過去の記録

過去の記録 ~08/17本日 08/18 | 今後の予定 08/19~

2007年12月17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
寺杣友秀 氏 (東京大学)
種数3の曲線とあるCalabi-Yau threefoldの代数的対応(松本圭司氏との共同研究)

Kavli IPMU Komaba Seminar

17:00-18:30   数理科学研究科棟(駒場) 002号室
Ken-Ichi Yoshikawa 氏 (The University of Tokyo)
Analytic torsion for Calabi-Yau threefolds
[ 講演概要 ]
In 1994, Bershadky-Cecotti-Ooguri-Vafa conjectured that analytic torsion
gives rise to a function on the moduli space of Calabi-Yau threefolds and
that it coincides with the quantity $F_{1}$ in string theory.
Since the holomorphic part of $F_{1}$ is conjecturally the generating function
of the counting problem of elliptic curves in the mirror Calabi-Yau threefold,
this implies the conjectural equivalence of analytic torsion and the counting
problem of elliptic curves for Calabi-Yau threefolds through mirror symmetry.

After Bershadsky-Cecotti-Ooguri-Vafa, we introduced an invariant of
Calabi-Yau threefolds, which we obtained using analytic torsion and
a Bott-Chern secondary class. In this talk, we will talk about the construction
and some explicit formulae of this analytic torsion invariant.
Some part of this talk is based on the joint work with H. Fang and Z. Lu.

2007年12月13日(木)

講演会

10:40-12:10   数理科学研究科棟(駒場) 128号室
Mikael Pichot 氏 (東大数理)
Topics in ergodic theory, von Neumann algebras, and rigidity
[ 講演参考URL ]
http://www.ms.u-tokyo.ac.jp/~yasuyuki/pichot.htm

応用解析セミナー

16:00-17:30   数理科学研究科棟(駒場) 126号室
Danielle Hilhorst 氏 (CNRS / パリ第11大学)
Singular limit of a competition-diffusion system
[ 講演概要 ]
We revisit a competition-diffusion system for the densities of biological populations, and (i) prove the strong convergence in L^2 of the densities of the biological species (joint work with Iida, Mimura and Ninomiya); (ii) derive the singular limit of some reaction terms as the reaction coefficient tends to infinity (joint work with Martin and Mimura).

2007年12月12日(水)

統計数学セミナー

15:20-16:30   数理科学研究科棟(駒場) 122号室
Stefano IACUS 氏 (Department of Economics, Business and Statistics, University of Milan)
Inference problems for the telegraph process observed at discrete times
[ 講演概要 ]
The telegraph process {X(t), t>0}, has been introduced (see
Goldstein, 1951) as an alternative model to the Brownian motion B(t).
This process describes a motion of a particle on the real line which
alternates its velocity, at Poissonian times, from +v to -v. The
density of the distribution of the position of the particle at time t
solves the hyperbolic differential equation called telegraph equation
and hence the name of the process.
Contrary to B(t) the process X(t) has finite variation and
continuous and differentiable paths. At the same time it is
mathematically challenging to handle. Several variation of this
process have been recently introduced in the context of Finance.

In this talk we will discuss pseudo-likelihood and moment type
estimators of the intensity of the Poisson process, from discrete
time observations of standard telegraph process X(t). We also
discuss the problem of change point estimation for the intensity of
the underlying Poisson process and show the performance of this
estimator on real data.
[ 講演参考URL ]
http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2007/12.html

2007年12月11日(火)

トポロジー火曜セミナー

16:30-18:40   数理科学研究科棟(駒場) 056号室
Tea: 16:00 - 16:30 コモンルーム
Xavier G\'omez-Mont 氏 (CIMAT, Mexico) 16:30-17:30
A Singular Version of The Poincar\\'e-Hopf Theorem
[ 講演概要 ]
The Poincar\\'e-Hopf Theorem asserts that the Euler Characteristic of a compact manifold is the sum of the indices of any vector field on it with isolated singularities.

A hypersurface in real or complex number space may be considered as the limit of the smooth hypersurfaces obtained from nearby regular values. The singularity contains “hidden” topology, which is unfolded by a smooth regeneration. At the singularity one has an algebraic invariant, the Jacobi Algebra, which is obtained by considering analytic functions modulo the partial derivatives. It contains topological information of the singularity.

