過去の記録

過去の記録 ~11/02本日 11/03 | 今後の予定 11/04~

2012年03月07日(水)

GCOEセミナー

17:00-18:00   数理科学研究科棟(駒場) 370号室
Kazufumi Ito 氏 (North Carolina State Univ.)
Nonsmooth Optimization, Theory and Applications. (ENGLISH)
[ 講演概要 ]
We develop a Lagrange multiplier theory for Nonsmooth optimization, including $L^¥infty$ and $L^1$ optimizations, $¥ell^0$ (counting meric) and $L^0$ (Ekeland mertic), Binary and Mixed integer optimizations and Data mining. A multitude of important problems can be treated by our approach and numerical algorithms are developed based on the Lagrange multiplier theory.

2012年03月06日(火)

GCOEセミナー

16:00-17:00   数理科学研究科棟(駒場) 370号室
Dietmar Hoemberg 氏 (Weierstrass Institute, Berlin)
On the phase field approach to shape and topology optimization (ENGLISH)
[ 講演概要 ]
Owing to different densities of the respective phases, solid-solid phase transitions often are accompanied by (often undesired) changes in workpiece size and shape. In my talk I will address the reverse question of finding an optimal phase mixture in order to accomplish a desired workpiece shape.
From mathematical point of view this corresponds to an optimal shape design problem subject to a static mechanical equilibrium problem with phase dependent stiffness tensor, in which the two phases exhibit different densities leading to different internal stresses. Our goal is to tackle this problem using a phasefield relaxation.
To this end we first briefly recall previous works regarding phasefield approaches to topology optimization (e.g. by Bourdin ¥& Chambolle, Burger ¥& Stainko and Blank, Garcke et al.).
We add a Ginzburg-Landau term to our cost functional, derive an adjoint equation for the displacement and choose a gradient flow dynamics with an articial time variable for our phasefield variable. We discuss well-posedness results for the resulting system and conclude with some numerical results.

GCOEセミナー

17:00-18:00   数理科学研究科棟(駒場) 370号室
Thomas Petzold 氏 (Weierstrass Institute, Berlin)
Finite element simulations of induction hardening of steel parts (ENGLISH)
[ 講演概要 ]
Induction hardening is a modern method for the heat treatment of steel parts.
A well directed heating by electromagnetic waves and subsequent quenching of the workpiece increases the hardness of the surface layer.
The process is very fast and energy efficient and plays a big role in modern manufacturing facilities in many industrial application areas.
In this talk a model for induction hardening of steel parts is presented. It consist of a system of partial differential equations including Maxwell's equations and the heat equation.
The finite element method is used to perform numerical simulations in 3D.
This requires a suitable discretization of Maxwell's equations leading to so called edge-finite-elements.
We will give a short overview of edge elements and present numerical simulations of induction hardening.
We will address some of the difficulties arising when solving the large system of non-linear coupled PDEs in three space dimensions.

2012年02月29日(水)

GCOEセミナー

16:00-17:00   数理科学研究科棟(駒場) 270号室
Johannes Elschner 氏 (Weierstrass Institute, Germany)
Direct and inverse scattering of elastic waves by diffraction gratings (ENGLISH)
[ 講演概要 ]
The talk presents joint work with Guanghui Hu on the scattering of time-harmonic plane elastic waves by two-dimensional periodic structures. The first part presents existence and uniqueness results for the direct problem , using a variational approach. For the inverse problem, we discuss global uniqueness results with a minimal number of incident pressure or shear waves under the boundary conditions of the third and fourth kind. Generalizations to biperiodic elastic diffraction gratings in 3D are also mentioned. Finally we consider a reconstruction method applied to the inverse Dirichlet problem for the quasi-periodic 2D Navier equation.

2012年02月22日(水)

代数学コロキウム

18:00-19:00   数理科学研究科棟(駒場) 056号室
望月拓郎 氏 (京都大学数理解析研究所)
Twistor $D$-module and harmonic bundle (ENGLISH)
[ 講演概要 ]
Abstract:
We shall overview the theory of twistor $D$-modules and
harmonic bundles. I am planning to survey the following topics,
motivated by the Hard Lefschetz Theorem for semisimple holonomic
$D$-modules:

1. What is a twistor $D$-module?
2. Local structure of meromorphic flat bundles
3. Wild harmonic bundles from local and global viewpoints

(本講演は「東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とIHESとの双方向同時中継で行います。)

