過去の記録

過去の記録 ~11/14本日 11/15 | 今後の予定 11/16~

2011年04月26日(火)

数値解析セミナー

16:30-18:00   数理科学研究科棟(駒場) 002号室
本セミナーは、グローバルCOE事業「数学新展開の研究教育拠点」(東京大学)の援助を受け、GCOEセミナーして行われています。
http://www.ms.u-tokyo.ac.jp/gcoe/index.html

菊地文雄 氏 (一橋大学大学院経済学研究科)
不連続ガレルキン有限要素法に関する若干の体験 (JAPANESE)
[ 講演概要 ]
前世紀の終わり頃から,(偏)微分方程式の離散化手法として,不連続ガレルキン有限要素法(DGFEM)の研究が海外で盛んになり,論文のみならず書籍もすでに刊行されている.手法の要点は,近似関数として有限要素間境界で不連続なものも許容するかわりに,不連続性を考慮した弱定式化を導き,それにもとづいて有限要素法としての離散化をおこなうことである.不連続性の処理法としては,処罰法,未定乗数法などがすぐ思い浮かぶ.ここでは,対象を主に楕円型方程式に限定し,講演者が関与したハイブリッド型定式化を中心に,手法や数学的議論の概要,数値例, DGFEM固有の可能性などについて,私見を述べる.
[ 講演参考URL ]
http://www.infsup.jp/utnas/

Lie群論・表現論セミナー

16:30-18:00   数理科学研究科棟(駒場) 056号室
トポロジー火曜セミナーと合同です。いつもと場所が違います
吉野太郎 氏 (東京大学大学院数理科学研究科)
Topological Blow-up (JAPANESE)
[ 講演概要 ]
Suppose that a Lie group $G$ acts on a manifold
$M$. The quotient space $X:=G\\backslash M$ is locally compact,
but not Hausdorff in general. Our aim is to understand
such a non-Hausdorff space $X$.
The space $X$ has the crack $S$. Rougly speaking, $S$ is
the causal subset of non-Hausdorffness of $X$, and especially
$X\\setminus S$ is Hausdorff.

We introduce the concept of `topological blow-up' as a `repair'
of the crack. The `repaired' space $\\tilde{X}$ is
locally compact and Hausdorff space containing $X\\setminus S$
as its open subset. Moreover, the original space $X$ can be
recovered from the pair of $(\\tilde{X}, S)$.

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, Lie群論・表現論セミナーと合同
吉野 太郎 氏 (東京大学大学院数理科学研究科)
Topological Blow-up (JAPANESE)
[ 講演概要 ]
Suppose that a Lie group $G$ acts on a manifold
$M$. The quotient space $X:=G\\backslash M$ is locally compact,
but not Hausdorff in general. Our aim is to understand
such a non-Hausdorff space $X$.
The space $X$ has the crack $S$. Roughly speaking, $S$ is
the causal subset of non-Hausdorffness of $X$, and especially
$X\\setminus S$ is Hausdorff.

We introduce the concept of `topological blow-up' as a `repair'
of the crack. The `repaired' space $\\tilde{X}$ is
locally compact and Hausdorff space containing $X\\setminus S$
as its open subset. Moreover, the original space $X$ can be
recovered from the pair of $(\\tilde{X}, S)$.

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
片岡 清臣 氏 (東京大学大学院数理科学研究科)
On the system of fifth-order differential equations which describes surfaces containing six continuous families of circles (JAPANESE)

2011年04月25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) 126号室
高木 寛通 氏 (東京大学数理科学研究科)
Mirror symmetry and projective geometry of Reye congruences (JAPANESE)
[ 講演概要 ]
This is a joint work with Shinobu Hosono.
It is well-known that the projective dual of the second Veronese variety v_2(P^n) is the symmetric determinantal hypersurface H. However, in the context of homological projective duality after Kuznetsov, it is natural to consider that the Chow^2 P^n and H are dual (note that Chow^2 P^n is the secant variety of v_2(P^n)).
Though we did not yet formulate what this duality exactly means in full generality, we show some results in this context for the values n¥leq 4.
For example, let n=4. We consider Chow^2 P^4 in P(S^2 V) and H in P(S^2 V^*), where V is the vector space such that P^4 =P(V). Take a general 4-plane P in
P(S^2 V^*) and let P' be the orthogonal space to P in P(S^2 V). Then X:=Chow^2 P^4 ¥cap P' is a smooth Calabi-Yau 3-fold, and there exists a natural double cover Y -> H¥cap P with a smooth Calabi-Yau 3-fold Y. It is easy to check
that X and Y are not birational each other.
Our main result asserts the derived equivalence of X and Y. This derived equivalence is given by the Fourier Mukai functor D(X)-> D(Y) whose kernel is the ideal sheaf in X×Y of a flat family of curves on Y parameterized by X.
Curves on Y in this family have degree 5 and arithmetic genus 3, and these have a nice interpretation by a BPS number of Y. The proof of the derived equivalence is slightly involved so I explain a similar result in the case where n=3. In this case, we obtain a fully faithful functor from D(X)-> D(Y), where X is a so called the Reye congruence Enriques surface and Y is the 'big resolution' of the Artin-Mumford quartic double solid.

