Seminar information archive

Seminar information archive ~02/19Today's seminar 02/20 | Future seminars 02/21~

Lectures

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 ]
http://www.ms.u-tokyo.ac.jp/top/general-access.html

2008/05/15

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)
非等方的平均曲率一定曲面の安定性と一意性について
( Stability and uniqueness for surfaces with constant anisotropic mean curvature)
[ Abstract ]
曲面の非等方的表面エネルギーは,法線方向に依存する関数の曲面上での積分として
定義され,結晶やある種の液晶のエネルギーの数学的モデルを与える.曲面が囲む体積
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
面(CAMC曲面)という.CAMC曲面が安定であるとは,対応する変分問題の第2変分が非負で
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.
本講演では,与えられた平行な二平面上に自由境界を持つ曲面全体の中での,囲む体
積一定の条件のもとでの非等方的表面エネルギーと境界での濡れエネルギーの和の臨
界点について論じる.エネルギー汎関数に対するある自然な仮定のもとで,安定解の存
在と一意性を示し,その幾何学的性質を決定する.

2008/05/13

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 ]
http://akagi.ms.u-tokyo.ac.jp/seminar.html

2008/05/12

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)
無限次元タイヒミュラー空間と複素解析的モジュライ空間の構造

2008/05/08

Operator Algebra Seminars

16:30-18:00   Room #056 (Graduate School of Math. Sci. Bldg.)
勝良健史 (慶應大学)
Non-separable UHF algebras

2008/05/07

Number Theory Seminar

16:30-17:30   Room #117 (Graduate School of Math. Sci. Bldg.)
今井 直毅
(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

2008/05/01

Operator Algebra Seminars

16:30-18:00   Room #056 (Graduate School of Math. Sci. Bldg.)
Rune Johansen (Copenhagen 大学)
On the structure of graph algebras of presentations of a sofic shift


2008/04/30

Geometry Seminar

14:40-18:00   Room #056 (Graduate School of Math. Sci. Bldg.)
今野宏 (東京大学大学院数理科学研究科) 14:40-16:10
Morse theory for abelian hyperkahler quotients
[ Abstract ]
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.
赤穂まなぶ (首都大学東京 都市教養学部理工学系) 16:30-18:00
ラグランジュはめ込みのフレアー理論について
[ Abstract ]
深谷・Oh・太田・小野は,シンプレクティック多様体 M の中のラグランジュ部分多様体 L に対して,種数 0 の prestable な境界付きリーマン面から M への安定写像で,境界値が L に含まれるようなものを考えることにより,L の鎖複体(の部分複体)上にギャップ・フィルター付き A 無限大代数の構造を定義した.本講演では,上の結果をラグランジュ部分多様体から(横断的な自己交叉をもつ)ラグランジュはめ込みへと拡張する.これにより,(横断的に交わる)有限個のラグランジュ部分多様体の和集合を一つのラグランジュはめ込みと見なすことができるなど,新しい視点が得られることを説明する.

Number Theory Seminar

16:30-17:30   Room #117 (Graduate School of Math. Sci. Bldg.)
原 隆 (東京大学大学院数理科学研究科)
Iwasawa theory of totally real fields for certain non-commutative $p$-extensions
[ Abstract ]
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.

2008/04/24

Applied Analysis

16:00-17:30   Room #002 (Graduate School of Math. Sci. Bldg.)
宮本 安人 (東京工業大学 大学院理工学研究科)
円盤領域におけるNeumann問題の分岐問題について
[ Abstract ]
円盤領域(2次元球領域)におけるNeumann問題 Δu+\\lambda f(u)=0 を考える.広いクラスの非線形項 f に対して,第2固有値と第3固有値から非球対称解からなる大域的な枝(シート)が分岐することを示し,第2固有値からの分岐の枝は,分岐直後は一意的であることを示す.

Seminar on Probability and Statistics

16:20-17:30   Room #126 (Graduate School of Math. Sci. Bldg.)
白石 友一 (統計数理研究所)
二値判別機の組合せによる多値判別問題へのゲーム理論的アプローチ
[ Abstract ]
多値判別という学習理論の問題に対して、ゲーム理論的なアプローチを試みた結果についてお話したいと思います。多値判別問題を解くために実用的に広く用いられている方法に、2値判別機を組み合わせる方法があります。その際に2値判別機の出力結果に誤り訂正符号のモデルを仮定し、MAP推定により出力を決める方法が一般的です。本発表では2値判別機の組合せによる多値判別の問題を、「決定者」と「自然」のゲームとして捉え、既存の手法の解析や新しい手法の提案を行います。まず、多値判別問題における、誤り訂正符号による方法がミニマックスとなるための条件をネットワークフローにより表します。そして、one-vs-oneやone-vs-allなどの方法が自然な条件下でミニマックス戦略となることを検証します。次に、誤り訂正符号による方法に拡張を加え、「自然」の範囲をデータからある程度特定したときのミニマックス戦略を求める方法を提案し、これを2次錐計画法により定式化します。またミニマックス定理やエントロピーなどとの関連についての考察を行います。キーワードとしては
・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。
[ Reference URL ]
http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2008/01.html

Kavli IPMU Komaba Seminar

17:00-18:30   Room #056 (Graduate School of Math. Sci. Bldg.)
Motohico Mulase (University of California, Davis)
Recursion relations in intersection theory on the moduli spaces of Riemann surfaces
[ Abstract ]
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.

