過去の記録

過去の記録 ~02/17本日 02/18 | 今後の予定 02/19~

GCOEセミナー

17:00-18:00   数理科学研究科棟(駒場) 370号室
Jin Cheng 氏 (Fudan University)
A numerical method for solving the inverse heat conduction problem without initial value (ENGLISH)
[ 講演概要 ]
In this talk, we will present some results for the inverse heat conduction problem for the heat equation of determining a boundary value at in an unreachable part of the boundary. The main difficulty for this problem is that the initial value is unknown by the practical reason. A new method is prposed to solve this problem and the nuemrical tests show the effective of this method. Some theoretic analysis will be presented. This is a joint work with J Nakagawa, YB Wang, M Yamamoto.

代数学コロキウム

16:40-17:40   数理科学研究科棟(駒場) 056号室
Stephen Lichtenbaum 氏 (Brown University)
Special values of zeta-functions of schemes (ENGLISH)
[ 講演概要 ]
We will give conjectured formulas giving the behavior of the
seta-function of regular schemes projective and flat over Spec Z at
non-positive integers in terms of Weil-etale cohomology. We will also
explain the conjectured relationship of Weil-etale cohomology to etale
cohomology, which makes it possible to express these formulas also in terms
of etale cohomology.

2014年01月14日(火)

FMSPレクチャーズ

14:50-16:20   数理科学研究科棟(駒場) 056号室
Rinat Kashaev 氏 (University of Geneva)
Lectures on quantum Teichmüller theory III (ENGLISH)
[ 講演概要 ]
Quantum Teichmüller theory leads to a family of unitary infinite dimensional projective representations of the mapping class groups of punctured surfaces. One of the recent applications of this theory is the construction of state integral three-manifold invariants related with hyperbolic geometry.
In these lectures it is planned to address the following subjects:
1) Penner’s coordinates in the decorated Teichmüller space.
2) Ratio coordinates.
3) Quantization.
4) The length spectrum of simple closed curves.
[ 講演参考URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Kashaev.pdf

トポロジー火曜セミナー

17:00-18:00   数理科学研究科棟(駒場) 056号室
Tea: 16:30 - 17:00 コモンルーム
Rinat Kashaev 氏 (University of Geneva)
State-integral partition functions on shaped triangulations (ENGLISH)
[ 講演概要 ]
Quantum Teichm\\"uller theory can be promoted to a
generalized TQFT within the combinatorial framework of shaped
triangulations with the tetrahedral weight functions given in
terms of the Weil-Gelfand-Zak transformation of Faddeev.FN"s
quantum dilogarithm. By using simple examples, I will
illustrate the connection of this theory with the hyperbolic
geometry in three dimensions.

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
伊藤 健一 氏 (筑波大)
Threshold properties for one-dimensional discrete Schr\\"odinger operators (JAPANESE)
[ 講演概要 ]
We study the relation between the generalized eigenspace and the asymptotic expansion of the resolvent around the threshold $0$ for the one-dimensional discrete Schr\\"odinger operator on $\\mathbb Z$. We decompose the generalized eigenspace into the subspaces corresponding to the eigenstates and the resonance states only by their asymptotics at infinity, and classify the coefficient operators of the singlar part of resolvent expansion completely in terms of these eigenspaces. Here the generalized eigenspace we consider is largest possible. For an explicit computation of the resolvent expansion we apply the expansion scheme of Jensen-Nenciu (2001). This talk is based on the recent joint work with Arne Jensen (Aalborg University).

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
森真樹 氏 (東京大学大学院数理科学研究科)
セルラー代数の手法によるHecke-Cliffordスーパー代数の単純加群の分類
(JAPANESE)
[ 講演概要 ]
Hecke--Cliffordスーパー代数はA型岩堀--Hecke代数のスーパー版である。
その単純加群の分類は、Brundan, Kleshchevと土岡により
アフィンLie代数の圏論化の手法を用いて行われた。しかしこの構成は
とても抽象的であり実際に単純加群の構造を詳しく調べるのは難しい。
そこで本講演では、より具体的な単純加群の構成方法を紹介する。
これはGrahamとLehrerによるセルラー代数の理論を拡張した手法である。
ここではSpecht加群のスーパー類似にCliffordスーパー代数が
右から作用することが鍵となる。森田コンテクストと呼ばれる
道具を用いることで、このCliffordスーパー代数の単純加群から
Hecke--Cliffordスーパー代数の単純加群を作ることができる。

GCOEセミナー

15:00-16:00   数理科学研究科棟(駒場) 118号室
Oleg Emanouilov 氏 (Colorado State University)
Calderon problem for Maxwell's equations in cylindrical domain (ENGLISH)
[ 講演概要 ]
We prove some uniqueness results in determination of the conductivity, the permeability and the permittivity of Maxwell's equations from partial Dirichlet-to-Neumann map.

