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過去の記録
過去の記録 ～04/18｜本日 04/19 | 今後の予定 04/20～
2008年01月23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
Weizhe Zheng 氏 (Universite Paris-Sud 11)
Integrality, Rationality, and Independence of l in l-adic Cohomology over Local Fields
Weizhe Zheng 氏 (Universite Paris-Sud 11)
Integrality, Rationality, and Independence of l in l-adic Cohomology over Local Fields
[ 講演概要 ]
I will discuss two problems on traces in l-adic cohomology over local fields with finite residue field. In the first part, I will describe the behavior of integral complexes of l-adic sheaves under Grothendieck's six operations and the nearby cycle functor. In the second part, I will talk about rationality and independence of l. More precisely, I will introduce a notion of compatibility for systems of l-adic complexes and explain the proof of its stability by the above operations, in a slightly more general context (equivariant under finite groups). The main tool in this talk is a theorem of de Jong on
alterations.
I will discuss two problems on traces in l-adic cohomology over local fields with finite residue field. In the first part, I will describe the behavior of integral complexes of l-adic sheaves under Grothendieck's six operations and the nearby cycle functor. In the second part, I will talk about rationality and independence of l. More precisely, I will introduce a notion of compatibility for systems of l-adic complexes and explain the proof of its stability by the above operations, in a slightly more general context (equivariant under finite groups). The main tool in this talk is a theorem of de Jong on
alterations.
数理ファイナンスセミナー
17:30-19:00 数理科学研究科棟(駒場) 128号室
二宮 真理子 氏 (東京大)
確率微分方程式に対するRunge-Kutta法を用いた新たな弱近似手法
二宮 真理子 氏 (東京大)
確率微分方程式に対するRunge-Kutta法を用いた新たな弱近似手法
2008年01月22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
Serge Richard 氏 (Univ. Lyon 1)
Magnetic Schroedinger operators and twisted crossed product
Serge Richard 氏 (Univ. Lyon 1)
Magnetic Schroedinger operators and twisted crossed product
[ 講演概要 ]
During this seminar, we shall study spectral properties of generalized
magnetic Schroedinger operators H(B,V) with anisotropic magnetic field B
and scalar potential V. The essential spectrum of such operators is
expressed as a union of spectra of some asymptotic operators supported by
the quasi-orbits of a suitable dynamical system. A localization property
of the functional calculus of H(B,V) will also be presented. It directly
implies a non-propagation result for the unitary group generated by this
operator. The proofs rely on the use of twisted crossed product
C*-algebras. Twisted dynamical systems and their corresponding algebras
will be introduced and the natural link with magnetic Schroedinger
operators will be clearly established.
During this seminar, we shall study spectral properties of generalized
magnetic Schroedinger operators H(B,V) with anisotropic magnetic field B
and scalar potential V. The essential spectrum of such operators is
expressed as a union of spectra of some asymptotic operators supported by
the quasi-orbits of a suitable dynamical system. A localization property
of the functional calculus of H(B,V) will also be presented. It directly
implies a non-propagation result for the unitary group generated by this
operator. The proofs rely on the use of twisted crossed product
C*-algebras. Twisted dynamical systems and their corresponding algebras
will be introduced and the natural link with magnetic Schroedinger
operators will be clearly established.
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
大島 利雄 氏 (東京大学)
Connecion problems for Fuchsian differential equations free from accessory parameters
http://akagi.ms.u-tokyo.ac.jp/seminar.html
大島 利雄 氏 (東京大学)
Connecion problems for Fuchsian differential equations free from accessory parameters
[ 講演概要 ]
The classification of Fuchsian equations without accessory parameters was formulated as Deligne-Simpson problem, which was solved by Katz and they are studied by Haraoka and Yokoyama.
If the number of singular points of such equations is three, they have no geometric moduli.
We give a unified connection formula for such differential equations as a conjecture and show that it is true for the equations whose local monodromy at a singular point has distinct eigenvalues.
Other Fuchsian differential equations with accessory parameters and hypergeometric functions with multi-variables are also discussed.
[ 参考URL ]The classification of Fuchsian equations without accessory parameters was formulated as Deligne-Simpson problem, which was solved by Katz and they are studied by Haraoka and Yokoyama.
If the number of singular points of such equations is three, they have no geometric moduli.
We give a unified connection formula for such differential equations as a conjecture and show that it is true for the equations whose local monodromy at a singular point has distinct eigenvalues.