One may consider vector fields tangent to a hypersurface with isolated singularities, and define topologically an index, which coincides with the sum of the Poincar\\'e-Hopf indices of a regeneration of it tangent to a nearby smooth hypersurface.

I will explain how to compute the index of a vector field X tangent to an isolated hypersurface singularity V using Homological Algebra, as the Euler Characteristic of the homology of the complex obtained by contracting differential forms on V with the vector field X. The formula contains several terms, but the higher order terms may be translated from the invariants of the singular point to invariants in the Jacobi Algebra, making this translation a local version of the Poincar\\'e-Hopf Theorem.

I will also explain how some of these ideas can be extended to complete intersections.
Miguel A. Xicotencatl 氏 (CINVESTAV, Mexico) 17:40-18:40
Chen Ruan cohomology of cotangent orbifolds and Chas-Sullivan string topology
[ 講演概要 ]
(Joint with: A. Gonzalez, E. Lupercio, C. Segovia, and B. Uribe)

At the end of 90's, two theories of topology were invented roughly at the same time and attracted considerable interest in the mathematical community. One is the Chas-Sullivan's loop product on the homology of loop space and the second one is Chen-Ruan's stringy cohomology of orbifold. It was an observation of Chen that inertia orbifold (which carries Chen-Ruan cohomology) is the space of constant loops of an orbifold. Therefore, two theories should interact. In this work we show that for an interesting family of orbifolds, the virtual orbifold cohomology, turns out to be a subalgebra of the homology of the loop orbifold, and is isomorphic, as algebras, to the Chen-Ruan orbifold cohomology of its cotangent orbifold.

代数幾何学セミナー

10:00-12:00   数理科学研究科棟(駒場) 128号室
次回は2008年1月8日です.
Dmitry KALEDIN 氏 (Steklov研究所, 東大数理)
Homological methods in non-commutative geometry, part 7

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
井上順子 氏 (鳥取大学)
Characterization of some smooth vectors for irreducible representations of exponential solvable Lie groups
[ 講演参考URL ]
http://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html

2007年12月10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
杉山健一 氏 (千葉大学)
岩澤予想の幾何学的類似の量子化(予想される結果)

Kavli IPMU Komaba Seminar

17:00-18:30   数理科学研究科棟(駒場) 002号室
Dmitry Kaledin 氏 (Steklov Institute and The University of Tokyo)
Deligne conjecture and the Drinfeld double.
[ 講演概要 ]
Deligne conjecture describes the structure which exists on
the Hochschild cohomology $HH(A)$ of an associative algebra
$A$. Several proofs exists, but they all combinatorial to a certain
extent. I will present another proof which is more categorical in
nature (in particular, the input data are not the algebra $A$, but
rather, the tensor category of $A$-bimodules). Combinatorics is
still there, but now it looks more natural -- in particular, the
action of the Gerstenhaber operad, which is know to consist of
homology of pure braid groups, is induced by the action of the braid
groups themselves on the so-called "Drinfeld double" of the category
$A$-bimod.

If time permits, I will also discuss what additional structures
appear in the Calabi-Yau case, and what one needs to impose to
insure Hodge-to-de Rham degeneration.

2007年12月06日(木)

講演会

10:40-12:10   数理科学研究科棟(駒場) 128号室
Mikael Pichot 氏 (東大数理)
Topics in ergodic theory, von Neumann algebras, and rigidity
[ 講演参考URL ]
http://www.ms.u-tokyo.ac.jp/~yasuyuki/pichot.htm

応用解析セミナー

16:00-17:30   数理科学研究科棟(駒場) 126号室
柳田 英二 氏 (東北大学大学院理学研究科)
藤田型方程式における時間大域解の挙動について
[ 講演概要 ]
この講演では,藤田型の半線形放物型偏微分方程式に関する M. Fila, J. King, P. Polacik, M. Winkler らとの共同研究による成果についてその概要を紹介する.全空間上の藤田型方程式については,これまで様々な挙動を示す時間大域解の存在が示されている.そこで大域解の時間的挙動と初期値の空間的挙動の関係を詳細に調べることにより,大域解をいくつかに分類し,その挙動がそれぞれ異なるメカニズムに支配されていることを明らかにする.時間が許せば,最近の進展や関連する話題についても触れる予定である.