2014年01月11日(土)

保型形式の整数論月例セミナー

14:00-16:00   数理科学研究科棟(駒場) 123号室
Dihua Jiang 氏 (School of Mathematics, University of Minnesota) 14:00-14:45
A product of tensor product L-functions of quasi-split classical groups of Hermitian type. (jointly with Lei Zhang) (ENGLISH)
Dihua Jiang 氏 (School of Mathematics, University of Minnesota) 15:00-15:45
A product of tensor product L-functions of quasi-split classical groups of Hermitian type, Part II. (jointly with Lei Zhang) (ENGLISH)

2014年01月10日(金)

FMSPレクチャーズ

14:50-16:20   数理科学研究科棟(駒場) 056号室
Rinat Kashaev 氏 (University of Geneva)
Lectures on quantum Teichmüller theory II (ENGLISH)
[ 講演概要 ]
Quantum Teichmüller theory leads to a family of unitary infinite dimensional projective representations of the mapping class groups of punctured surfaces. One of the recent applications of this theory is the construction of state integral three-manifold invariants related with hyperbolic geometry.
In these lectures it is planned to address the following subjects:
1) Penner’s coordinates in the decorated Teichmüller space.
2) Ratio coordinates.
3) Quantization.
4) The length spectrum of simple closed curves.
[ 講演参考URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Kashaev.pdf

2014年01月09日(木)

FMSPレクチャーズ

14:50-16:20   数理科学研究科棟(駒場) 056号室
Rinat Kashaev 氏 (University of Geneva)
Lectures on quantum Teichmüller theory I (ENGLISH)
[ 講演概要 ]
Quantum Teichmüller theory leads to a family of unitary infinite dimensional projective representations of the mapping class groups of punctured surfaces. One of the recent applications of this theory is the construction of state integral three-manifold invariants related with hyperbolic geometry.
In these lectures it is planned to address the following subjects:
1) Penner’s coordinates in the decorated Teichmüller space.
2) Ratio coordinates.
3) Quantization.
4) The length spectrum of simple closed curves.
[ 講演参考URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Kashaev.pdf

2014年01月08日(水)

作用素環セミナー

16:30-18:00   数理科学研究科棟(駒場) 122号室
渕野昌 氏 (神戸大)
Dow's metrization theorem and beyond (JAPANESE)

代数学コロキウム

16:40-17:40   数理科学研究科棟(駒場) 056号室
吉川祥 氏 (東京大学数理科学研究科)
楕円曲線の判別式の巾根と等分点 (JAPANESE)
[ 講演概要 ]
We give an explicit and intrinsic description of (the torsor defined by the 12th roots of) the discriminant of an elliptic curve using the group of its 12-torsion points and the Weil pairing. As an application, we extend a result of Coates (which deals with the characteristic 0 case) to the case where the characteristic of the base field is not 2 or 3. This is a joint work with Kohei Fukuda.

2013年12月26日(木)

作用素環セミナー

16:30-18:00   数理科学研究科棟(駒場) 118号室
増本周平 氏 (東大数理)
Countable Chain Condition for $C^*$-algebras (ENGLISH)

2013年12月25日(水)

GCOEセミナー

16:00-17:00   数理科学研究科棟(駒場) 270号室
Kazufumi Ito 氏 (North Carolina State University)
Nonsmooth Nonconvex Optimization Problems (ENGLISH)
[ 講演概要 ]
A general class of nonsmooth nonconvex optimization problems is discussed. A general existence theory of solutions, the Lagrange multiplier theory and sensitivity analysis of the optimal value function are developed. Concrete examples are presented to demonstrate the applicability of our approach.

2013年12月24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
Tirasan Khandhawit 氏 (Kavli IPMU)
Stable homotopy type for monopole Floer homology (ENGLISH)
[ 講演概要 ]
In this talk, I will try to give an overview of the
construction of stable homotopy type for monopole Floer homology. The
construction associates a stable homotopy object to 3-manifolds, which
will recover the Floer groups by appropriate homology theory. The main
ingredients are finite dimensional approximation technique and Conley
index theory. In addition, I will demonstrate construction for certain
3-manifolds such as the 3-torus.

2013年12月20日(金)

GCOEセミナー

15:00-16:00   数理科学研究科棟(駒場) 118号室
Mourad Bellassoued 氏 (Bizerte University)
Determination of the magnetic field in an anisotropic Schrodinger equation (ENGLISH)
[ 講演概要 ]
This talk is devoted to the study of the following inverse boundary value problem: given a Riemannian manifold with boundary, determine the magnetic potential in a dynamical Schroedinger equation in a magnetic field from the observations made at the boundary.