Other Fuchsian differential equations with accessory parameters and hypergeometric functions with multi-variables are also discussed.
http://akagi.ms.u-tokyo.ac.jp/seminar.html
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
Dmitry KALEDIN 氏 (Steklov研究所, 東大数理)
Homological methods in non-commutative geometry, part 10
[ 参考URL ]
http://imperium.lenin.ru/~kaledin/math/tokyo/
Dmitry KALEDIN 氏 (Steklov研究所, 東大数理)
Homological methods in non-commutative geometry, part 10
[ 参考URL ]
http://imperium.lenin.ru/~kaledin/math/tokyo/
講演会
16:30-18:00 数理科学研究科棟(駒場) 118号室
連続講演
Luc Illusie 氏 (パリ南大学)
On Gabber's refined uniformization theorem and applications
連続講演
Luc Illusie 氏 (パリ南大学)
On Gabber's refined uniformization theorem and applications
[ 講演概要 ]
Gabber has announced the following theorem : if X is a noetherian quasi-excellent scheme, Z a nowhere dense closed subset, and l a prime number invertible on X, then, locally for the topology on schemes of finite type over X generated, up to thickenings, by proper surjective maps which are generically finite of degree prime to l and by Nisnevich covers, the pair (X,Z) can be uniformized, i. e. replaced by a pair (Y,D), where Y is regular and D a strict normal crossings divisor. The whole proof is not yet written. I will give an overview. The plan is :
1. Statement and reduction to the complete local case (techniques of approximation)
2. Refined partial algebraization of complete local noetherian rings
3. Reduction to the equivariant log regular case (de Jong's techniques)
4. Making actions very tame, end of proof.
If time permits, I will show how the above theorem provides a short proof of Gabber's finiteness theorem for higher direct images of constructible sheaves of torsion prime to the characteristics by morphisms of finite type between quasi-excellent noetherian schemes.
Gabber has announced the following theorem : if X is a noetherian quasi-excellent scheme, Z a nowhere dense closed subset, and l a prime number invertible on X, then, locally for the topology on schemes of finite type over X generated, up to thickenings, by proper surjective maps which are generically finite of degree prime to l and by Nisnevich covers, the pair (X,Z) can be uniformized, i. e. replaced by a pair (Y,D), where Y is regular and D a strict normal crossings divisor. The whole proof is not yet written. I will give an overview. The plan is :
1. Statement and reduction to the complete local case (techniques of approximation)
2. Refined partial algebraization of complete local noetherian rings
3. Reduction to the equivariant log regular case (de Jong's techniques)
4. Making actions very tame, end of proof.
If time permits, I will show how the above theorem provides a short proof of Gabber's finiteness theorem for higher direct images of constructible sheaves of torsion prime to the characteristics by morphisms of finite type between quasi-excellent noetherian schemes.
2008年01月21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
篠原知子 氏 (都立産業技術高専)
周期的不定点に存在する不変曲線族の構成
篠原知子 氏 (都立産業技術高専)
周期的不定点に存在する不変曲線族の構成
講演会
16:00-17:30 数理科学研究科棟(駒場) 126号室
Torbjorn Lundh 氏 (Chalmers & Göteborg University)
Potential theory of funnels and wounds
Torbjorn Lundh 氏 (Chalmers & Göteborg University)
Potential theory of funnels and wounds
[ 講演概要 ]
We will talk about a result concerning Green functions, namely the so called 3G-inequality, which I studied together with H. Aikawa. The focus of the talk will be on the description of the way to that result, where we among other tools used numerical methods to get a better intuitive understanding the situation. We will also discuss a possible potential theoretic view-point of an ancient wound healing question.
We will talk about a result concerning Green functions, namely the so called 3G-inequality, which I studied together with H. Aikawa. The focus of the talk will be on the description of the way to that result, where we among other tools used numerical methods to get a better intuitive understanding the situation. We will also discuss a possible potential theoretic view-point of an ancient wound healing question.
2008年01月17日(木)
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
山下真 氏 (東大数理)
Cup product on the Periodic Cyclic Cohomology
山下真 氏 (東大数理)
Cup product on the Periodic Cyclic Cohomology
Lie群論・表現論セミナー
17:00-18:00 数理科学研究科棟(駒場) 123号室
手塚勝貴 氏 (東大数理)
Proper actions of SL(2,R) on irreducible complex symmetric spaces
https://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html
手塚勝貴 氏 (東大数理)
Proper actions of SL(2,R) on irreducible complex symmetric spaces
[ 講演概要 ]
We determine the irreducible complex symmetric spaces on which SL(2,R) acts properly. We use the T. Kobayashi's criterion for the proper actions. Also we use the symmetry or unsymmetry of the weighted Dynkin diagram of the theory of nilpotent orbits.