2007年12月05日(水)

代数学コロキウム

16:30-17:30   数理科学研究科棟(駒場) 117号室
中村健太郎 氏 (東京大学大学院数理科学研究科)
Classification of two dimensional trianguline representations of p-adic fields
[ 講演概要 ]
Trianguline representation is a class of p-adic Galois representations of p-adic fields. This was defined by P.Colmez by using ($\\varphi, \\Gamma$)-modules over Robba ring. In his study of p-adic local Langlands correspondence of GL_2(Q_p), he completely classified two dimensional trianguline representations of Q_p. On the other hand, L.Berger recently defined the category of B-pairs and established the equivalence between the category of B-pairs and the category of ($\\varphi,\\Gamma$)-modules over Robba ring. In this talk, we extend the Colmez's result by using B-pairs. We completely classify two dimensional trianguline representations of K for any finite extension of Q_p. We also talk about a relation between two dimensional trianguline representations and principal series or special series of GL_2(K).

統計数学セミナー

16:20-17:30   数理科学研究科棟(駒場) 122号室
今野 良彦 氏 (日本女子大学理学部)
A Decision-Theoretic Approach to Estimation from Wishart matrices on Symmetric Cones
[ 講演概要 ]
James and Stein(1961) have considered the problem of estimating the mean matrix of Wishart distributions under so-called Stein's loss function and obtained a minimax estimator with a constant risk. Later Stein(1977) has given an unbiased risk estimate for a class of orthogonally invariant estimators, from which he obtained orthogonally invariant minimax estimators which are uniformly better than the best triangular-invariant estimator in James and Stein(1961). The works mentioned above lead to the following natural question: Is it possible for any estimators to improve upon the maximum likelihood estimator for the mean matrix of the complex or quaternion Wishart distributions? This talk shows that we can obtain improved estimators for the mean matrix under these models in a unified manner. The method involves an abstract theory of finite-dimensional Euclidean simple Jordan algebra
[ 講演参考URL ]
http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2007/11.html

2007年12月04日(火)

諸分野のための数学研究会

15:00-17:15   数理科学研究科棟(駒場) 122号室
Pavel Krejci 氏 (Weierstrass Institute for Applied Analysis and Stochastics) 15:00-16:00
Quasilinear hyperbolic equations with hysteresis
[ 講演概要 ]
We consider a wave propagation problem in a rate independent elastoplastic material described by a counterclockwise convex hysteresis operator. Unlike in viscoelasticity, the speed of propagation is bounded above by the speed of the corresponding elastic waves. The smoothening dissipative effect is due to the convexity of the hysteresis branches. We present some recent results on the long time behavior of solutions under various boundary conditions, including the stability of time periodic solutions under periodic forcing.
[ 講演参考URL ]
http://coe.math.sci.hokudai.ac.jp/sympo/various/index.html
Victor Isakov 氏 (Wichita State University) 16:15-17:15
Carleman estimates for second order operators with two large parameters
[ 講演概要 ]
We obtain new Carleman type estimates for general second order linear partial differential operators. These estimates hold for the weight functions under pseudoconvexity conditions relating the operator and weight function. We discuss these conditions. We give applications to uniqueness and stability of the continuation and inverse problems for elasticity system with residual stress without smallness assumptions on residual stress. This is a joint work with Nanhee Kim.
[ 講演参考URL ]
http://coe.math.sci.hokudai.ac.jp/sympo/various/index.html

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
今野 宏 氏 (東京大学大学院数理科学研究科)
Morse theory for abelian hyperkahler quotients

[ 講演概要 ]
In 1980's Kirwan computed Betti numbers of symplectic quotients by using Morse theory. In this talk, we develop this method to hyperkahler quotients by abelian Lie groups. In this method, many computations are much more simplified in the case of hyperkahler quotients than the case of symplectic quotients. As a result we compute not only the Betti numbers, but also the cohomology rings of abelian hyperkahler quotients.