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
林本厚志 氏 (長野工業高等専門学校)
擬楕円体のCR写像の分類についての一考察 (JAPANESE)

2011年04月20日(水)

PDE実解析研究会

10:30-11:30   数理科学研究科棟(駒場) 056号室
北海道大学のHPには、第1回(2004年9月29日)~第38回(2008年10月15日)までの情報が掲載されております。
吉田伸生 氏 (京都大学大学院理学研究科/理学部数学教室)
Stochastic power law fluids (JAPANESE)
[ 講演概要 ]
This talk is based in part on a joint work with Yutaka Terasawa.
We consider a SPDE (stochastic partial differential equation) which describes the velocity field of a viscous, incompressible non-Newtonian fluid subject to a random force.
Here, the extra stress tensor of the fluid is given by a polynomial of degree $p-1$ of the rate of strain tensor, while the colored noise is considered as a random force.
We first investigate the existence and the uniqueness of weak solutions to this SPDE.
We next turn to the special case: $p \\in [1 + {d \\over 2},{2d\\overd-2})$,
where $d$ is the dimension of the space. We prove there that the Galerkin scheme approximates the velocity field in a strong sense. As a consequence, we establish the energy equality for the velocity field.
[ 講演参考URL ]
http://www.math.kyoto-u.ac.jp/~nobuo/

2011年04月18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) 126号室
川北 真之 氏 (京都大学数理解析研究所)
Ideal-adic semi-continuity problem for minimal log discrepancies (JAPANESE)
[ 講演概要 ]
De Fernex, Ein and Mustaţă, after Kollár, proved the ideal-adic semi-continuity of log canonicity to obtain Shokurov's ACC conjecture for log canonical thresholds on l.c.i. varieties. I discuss its generalisation to minimal log discrepancies, proposed by Mustaţă.

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
松村慎一 氏 (東大数理)
Asymptotic cohomology vanishing and a converse of the Andreotti-Grauert theorem on surface (JAPANESE)

2011年04月14日(木)

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
松村真義 氏 (東大数理)
Amenable actions and crossed products of $C^*$-algebras (JAPANESE)

応用解析セミナー

16:00-17:30   数理科学研究科棟(駒場) 128号室
Marek FILA 氏 (Comenius University (Slovakia))
Homoclinic and heteroclinic orbits for a semilinear parabolic equation (ENGLISH)
[ 講演概要 ]
We study the existence of connecting orbits for the Fujita equation

u_t=\\Delta u+u^p

with a critical or supercritical exponent $p$. For certain ranges of the exponent we prove the existence of heteroclinic connections from positive steady states to zero and the existence of a homoclinic orbit with respect to zero. This is a joint work with Eiji Yanagida.

2011年04月13日(水)

関数解析セミナー

15:00-17:00   数理科学研究科棟(駒場) 128号室
Alexander Pushnitski 氏 (King's College, London)
Spectral theory for functions of self-adjoint operators (ENGLISH)
[ 講演概要 ]
Let A, B be self-adjoint operators such that the standard assumptions of smooth scattering theory for the pair A, B are satisfied. The spectral theory of the operators of the type f(A)-f(B) will be discussed, with a particular attention to the case of discontinuous functions f. It turns out that the spectrum of f(A)-f(B) can often be explicitly described in terms of the spectrum of the scattering matrix for the pair A,B. This is joint work with D.Yafaev.

2011年04月12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
廣瀬 進 氏 (東京理科大学理工学部数学科)
On diffeomorphisms over non-orientable surfaces embedded in the 4-sphere (JAPANESE)
[ 講演概要 ]
4次元球面内に標準的に埋め込まれた向き付け可能曲面上の
向きを保つ可微分同相写像が向きを保つ4次元球面上の可微分同相写像に
拡張できるための必要十分条件は,その曲面に対する Rokhlin の2次形式を
保つことであることが知られている.
本講演では,向き付け不可能な閉曲面に対する同様の問題についての
現在進行中の試みについて話す.