[ 参考URL ]We determine the irreducible complex symmetric spaces on which SL(2,R) acts properly. We use the T. Kobayashi's criterion for the proper actions. Also we use the symmetry or unsymmetry of the weighted Dynkin diagram of the theory of nilpotent orbits.
https://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html
講演会
16:30-18:00 数理科学研究科棟(駒場) 118号室
連続講演
Luc Illusie 氏 (パリ南大学)
On Gabber's refined uniformization theorem and applications
連続講演
Luc Illusie 氏 (パリ南大学)
On Gabber's refined uniformization theorem and applications
[ 講演概要 ]
Gabber has announced the following theorem : if X is a noetherian quasi-excellent scheme, Z a nowhere dense closed subset, and l a prime number invertible on X, then, locally for the topology on schemes of finite type over X generated, up to thickenings, by proper surjective maps which are generically finite of degree prime to l and by Nisnevich covers, the pair (X,Z) can be uniformized, i. e. replaced by a pair (Y,D), where Y is regular and D a strict normal crossings divisor. The whole proof is not yet written. I will give an overview. The plan is :
1. Statement and reduction to the complete local case (techniques of approximation)
2. Refined partial algebraization of complete local noetherian rings
3. Reduction to the equivariant log regular case (de Jong's techniques)
4. Making actions very tame, end of proof.
If time permits, I will show how the above theorem provides a short proof of Gabber's finiteness theorem for higher direct images of constructible sheaves of torsion prime to the characteristics by morphisms of finite type between quasi-excellent noetherian schemes.
Gabber has announced the following theorem : if X is a noetherian quasi-excellent scheme, Z a nowhere dense closed subset, and l a prime number invertible on X, then, locally for the topology on schemes of finite type over X generated, up to thickenings, by proper surjective maps which are generically finite of degree prime to l and by Nisnevich covers, the pair (X,Z) can be uniformized, i. e. replaced by a pair (Y,D), where Y is regular and D a strict normal crossings divisor. The whole proof is not yet written. I will give an overview. The plan is :
1. Statement and reduction to the complete local case (techniques of approximation)
2. Refined partial algebraization of complete local noetherian rings
3. Reduction to the equivariant log regular case (de Jong's techniques)
4. Making actions very tame, end of proof.
If time permits, I will show how the above theorem provides a short proof of Gabber's finiteness theorem for higher direct images of constructible sheaves of torsion prime to the characteristics by morphisms of finite type between quasi-excellent noetherian schemes.
2008年01月16日(水)
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
清水 泰隆 氏 (大阪大学大学院 基礎工学研究科)
Implementation of a jump-detection method and applications to real markets
https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2007/15.html
清水 泰隆 氏 (大阪大学大学院 基礎工学研究科)
Implementation of a jump-detection method and applications to real markets
[ 講演概要 ]
株価の確率モデルとして,ジャンプ型拡散過程は収益率分布の裾の厚さを表現しうる モデルとして有用な候補の一つである.その際,離散データによる統計推測は,Mancini('03), Shimizu and Yoshida('06)らによるジャンプ検出フィルターを用いることで可能になる. Shimizu('07)は有限個の離散データからのフィルターの決定法を提案し,実データへの応用を 可能にした.本報告では,これらの手法を計算機に実装する際の問題点とその解決法について 議論した後,日経平均や為替の日次データにMerton('76), Kou('02)など,いくつかのジャンプ型 モデルを仮定して,ジャンプの検出とモデルフィッティングを試みる.