GCOEセミナー

15:00-16:00   数理科学研究科棟(駒場) 270号室
Bernadette Miara 氏 (Université Paris-Est, ESIEE, France)
Justification of a Shallow Shell Model in Unilateral Contact with an Obstacle (ENGLISH)
[ 講演概要 ]
We consider a three-dimensional elastic shell in unilateral contact with a plane. This lecture aims at justifying the asymptotic limit of the set of equilibrium equations of the structure when the thickness of the shell goes to zero. More precisely, we start with the 3D Signorini problem (with finite thickness) and obtain at the limit an obstacle 2D problem. This problem has already been studied [4] in the Cartesian framework on the basis of the bi-lateral problem [3]. The interest and the difficulty of the approach in the curvilinear framework (more appropriate to handle general shells) is due to the coupling between the tangential and transverse covariant components of the elastic field in the expression of the nonpenetrability conditions.
The procedure is the same as the one used in the asymptotic analysis of 3D bilateral structures [1, 2]: assumptions on the data, (loads and geometry of the middle surface of the shell) and re-scalling of the unknowns (displacement field or stress tensor); the new feature is the special handling of the components coupling.
The main result we obtain is as follows:
i) Under the assumption of regularity of the external volume and surface loads, and of the mapping that defines the middle surface of the shell, we establish that the family of elastic displacements converges strongly as the thickness tends to zero in an appropriate set which is a convex cone.
ii) The limit elastic displacement is a Kirchhoff-Love field given by a variational problem which will be analysed into details. The contact conditions are fully explicited for any finite thickness and at the limit.
This is a joint work with Alain L´eger, CNRS, Laboratoire de M´ecanique et d’Acoustique, 13402, Marseille, France.

GCOEセミナー

16:15-17:15   数理科学研究科棟(駒場) 270号室
Oleg Emanouilov 氏 (Colorado State University)
Determination of first order coefficient in semilinear elliptic equation by partial Cauchy data. (ENGLISH)
[ 講演概要 ]
In a bounded domain in $R^2$, we consider a semilinear elliptic equation $¥Delta u +qu +f(u)=0$.
Under some conditions on $f$, we show that the coefficient $q$ can be uniquely determined by the following partial data
$$
{¥mathcal C}_q=¥{(u,¥frac{¥partial u}{¥partial¥nu})¥vert_{\\\\tilde Gamma}¥vert
- ¥Delta u +qu +f(u)=0, ¥,¥,¥, u¥vert_{¥Gamma_0}=0,¥,¥, u¥in H^1(¥Omega)¥}
$$
where $¥tilde ¥Gamma$ is an arbitrary fixed open set of
$¥partial¥Omega$ and $¥Gamma_0=¥partial¥Omega¥setminus¥tilde¥Gamma$.

2012年02月21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
見村 万佐人 氏 (東京大学大学院数理科学研究科)
Property (TT)/T and homomorphism superrigidity into mapping class groups (JAPANESE)
[ 講演概要 ]
コンパクトで向きづけられた曲面(パンクがあってもよい)の写像類群には,多くの謎めいた性質があることが知られている:写像類群はある場合には高ランク格子(つまり,高ランク代数群の既約格子)に近いふるまいをするが,別の場合にはランク1格子に近いふるまいをする.次に述べる定理はFarb--Kaimanovich--Masur超剛性と呼ばれており,写像類群のランク1格子に近いふるまいの顕著な例である:「高ランク格子(例えばSL(3,Z)や,SL(3,R)の余コンパクト格子など)から写像類群への任意の群準同型は有限の像をもつ.」

本講演では,この超剛性の以下のような拡張を証明する:「高ランク格子を(算術的とは限らない)一般の環上の適切な行列群に置き換えた時でも,上の定理が成り立つ.」考える群の主な例は「普遍格子」と呼ばれる群であり,これは整係数有限生成可換多項式環上の特殊線型群(SL(3,Z[x])など)のことを指す.この定理を示すために,群の"性質(TT)/T"という,Kazhdanの性質(T)を強めた性質を導入する.

以上の2性質を紹介し,群の(ユニタリ表現で捻じれた係数の)コホモロジー・有界コホモロジーとの関係を説明したい.その上で, 本講演の定理の証明の概略を述べたい.

2012年02月20日(月)

関数解析セミナー

16:30-17:30   数理科学研究科棟(駒場) 128号室
Jan Philip SOLOVEJ 氏 (コペンハーゲン大学)
Microscopic derivation of the Ginzburg-Landau model (ENGLISH)
[ 講演概要 ]
I will discuss how the \\emph{Ginzburg-Landau} (GL) model of superconductivity arises as an asymptotic limit of the microscopic Bardeen-Cooper-Schrieffer (BCS) model. The asymptotic limit may be seen as a semiclassical limit and one of the main difficulties is to derive a semiclassical expansion with minimal regularity assumptions. It is not rigorously understood how the BCS model approximates the underlying many-body quantum system. I will formulate the BCS model as a variational problem, but only heuristically discuss its relation to quantum mechanics.