2011年04月11日(月)

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
田島慎一 氏 (筑波大学)
レゾルベントの代数解析と行列の exact なスペクトル分解アルゴリズム (JAPANESE)

2011年03月31日(木)

講演会

13:00-14:00   数理科学研究科棟(駒場) 118号室
中止になりました。
Alain Joye 氏 (Univ. Grenoble)
Dynamical localization for unitary Anderson models (JAPANESE)

講演会

14:30-15:30   数理科学研究科棟(駒場) 118号室
中止になりました。
Gerard Ben Arous 氏 (Courant Institute, New York Univ.)
Stable limits for biased random walks on random trees (JAPANESE)
[ 講演概要 ]
It is well know that transport in random media can be hampered by dead-end regions and that the velocity can even vanish for strong drifts. We study this phenomenon in great detail for random trees. That is, we study the behavior of biased random walks on supercritical random trees with leaves, in the sub-ballistic regime. When the drift is strong enough it is well known that trapping in the dead-ends of the tree, causes the velocity to vanish. We study the behavior of the walk in this regime, and in particular find the exponents for the mean displacement and the time to reach a given large distance. We also establish a scaling limit result in the case where the drift are random and a non-lattice condition is satisfied. (Joint work with Alexander Fribergh, Alan Hammond, Nina Gantert)

2011年03月22日(火)

講演会

14:00-15:00   数理科学研究科棟(駒場) 128号室
中止になりました。
Amir Dembo 氏 (Stanford Univ.)
Potts models and Bethe states on sparse random graphs (JAPANESE)
[ 講演概要 ]
Theoretical models of disordered materials lead to challenging mathematical problems with applications to random combinatorial problems and coding theory. The underlying mathematical structure is that of many discrete variables that are strongly interacting according to a mean field model determined by a random sparse graph. Focusing on ferromagnetic Potts measures on random finite graphs that converge locally to trees we validate the `cavity' prediction for the limiting free energy per spin and show that local marginals are approximated well by the belief propagation algorithm. This is a concrete example of the more general approximation by Bethe measures, namely, the local convergence of the Boltzmann distribution on the original graph to the Boltzmann distribution on an appropriate infinite random tree (this talk is based on a joint work with Andrea Montanari and Nike Sun).

2011年03月08日(火)

GCOEセミナー

15:00-16:30   数理科学研究科棟(駒場) 128号室
Dimitri Yafaev 氏 (Univ. Rennes 1)
Diagonal singularities of the scattering matrix and the inverse problem at a fixed energy (ENGLISH)

2011年03月04日(金)

GCOEセミナー

17:00-18:00   数理科学研究科棟(駒場) 370号室
Oleg Emanouilov 氏 (Colorado State University)
Inverse boundary value problem by measuring Dirichlet data and Neumann data on disjoint sets (ENGLISH)
[ 講演概要 ]
We discuss the inverse boundary value problem of determining the conductivity in two dimensions from the pair of all input Dirichlet data supported on an open subset S1 and all the corresponding Neumann data measured on an open subset S2.
We prove the global uniqueness under some additional geometric condition, in the case where the intersection of S_1 and S_2 has no interior points, and we prove also the uniqueness for a similar inverse problem for the stationary Schr"odinger equation.
The key of the proof isthe construction of appropriate complex geometrical optics solutions using Carleman estimates with a singular weight.

2011年03月03日(木)

講演会

13:30-14:30   数理科学研究科棟(駒場) 270号室
Stefano Olla 氏 (Univ. Paris Dauphine)
Energy Diffusion: hydrodynamic, weak coupling, kinetic limits (ENGLISH)
[ 講演概要 ]
I will review recent results about weak coupling and kinetic limits for the energy diffusive evolution in hamiltonian systems perturbed by energy-conservating noise. Two universality classes of diffusion are obtained: Ginzburg-Landau dynamics that arise from weak coupling limit of anharmonic oscillators, and exclusion type processes that arise from kinetic limit (rarefied collisions) of interacting billiards. Works in collaboration with Carlangelo Liverani (weak coupling) and Francois Huveneers (kinetic limits).

講演会

14:45-15:45   数理科学研究科棟(駒場) 270号室
長田 博文 氏 (九大数理)
Singularity and absolute continuity of Palm measures of Ginibre random fields
(ENGLISH)
[ 講演概要 ]
The Ginibre random point field is a probability measure on the configuration space over the complex plane $\\mathbb{C}$, which is translation and rotation invariant. Intuitively, the interaction potential of this random point field is the two dimensional Coulomb potential with $\\beta = 2 $. This fact is justified by the integration by parts formula.
Since the two dimensional Coulomb potential is quite strong at infinity, the property of the Ginibre random point field is different from that of Gibbs measure with Ruelle class potentials. As an instance, we prove that the Palm measure of the Ginibre random point field is singular to the original Ginibre random point field. Moreover, all Palm measures conditioned at $x \\in \\mathbb{C}$ are mutually absolutely continuous.