[ 参考URL ]株価の確率モデルとして,ジャンプ型拡散過程は収益率分布の裾の厚さを表現しうる モデルとして有用な候補の一つである.その際,離散データによる統計推測は,Mancini('03), Shimizu and Yoshida('06)らによるジャンプ検出フィルターを用いることで可能になる. Shimizu('07)は有限個の離散データからのフィルターの決定法を提案し,実データへの応用を 可能にした.本報告では,これらの手法を計算機に実装する際の問題点とその解決法について 議論した後,日経平均や為替の日次データにMerton('76), Kou('02)など,いくつかのジャンプ型 モデルを仮定して,ジャンプの検出とモデルフィッティングを試みる.
https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2007/15.html
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
Antoine Chambert-Loir 氏 (Universite de Rennes 1)
Equidistribution theorems in Arakelov geometry
Antoine Chambert-Loir 氏 (Universite de Rennes 1)
Equidistribution theorems in Arakelov geometry
[ 講演概要 ]
The proof of Bogomolov's conjecture by Zhang made a crucial use
of an equidistribution property for the Galois orbits of points of small
heights in Abelian varieties defined over number fields.
Such an equidistribution property is proved using a method invented
by Szpiro, Ullmo and Zhang, and makes use of Arakelov theory.
This equidistribution theorem takes place in the complex torus
associated to the Abelian variety. I will show how a similar
equidistribution theorem can be proven for the p-adic topology ;
we have to use Berkovich space. Thanks to recent results of Yuan
about `big line bundles' in Arakelov geometry, the situation
is now very well understood.
The proof of Bogomolov's conjecture by Zhang made a crucial use
of an equidistribution property for the Galois orbits of points of small
heights in Abelian varieties defined over number fields.
Such an equidistribution property is proved using a method invented
by Szpiro, Ullmo and Zhang, and makes use of Arakelov theory.
This equidistribution theorem takes place in the complex torus
associated to the Abelian variety. I will show how a similar
equidistribution theorem can be proven for the p-adic topology ;
we have to use Berkovich space. Thanks to recent results of Yuan
about `big line bundles' in Arakelov geometry, the situation
is now very well understood.
統計数学セミナー
14:50-16:00 数理科学研究科棟(駒場) 122号室
Marc HOFFMANN 氏 (Universite Paris-est Marne la vallee)
Statistical analysis of fragmentation chains
https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2007/15.html
Marc HOFFMANN 氏 (Universite Paris-est Marne la vallee)
Statistical analysis of fragmentation chains
[ 講演概要 ]
We address statistical inference in self-similar conservative fragmentation chains, when only observations on the size of the fragments below a given threshold are available. (Possibly, the measurement of the fragments themselves are subject to further systematic experimental noise.) This framework, introduced by Bertoin and Martinez is motivated by mineral crushing in mining industry. We compute upper and lower rates of estimation for several functionals of the dislocation measure, both in a semi-parametric and a non-parametric framework. The underlying estimated object is the step distribution of the random walk associated to a randomly tagged fragment that evolves along the genealogical tree representation of the fragmentation process. We establish a formal link with the statistical problem of estimating the overshoot of the distribution as the crossing level goes to infinity with the size of the dataset; in particular the difficulty of the estimation problem in the non-parametric case is comparable to ill-posed linear inverse problems of order 1 in signal denoising.
[ 参考URL ]We address statistical inference in self-similar conservative fragmentation chains, when only observations on the size of the fragments below a given threshold are available. (Possibly, the measurement of the fragments themselves are subject to further systematic experimental noise.) This framework, introduced by Bertoin and Martinez is motivated by mineral crushing in mining industry. We compute upper and lower rates of estimation for several functionals of the dislocation measure, both in a semi-parametric and a non-parametric framework. The underlying estimated object is the step distribution of the random walk associated to a randomly tagged fragment that evolves along the genealogical tree representation of the fragmentation process. We establish a formal link with the statistical problem of estimating the overshoot of the distribution as the crossing level goes to infinity with the size of the dataset; in particular the difficulty of the estimation problem in the non-parametric case is comparable to ill-posed linear inverse problems of order 1 in signal denoising.
https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2007/15.html
2008年01月15日(火)
トポロジー火曜セミナー
16:30-17:30 数理科学研究科棟(駒場) 056号室
Tea: 16:00 - 16:30 コモンルーム
飯田 修一 氏 (東京大学大学院数理科学研究科)
Adiabatic limits of eta-invariants and the Meyer functions
Tea: 16:00 - 16:30 コモンルーム
飯田 修一 氏 (東京大学大学院数理科学研究科)
Adiabatic limits of eta-invariants and the Meyer functions
[ 講演概要 ]
The Meyer function is the function defined on the hyperelliptic
mapping class group, which gives a signature formula for surface
bundles over surfaces.
In this talk, we introduce certain generalizations of the Meyer
function by using eta-invariants and we discuss the uniqueness of this
function and compute the values for Dehn twists.
