsay)
A survey of Quillen metrics

[ Abstract ]
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.

Seminar on Geometric Complex Analysis

10:30-12:00   Room #128 (Graduate School of Math. Sci. Bldg.)
大沢 健夫 (名大多元数理)
On the projectively embeddable complex-foliated structures


16:00-17:30   Room #126 (Graduate School of Math. Sci. Bldg.)
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
[ Abstract ]
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.
[ Reference URL ]


Operator Algebra Seminars

16:30-18:00   Room #056 (Graduate School of Math. Sci. Bldg.)
Mikael Pichot (東大数理)
Property RD and CAT(0) geometry

Applied Analysis

16:00-17:30   Room #002 (Graduate School of Math. Sci. Bldg.)
小磯 深幸 (奈良女子大学理学部数学教室)
( Stability and uniqueness for surfaces with constant anisotropic mean curvature)
[ Abstract ]


Tuesday Seminar on Topology

16:30-18:00   Room #056 (Graduate School of Math. Sci. Bldg.)
Tamas Kalman (東京大学大学院数理科学研究科, JSPS)
The problem of maximum Thurston--Bennequin number for knots
[ Abstract ]
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
and positive) knots and links.

Tuesday Seminar of Analysis

16:30-18:00   Room #128 (Graduate School of Math. Sci. Bldg.)
Andr\'e Martinez (ボローニャ大学)
Resonances for non-analytic potentials (joint work with T. Ramond and J. Sj\\"ostrand)

Lie Groups and Representation Theory

16:30-18:00   Room #126 (Graduate School of Math. Sci. Bldg.)
加藤晃史 (東京大学)
On endomorphisms of the Weyl algebra
[ Abstract ]
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.
[ Reference URL ]


Kavli IPMU Komaba Seminar

17:00-18:30   Room #002 (Graduate School of Math. Sci. Bldg.)
Jean-Michel Bismut (Univ. Paris-Sud, Orsay)
The hypoelliptic Laplacian
[ Abstract ]
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.

Seminar on Geometric Complex Analysis

10:30-12:00   Room #128 (Graduate School of Math. Sci. Bldg.)
藤川 英華 (千葉大理)

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