2012年02月14日(火)

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
Michael Loss 氏 (Georgia Institute of Technology)
Symmetry results for Caffarelli-Kohn-Nirenberg inequalities (ENGLISH)

2012年02月07日(火)

GCOEセミナー

14:00-15:00   数理科学研究科棟(駒場) 370号室
Piermarco Cannarsa 氏 (Mat. Univ. Roma "Tor Vergata")
Controllability results for degenerate parabolic operators (ENGLISH)
[ 講演概要 ]
UnlikeCuniformly parabolic equations, parabolic operators that degenerate on subsets of the space domain exhibit very different behaviors from the point of view of controllability. For instance, null controllability in arbitrary time may be true or false according to the degree of degeneracy, and there are also examples where a finite time is needed to ensure such a property. This talk will survey most of the theory that has been established so far for operators with boundary degeneracy, and discuss recent results for operators of Grushin type which degenerate in the interior.

2012年02月03日(金)

博士論文発表会

09:45-11:00   数理科学研究科棟(駒場) 118号室
伊藤 敦 氏 (大学院数理科学研究科)
How to estimate Seshadri constants(セシャドリ定数を評価する方法)
(JAPANESE)

博士論文発表会

11:00-12:15   数理科学研究科棟(駒場) 118号室
宗野 惠樹 氏 (東京大学大学院数理科学研究科)
Spherical functions associated to the principal series representations of SL(3,R) and higher rank Epstein zeta functions(SL(3,R)の主系列表現に付随する球関数,及び高階Epsteinゼータ関数について)
(JAPANESE)

博士論文発表会

13:00-14:15   数理科学研究科棟(駒場) 118号室
伊藤 哲也 氏 (東京大学大学院数理科学研究科)
Construction of invariant group orderings from topological point of view(位相幾何の視点からの群の不変順序の構成)
(JAPANESE)

博士論文発表会

14:15-15:30   数理科学研究科棟(駒場) 118号室
田 然 氏 (東京大学大学院数理科学研究科)
The explicit calculation of Čech cohomology and an extension of Davenport’s inequality(Čechコホモロジーの明示的計算とDavenport不等式の拡張)
(JAPANESE)

博士論文発表会

09:45-11:00   数理科学研究科棟(駒場) 128号室
及川 一誠 氏 (東京大学大学院数理科学研究科)
Hybridized Discontinuous Galerkin Methods for Elliptic Problems(楕円型問題に対するハイブリッド型不連続ガレルキン法の研究)
(JAPANESE)

博士論文発表会

11:00-12:15   数理科学研究科棟(駒場) 128号室
横山 聡 氏 (東京大学大学院数理科学研究科)
Two-dimensional stochastic Navier-Stokes equations derived from a certain variational problem(ある変分問題から導かれる二次元確率ナビエ・ストークス方程式)
(JAPANESE)

博士論文発表会

13:00-14:15   数理科学研究科棟(駒場) 128号室
糸﨑 真一郎 氏 (東京大学大学院数理科学研究科)
Scattering Theory on Manifolds with Asympotically Polynomially Growing Ends(多項式増大する無限遠境界を持つ多様体上の散乱理論)
(JAPANESE)

博士論文発表会

14:15-15:30   数理科学研究科棟(駒場) 128号室
神本 晋吾 氏 (東京大学大学院数理科学研究科)
On the exact WKB analysis of Schrödinger equations(Schrödinger方程式の完全WKB解析に関して)
(JAPANESE)

2012年02月02日(木)

作用素環セミナー

16:30-18:00   数理科学研究科棟(駒場) 002号室
磯野優介 氏 (東大数理)
Weak Exactness for $C^*$-algebras and Application to Condition (AO) (JAPANESE)

博士論文発表会

11:00-12:15   数理科学研究科棟(駒場) 118号室
大川 新之介 氏 (東京大学大学院数理科学研究科)
Studies on the geometry of Mori dream spaces(森夢空間の幾何学に関する研究)
(JAPANESE)

博士論文発表会

13:00-14:15   数理科学研究科棟(駒場) 118号室
大久保 俊 氏 (大学院数理科学研究科)
The p-adic monodromy theorem in the imperfect residue field case(剰余体が非完全な場合のp進モノドロミー定理について)
(JAPANESE)

博士論文発表会

14:15-15:30   数理科学研究科棟(駒場) 118号室
張 祺智 氏 (大学院数理科学研究科)
On The Discrete Logarithm Problem in Finite Fields(有限体上の離散対数問題について)
(JAPANESE)

博士論文発表会

15:45-17:00   数理科学研究科棟(駒場) 118号室
馬 昭平 氏 (大学院数理科学研究科)
Rationality of the moduli spaces of 2-elementary K3 surfaces(対合付きK3曲面のモジュライの有理性)
(JAPANESE)

博士論文発表会

09:45-11:00   数理科学研究科棟(駒場) 128号室
柿澤 亮平 氏 (東京大学大学院数理科学研究科)
Determining nodes for semilinear parabolic evolution equations in Banach spaces(バナッハ空間上の半線型放物型発展方程式に対する確定節点)
(JAPANESE)

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