The Meyer function is the function defined on the hyperelliptic
mapping class group, which gives a signature formula for surface
bundles over surfaces.
In this talk, we introduce certain generalizations of the Meyer
function by using eta-invariants and we discuss the uniqueness of this
function and compute the values for Dehn twists.
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
Fulton Gonzalez 氏 (Tufts University)
Group contractions, invariant differential operators and the matrix Radon transform
https://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html
Fulton Gonzalez 氏 (Tufts University)
Group contractions, invariant differential operators and the matrix Radon transform
[ 講演概要 ]
Let $M_{n,k}$ denote the vector space of real $n\\times k$ matrices.
The matrix motion group is the semidirect product $(\\text O(n)\\times \\text O(k))\\ltimes M_{n,k}$, and is the Cartan motion group
associated with the real Grassmannian $G_{n,n+k}$.
The matrix Radon transform is an
integral transform associated with a double fibration involving
homogeneous spaces of this group. We provide a set of
algebraically independent generators of the subalgebra of its
universal enveloping algebra invariant under the Adjoint
representation. One of the elements of this set characterizes the range of the matrix Radon transform.
[ 参考URL ]Let $M_{n,k}$ denote the vector space of real $n\\times k$ matrices.
The matrix motion group is the semidirect product $(\\text O(n)\\times \\text O(k))\\ltimes M_{n,k}$, and is the Cartan motion group
associated with the real Grassmannian $G_{n,n+k}$.
The matrix Radon transform is an
integral transform associated with a double fibration involving
homogeneous spaces of this group. We provide a set of
algebraically independent generators of the subalgebra of its
universal enveloping algebra invariant under the Adjoint
representation. One of the elements of this set characterizes the range of the matrix Radon transform.
https://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html
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
Dmitry KALEDIN 氏 (Steklov研究所, 東大数理)
Homological methods in non-commutative geometry, part 9
[ 参考URL ]
http://imperium.lenin.ru/~kaledin/math/tokyo/
Dmitry KALEDIN 氏 (Steklov研究所, 東大数理)
Homological methods in non-commutative geometry, part 9
[ 参考URL ]
http://imperium.lenin.ru/~kaledin/math/tokyo/
2008年01月09日(水)
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
金川 秀也 氏 (武蔵工業大学)
Parameter estimated standardized U-statistics with degenerate kernel for weakly dependent random variables
https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2007/14.html
金川 秀也 氏 (武蔵工業大学)
Parameter estimated standardized U-statistics with degenerate kernel for weakly dependent random variables
[ 講演概要 ]
In this paper, extending the results of Gombay and Horv'{a}th (1998), we prove limit theorems for the maximum of standardized degenerate U-statistics defined by some absolutely regular sequences or functionals of them.
[ 参考URL ]In this paper, extending the results of Gombay and Horv'{a}th (1998), we prove limit theorems for the maximum of standardized degenerate U-statistics defined by some absolutely regular sequences or functionals of them.
https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2007/14.html
2008年01月08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
Nikolay Tzvetkov 氏 (Lille大学)
On the restrictions of Laplace-Beltrami eigenfunctions to curves
Nikolay Tzvetkov 氏 (Lille大学)
On the restrictions of Laplace-Beltrami eigenfunctions to curves
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
Dmitry KALEDIN 氏 (Steklov研究所, 東大数理)
Homological methods in non-commutative geometry, part 8
Dmitry KALEDIN 氏 (Steklov研究所, 東大数理)
Homological methods in non-commutative geometry, part 8
2008年01月07日(月)
諸分野のための数学研究会
13:30-14:30 数理科学研究科棟(駒場) 056号室
伊藤一文 氏 (North Carolina State University)
An Optimal Feedback Solution to Quantum Control Problems.
http://coe.math.sci.hokudai.ac.jp/sympo/various/index.html
伊藤一文 氏 (North Carolina State University)
An Optimal Feedback Solution to Quantum Control Problems.
[ 講演概要 ]
Control of quantum systems described by Schrodinger equation is considered. Feedback control laws are developed for the orbit tracking via a controled Hamiltonian. Asymptotic tracking properties of the feedback laws are analyzed. Numerical integrations via time-splitting are also analyzed and used to demonstrate the feasibility of the proposed feedback laws.