2013年12月19日(木)

講演会

17:00-18:00   数理科学研究科棟(駒場) 270号室
Guanghui Hu 氏 (WIAS, Germany)
Inverse elastic wave scattering from rigid diffraction gratings (ENGLISH)
[ 講演概要 ]
In recent years, Schwarz reflection principles have been used to prove uniqueness in inverse scattering by bounded obstacles and unbounded periodic structures of polygonal or polyhedral type with only one or several incident plane waves.
Such a principle for the Navier equation is established by far only underthe third or fourth kind boundary conditions, and still remains unknown in the more practical case of the Dirichlet boundary condition.
In this talk we will discuss the uniqueness in inverse elastic scattering from rigid diffraction gratings of polygonal type, where the total displacement vanishes on the scattering surface. Mathematically, this can be modeled by the Dirichlet boundary value problem for the Navier equation in periodic structures. We prove that such diffraction gratings can be uniquely
determined from the near-field data corresponding to a finite number of incident elastic plane waves.
This is a joint work with J. Elschner and M. Yamamoto.

FMSPレクチャーズ

17:00-18:00   数理科学研究科棟(駒場) 270号室
Guanghui Hu 氏 (WIAS, Germany)
Inverse elastic wave scattering from rigid diffraction gratings (ENGLISH)
[ 講演概要 ]
In recent years, Schwarz reflection principles have been used to prove uniqueness in inverse scattering by bounded obstacles and unbounded periodic structures of polygonal or polyhedral type with only one or several incident plane waves.
Such a principle for the Navier equation is established by far only underthe third or fourth kind boundary conditions, and still remains unknown in the more practical case of the Dirichlet boundary condition.
In this talk we will discuss the uniqueness in inverse elastic scattering from rigid diffraction gratings of polygonal type, where the total displacement vanishes on the scattering surface. Mathematically, this can be modeled by the Dirichlet boundary value problem for the Navier equation in periodic structures. We prove that such diffraction gratings can be uniquely
determined from the near-field data corresponding to a finite number of incident elastic plane waves.
This is a joint work with J. Elschner and M. Yamamoto.
[ 講演参考URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Hu.pdf

2013年12月18日(水)

代数学コロキウム

18:00-19:00   数理科学研究科棟(駒場) 117号室
いつもと場所が異なりますのでご注意ください
加藤和也 氏 (シカゴ大学)
Heights of motives (ENGLISH)
[ 講演概要 ]
The height of a rational number a/b (a, b integers which are coprime) is defined as max(|a|, |b|). A rational number with small (resp. big) height is a simple (resp. complicated)  number. Though the notion height is so naive, height has played fundamental roles in number theory. There are important variants of this notion. In 1983, when Faltings proved Mordell conjecture, Faltings first proved Tate conjecture for abelian variaties by defining heights of abelian varieties, and then he deduced Mordell conjecture from the latter conjecture. I explain that his height of an abelian variety is generalized to the height of a motive. This generalization of height is related to open problems in number theory. If we can prove finiteness of the number of motives of bounded heights, we can prove important conjectures in number theory such as general Tate conjecture and Mordell-Weil type conjectures in many cases.
(本講演は「東京北京パリ数論幾何セミナー」として, インターネットによる東大数理, Morningside Center of MathematicsとIHESの双方向同時中継で行います.)

2013年12月17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
中村 伊南沙 氏 (東京大学大学院数理科学研究科)
Satellites of an oriented surface link and their local moves (JAPANESE)
[ 講演概要 ]
For an oriented surface link $F$ in $\\mathbb{R}^4$,
we consider a satellite construction of a surface link, called a
2-dimensional braid over $F$, which is in the form of a covering over
$F$. We introduce the notion of an $m$-chart on a surface diagram
$p(F)\\subset \\mathbb{R}^3$ of $F$, which is a finite graph on $p(F)$
satisfying certain conditions and is an extended notion of an
$m$-chart on a 2-disk presenting a surface braid.
A 2-dimensional braid over $F$ is presented by an $m$-chart on $p(F)$.
It is known that two surface links are equivalent if and only if their
surface diagrams are related by a finite sequence of ambient isotopies
of $\\mathbb{R}^3$ and local moves called Roseman moves.
We show that Roseman moves for surface diagrams with $m$-charts can be
well-defined. Further, we give some applications.