2008/04/22

Tuesday Seminar on Topology

16:30-18:00   Room #056 (Graduate School of Math. Sci. Bldg.)
Sergey Yuzvinsky (University of Oregon)
Special fibers of pencils of hypersurfaces
[ Abstract ]
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.

2008/04/21

Algebraic Geometry Seminar

16:30-18:00   Room #122 (Graduate School of Math. Sci. Bldg.)
高木寛通 (東大数理)
Scorza quartics of trigonal spin curves and their varieties of power sums
[ Abstract ]
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.

Seminar on Geometric Complex Analysis

10:30-12:00   Room #128 (Graduate School of Math. Sci. Bldg.)
平地 健吾 (東大数理)
Ambient realization of conformal jets and deformation complex

2008/04/17

Seminar on Probability and Statistics

16:20-17:30   Room #126 (Graduate School of Math. Sci. Bldg.)
中野 張 (科学技術振興機構)
動的なリスク分散による保険料計算原理について
[ Abstract ]
生命保険や銀行貸付け等の長期の商品に対しては、
時間依存の安全割増によるリスク評価を行うことが求められる。
今回の発表では、効用関数の畳み込みにより生成される動的リスク尺度によるアプローチを紹介する。
[ Reference URL ]
http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2008/00.html

Operator Algebra Seminars

16:30-18:00   Room #056 (Graduate School of Math. Sci. Bldg.)
小沢登高 (東大数理)
On a class of II$_1$ factors with at most one Cartan subalgebra II

Applied Analysis

16:00-17:30   Room #002 (Graduate School of Math. Sci. Bldg.)
WEISS Georg (東京大学大学院数理科学研究科)
Hidden dynamics and pulsating waves in self-propagating high temperature synthesis
[ Abstract ]
We derive the precise limit of SHS in the high activation energy scaling suggested by B.J. Matkowksy-G.I. Sivashinsky in 1978 and by A. Bayliss-B.J. Matkowksy-A.P. Aldushin in 2002. In the time-increasing case the limit coincides with the Stefan problem for supercooled water with spatially inhomogeneous coefficients. In general it is a nonlinear forward-backward parabolic equation with discontinuous hysteresis term.

In the first part we give a complete characterization of the limit problem in the case of one space dimension. In the second part we construct in any finite dimension a rather large family of pulsating waves for the limit problem. In the third part, we prove that for constant coefficients the limit problem in any finite dimension does not admit non-trivial pulsating waves.
This is a joint work with Regis MONNEAU (CERMICS, France).

2008/04/15

Tuesday Seminar on Topology

16:30-18:00   Room #056 (Graduate School of Math. Sci. Bldg.)
村上 順 (早稲田大学理工)
On the invariants of knots and 3-manifolds related to the restricted quantum group
[ Abstract ]
I would like to talk about the colored Alexander invariant and the logarithmic
invariant of knots and links. They are constructed from the universal R-matrices
of the semi-resetricted and restricted quantum groups of sl(2) respectively,
and they are related to the hyperbolic volumes of the cone manifolds along
the knot. I also would like to explain an attempt to generalize these invariants to
a three manifold invariant which relates to the volume of the manifold actually.

2008/04/14

Seminar on Geometric Complex Analysis

10:30-12:00   Room #128 (Graduate School of Math. Sci. Bldg.)
佐野 友二 (東大IPMU)
トーリック・ファノ多様体のマルチプライア・イデアル層と二木不変量の関係について

2008/04/08

Kavli IPMU Komaba Seminar

10:30-12:00   Room #002 (Graduate School of Math. Sci. Bldg.)
Akihiro Tsuchiya (IPMU, The University of Tokyo)
IPMU Komaba Lectures,Homotopy Theory (before 1970)

[ Abstract ]
Tuesday, April -- July, 2008
First Lecture Aprl 8


Recently the notion of homotopy theory has been widely used in many areas of
contemporary mathematics including mathematical physics.
The purpose of the lectures is to present an overview of the developments
of homotopy theory mainly from 1940's through 1960's, partly in view of
more recent progress in other areas.

(1) Prehistory of homotopy theory
-- Hurewicz theorem, Hopf theorem, Freudentahl suspension theorem
(2) Eilenberg-MacLane space and Postnikov system
(3) Steenrod algebras
(4) Serre's theorem on the homotopy groups of spheres
(5) Rational homotopy theory
(6) Stable homotopy category and Adams spectral sequence
(7) Vector bundles and characteristic classes
(8) Complex cobordism and Quillen's theorem
(9) Miscellaneous topics
Rereferences :
(1) J.P.May, A Concise Course in Algebraic Topology,
The University of Chicago Press
http://www.math.uchicago.edu/~may/CONCISE/ConciseRevised.pdf
(2) Douglas Ravenel, Complex cobordism and stable homotopy groups of spheres

The second edition, AMS Chelsea Series
http://www.math.rochester.edu/u/faculty/doug/mu.html
(3) Mark Hovey, Model Category, AMS
(4) Gelfand and Manin, Homology Algebra

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