[ 参考URL ]Control of quantum systems described by Schrodinger equation is considered. Feedback control laws are developed for the orbit tracking via a controled Hamiltonian. Asymptotic tracking properties of the feedback laws are analyzed. Numerical integrations via time-splitting are also analyzed and used to demonstrate the feasibility of the proposed feedback laws.
http://coe.math.sci.hokudai.ac.jp/sympo/various/index.html
2008年01月06日(日)
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
青木 貴史 氏 (近畿大理工)
野海・山田方程式系のWKB解に付随する幾何的構造
青木 貴史 氏 (近畿大理工)
野海・山田方程式系のWKB解に付随する幾何的構造
[ 講演概要 ]
本多尚文氏、梅田陽子氏との共同研究
本多尚文氏、梅田陽子氏との共同研究
2007年12月26日(水)
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
Pinhas Grossman 氏 (Vanderbilt University)
Pairs of intermediate subfactors
Pinhas Grossman 氏 (Vanderbilt University)
Pairs of intermediate subfactors
2007年12月25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
Gregory Eskin 氏 (UCLA)
Inverse boundary value problems for the Schrodinger equation with time-dependent electromagnetic potentials and the Aharonov-Bohm effect
Gregory Eskin 氏 (UCLA)
Inverse boundary value problems for the Schrodinger equation with time-dependent electromagnetic potentials and the Aharonov-Bohm effect
[ 講演概要 ]
We consider the determination of the time-dependent magnetic and electric potentials (modulo gauge transforamtions) by the boundary measurements in domains with obstacles. We use the geometric optics and the tomography of broken rays. The presence of the obstacles leads to the Aharonov-Bohm effect caused by the magnetic and electric fluxes.
We consider the determination of the time-dependent magnetic and electric potentials (modulo gauge transforamtions) by the boundary measurements in domains with obstacles. We use the geometric optics and the tomography of broken rays. The presence of the obstacles leads to the Aharonov-Bohm effect caused by the magnetic and electric fluxes.
2007年12月22日(土)
東京無限可積分系セミナー
13:00-16:30 数理科学研究科棟(駒場) 117号室
池田岳 氏 (岡山理大理) 13:00-14:30
Double Schubert polynomials for the classical Lie groups
Nichols-Woronowicz model of the K-ring of flag vaieties G/B
池田岳 氏 (岡山理大理) 13:00-14:30
Double Schubert polynomials for the classical Lie groups
[ 講演概要 ]
For each infinite series of the classical Lie groups of type $B$,
$C$ or $D$, we introduce a family of polynomials parametrized by the
elements of the corresponding Weyl group of infinite rank. These
polynomials
represent the Schubert classes in the equivariant cohomology of the
corresponding
flag variety. When indexed by maximal Grassmannian elements of the Weyl
group,
these polynomials are equal to the factorial analogues of Schur $Q$- or
$P$-functions defined earlier by Ivanov. This talk is based on joint work
with L. Mihalcea and H. Naruse.
前野 俊昭 氏 (京大工) 15:00-16:30For each infinite series of the classical Lie groups of type $B$,
$C$ or $D$, we introduce a family of polynomials parametrized by the
elements of the corresponding Weyl group of infinite rank. These
polynomials
represent the Schubert classes in the equivariant cohomology of the
corresponding
flag variety. When indexed by maximal Grassmannian elements of the Weyl
group,
these polynomials are equal to the factorial analogues of Schur $Q$- or
$P$-functions defined earlier by Ivanov. This talk is based on joint work
with L. Mihalcea and H. Naruse.
Nichols-Woronowicz model of the K-ring of flag vaieties G/B
[ 講演概要 ]
We give a model of the equivariant $K$-ring $K_T(G/B)$ for
generalized flag varieties $G/B$ in the braided Hopf algebra
called Nichols-Woronowicz algebra. Our model is based on
the Chevalley-type formula for $K_T(G/B)$ due to Lenart
and Postnikov, which is described in terms of alcove paths.
We also discuss a conjecture on the model of the quantum
$K$-ring $QK(G/B)$.
We give a model of the equivariant $K$-ring $K_T(G/B)$ for
generalized flag varieties $G/B$ in the braided Hopf algebra
called Nichols-Woronowicz algebra. Our model is based on
the Chevalley-type formula for $K_T(G/B)$ due to Lenart
and Postnikov, which is described in terms of alcove paths.
We also discuss a conjecture on the model of the quantum
$K$-ring $QK(G/B)$.
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