2007年12月03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
甲斐千舟 氏 (九州大学)
等質有界領域の対称性条件、性質の良い有界領域実現について

2007年11月29日(木)

講演会

10:40-12:10   数理科学研究科棟(駒場) 128号室
Mikael Pichot 氏 (東大数理)
Topics in ergodic theory, von Neumann algebras, and rigidity
[ 講演参考URL ]
http://www.ms.u-tokyo.ac.jp/~yasuyuki/pichot.htm

2007年11月27日(火)

代数幾何学セミナー

16:30-18:00   数理科学研究科棟(駒場) 122号室
Alexander Kuznetsov 氏 (Steklov Inst)
Categorical resolutions of singularities
[ 講演概要 ]
I will give a definition of a categorical resolution of singularities and explain how such resolutions can be constructed.

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
小松 彦三郎 氏 (東大数理(名誉教授))
Heaviside's theory of signal transmission on submarine cables

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
石井 敦 氏 (京都大学数理解析研究所)
A quandle cocycle invariant for handlebody-links

[ 講演概要 ]
[joint work with Masahide Iwakiri (Osaka City University)]
A handlebody-link is a disjoint union of circles and a
finite trivalent graph embedded in a closed 3-manifold.
We consider it up to isotopies and IH-moves.
Then it represents an ambient isotopy class of
handlebodies embedded in the closed 3-manifold.
In this talk, I explain how a quandle cocycle invariant
is defined for handlebody-links.

2007年11月26日(月)

Kavli IPMU Komaba Seminar

17:00-18:30   数理科学研究科棟(駒場) 002号室
Mich\"ael Pevzner 氏 (Universit\'e de Reims and the University of Tokyo)
Kontsevich quantization of Poisson manifolds and Duflo isomorphism.
[ 講演概要 ]
Abstract: Since the fundamental results by Chevalley, Harish-Chandra and Dixmier one knows that the set of invariant polynomials on the dual of a Lie algebra of a particular type (solvable, simple or nilpotent) is isomorphic, as an algebra, to the center of the enveloping algebra. This fact was generalized to an arbitrary finite-dimensional real Lie algebra by M. Duflo in late 1970's. His proof was based on the Kirillov's orbits method that parametrizes infinitesimal characters of unitary irreducible representations of the corresponding Lie group in terms of co-adjoint orbits.

The Kontsevich' Formality theorem implies not only the existence of the Duflo map but shows that it is canonical. We shall describe this construction and indicate how does this construction extend to the whole Poisson cohomology of an arbitrary finite-dimensional real Lie algebra.

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
金子宏 氏 (東京理科大学)
Analysis related to probability theory based on p-adic hierarchical structure

2007年11月22日(木)

応用解析セミナー

16:00-17:30   数理科学研究科棟(駒場) 126号室
佐藤 洋平 氏 (早稲田大学・基幹理工学部・数学科)
Critical frequencyをもつ非線形シュレディンガー方程式のマルチピーク解
[ 講演概要 ]
非線形シュレディンガー方程式
$$ -\\epsilon2 \\Delta u +V(x)u= u^p, u>0 \\ \\hbox{in} \\R^N,
u\\in H1(\\R^N)$$
において、$\\epsilon \\to 0$ としたときに V(x) の k個の極小点にピークが集中していくマルチピーク解 $u_\\epsilon$ について考える。
ここで、p はsuperlinear, subcriticalの条件を満たし, ポテンシャル関数 V(x) は非負の有界な関数で $\\liminf_{|x|\\to \\infty}V(x)>0$ を満たすとする。

もし V(x) の各極小点に集中するピークがあるとしたら、そのピークの形状や大きさはその極小値が正であるか、0であるかによって大きく異なることが知られている。
この講演では V(x) の各極小値が正であるか 0 であるかにかかわらず、各 k個の極小点にピークが集中するマルチピーク解 $u_\\epsilon$ を構成する。

作用素環セミナー

16:30-18:00   数理科学研究科棟(駒場) 056号室
張欽 氏 (東大数理)
Spatial property of the canonical map associated to von Neumann algebras

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