講演会

16:00-16:30   数理科学研究科棟(駒場) 270号室
針谷 祐 氏 (東北大理)
A proof of the Brascamp-Lieb inequality based on Skorokhod embedding (ENGLISH)
[ 講演概要 ]
In this talk, we provide a probabilistic approach to the Brascamp-Lieb inequality based on Skorokhod embedding. An extension of the inequality to non-convex potentials will also be discussed.

2011年02月28日(月)

講演会

17:00-18:00   数理科学研究科棟(駒場) 470号室
Ying Tan 氏 (The University of Melbourne)
Extremum Seeking Control: history and recent developments (ENGLISH)
[ 講演概要 ]
A control system which is to determine and maintain the extremum value of a function is called extremum seeking control. The first extremum seeking control application appeared in 1922, in which the extremum seeking control was applied to electric railways. The first rigorous local stability analysis for an ESC scheme was recently proved in 2000 and later extended to semi-global stability analysis 2006.. This has spurred a renewed interest in this research area, leading to numerous practical implementations of the scheme. This talk will first revisit the history of extremum seeking control. It is followed by an explanation how the extremum seeking works. Finally, it will focus on the latest unifying framework that combines arbitrary continuous optimization algorithms with an estimator for derivatives of the unknown reference-to-output steady state map that contains an extremum.

2011年02月24日(木)

応用解析セミナー

16:00-18:10   数理科学研究科棟(駒場) 002号室
Arnaud Ducrot 氏 (University of Bordeaux 2) 16:00-17:00
Travelling waves for a size and space structured model in population dynamics: Point to sustained oscillating solution connections (ENGLISH)
[ 講演概要 ]
This work is devoted to the study of travelling wave solutions for some size structured model in population dynamics. The population under consideration is also spatially structured and has a nonlocal spatial reproduction. This phenomenon may model the invasion of plants within some empty landscape. Since the corresponding unspatially structured size structured models may induce oscillating dynamics due to Hopf bifurcations, the aim of this work is to prove the existence of point to sustained oscillating solution travelling waves for the spatially structured problem. From a biological viewpoint, such solutions represent the spatial invasion of some species with spatio-temporal patterns at the place where the population is established.
Enrique Zuazua 氏 (Basque Center for Applied Mathematics) 17:10-18:10
Some open problems in PDE control (ENGLISH)
[ 講演概要 ]
The field of PDE control has experienced a great progress in the last decades, developing new theories and tools that have also influenced other disciplines as Inverse Problem and Optimal Design Theories and Numerical Analysis. PDE control arises in most applications ranging from classical problems in fluid mechanics or structural engineering to modern molecular design experiments.

From a mathematical viewpoint the problems arising in this field are extremely challenging since the existing theory of existence and uniqueness of solutions and the corresponding numerical schemes is insufficient when addressing realistic control problems. Indeed, an efficient controller requires of an in depth understanding of how solutions depend on the various parameters of the problem (shape of the domain, time of control, coefficients of the equation, location
of the controller, nonlinearity in the equation,...)

In this lecture we shall briefly discuss some important advances and some challenging open problems. All of them shear some features. In particular they are simple to state and very likely hard to solve. We shall discuss in particular:
1.- Semilinear wave equations and their control properties.
2.- Microlocal optimal design of wave processes
3.- Sharp observability estimates for heat processes.
4.- Robustness on the control of finite-dimensional systems.
5.- Unique continuation for discrete elliptic models
6.- Control of Kolmogorov equations and other hypoelliptic models.

2011年02月23日(水)

関数解析セミナー

14:00-18:00   数理科学研究科棟(駒場) 118号室
Dimitri Yafaev 氏 (Univ. Rennes 1) 14:00-14:45
The semiclassical limit of eigenfunctions of the Schroedinger equation and the Bohr-Sommerfeld quantization condition, revisited (ENGLISH)
David Damanik 氏 (Rice University) 15:00-15:45
Uniform localization (ENGLISH)
Erik Skibsted 氏 (Aarhus University) 16:15-17:00
Global solutions to the eikonal equation (ENGLISH)
Christian Gerard 氏 (Univ. Paris Sud 11) 17:15-18:00
Applications of microlocal analysis to quantum field theory on curved space-times (ENGLISH)

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