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
Fabricio Macia 氏 (Universidad Politécnica de Madrid)
Dispersion and observability for completely integrable Schrödinger flows (ENGLISH)
[ 講演概要 ]
I will present some results on weak dispersion and unique continuation (observability) for linear Schrödinger
equations that are obtained as the quantization of a completely integrable Hamiltonian system.
The model case corresponds to the linear Schrödinger equation (with a potential) on the flat torus.
Our results are obtained through a detailed analysis of semiclassical measures corresponding to
sequences of solutions, which is performed using a two-microlocal approach.
This is a joint work with Nalini Anantharaman and Clotilde Fermanian-Kammerer.

Lie群論・表現論セミナー

16:30-17:30   数理科学研究科棟(駒場) 126号室
貝塚公一 氏 (筑波大学大学院 数理物質科学研究科)
非コンパクト型対称空間におけるポアソン変換の$L^{2}$-値域の特徴
付け (JAPANESE)
[ 講演概要 ]
Characterizations of the joint eigenspaces of invariant
differential operators in terms of the Poisson transform have been one of the central problems in harmonic analysis on symmetric spaces.
From the point of view of spectral theory, Strichartz (J. Funct.
Anal.(1989)) formulated a conjecture concerning a certain image
characterization of the Poisson transform of the $L^{2}$-space on the boundary on symmetric spaces of noncompact type. In this talk, we employ techniques in scattering theory to present a positive answer to the Strichartz conjecture.

2013年12月16日(月)

FMSPレクチャーズ

15:30-16:30   数理科学研究科棟(駒場) 056号室
Jon Nimmo 氏 (Univ. of Glasgow)
The discrete Schrodinger equation for compact support potentials (ENGLISH)
[ 講演概要 ]
We consider the exact form of the Jost solutions of the discrete Schrodinger equation for arbitrary potentials with compact support. Remarkably, these solutions may be written in terms of certain explicitly defined polynomials in the non-trivial values of the potential. These polynomials also arise in the work of Yamada (2000) in connection with a birational representation of the symmetric group.
Applications of this approach to the udKdV are also discussed.
[ 講演参考URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_%20NIMMO.pdf

複素解析幾何セミナー

10:30-12:00   数理科学研究科棟(駒場) 126号室
千葉 優作 氏 (東京工業大学)
Shilov boundaries of the pluricomplex Green function's level sets (JAPANESE)
[ 講演概要 ]
In this talk, we study a relation between the Shilov boundaries of the pluricomplex Green function's level sets and supports of Monge-Ampére type currents.

2013年12月12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
安田 勇輝 氏 (東京大学大学院理学系研究科(地球惑星科学専攻))
くりこみ群の方法による大気重力波の自発的放射メカニズムの解明 (JAPANESE)
[ 講演概要 ]
大気の運動は速いモード (重力波) と遅いモード (地衡流運動) に分けることができる。元の支配方程式系から、遅いモードの相互作用のみを取り出した方程式系をバランスモデルとよぶ。バランスモデルは、重力波を一切含まず、位相空間内の遅い多様体上の運動を記述する。バランスモデルによって大気の大規模運動は良く記述できる。しかし、近年、初期状態が遅い多様体上にあるにも関わらず、後の時間発展と共に重力波が放射され、解の軌道が遅い多様体上から離れることが分かってきた。この現象を重力波の自発的放射とよぶ。

本研究は逓減摂動法の一種であるくりこみ群の方法を用いて、自発的放射を記述する方程式系を導出した。遅いモードと重力波 (速いモード) が効率的に相互作用するためには、時間スケールの一致が必要である。そこで、ドップラー効果を取り込むことで、速いモードが遅い時間スケールを持つことを可能にした。一方で、ドップラー効果とは別に、遅いモード同士の相互作用により、遅い時間スケールを持つ速いモードも励起される。これら二種類の速いモードを別に考えるため、合計三つのモードを導入した。すなわち、遅いモード、「ドップラー効果」により遅い時間スケールを持つ速いモード、「非線形効果」により遅い時間スケールを持つ速いモードである。その上で、くりこみ群の方法を適用し、系の時間発展を記述するくりこみ群方程式系を導出した。くりこみ群方程式系は、遅いモードに従属した成分との準共鳴により、重力波が自発的に放射されることを明らかにする。

気象庁非静力学モデルによる元の支配方程式系の数値積分により、導出したくりこみ群方程式系の妥当性を確認した。さらに、くりこみ群方程式系を用いて、自発的放射の物理的解釈を行った。重力波の放射メカニズムは、山岳波的メカニズムと速度変化メカニズムの二つに分けられ、どちらが主要になるかは、大規模な流れ場の形状によって決定される。また、数値モデルのデータを解析したところ、重力波の振幅は系の無次元パラメータの約 3 乗に比例することがわかった。この結果は、理論的な見積りと整合的であり、実際の解の軌道が遅い多様体からどの程度離れるかの指標を与える。

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