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過去の記録
過去の記録 ～07/26｜本日 07/27 | 今後の予定 07/28～
2009年04月28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
平地 健吾 氏 (東京大学大学院数理科学研究科)
The ambient metric in conformal geometry
Tea: 16:00 - 16:30 コモンルーム
平地 健吾 氏 (東京大学大学院数理科学研究科)
The ambient metric in conformal geometry
[ 講演概要 ]
In 1985, Charles Fefferman and Robin Graham gave a method for realizing a conformal manifold of dimension n as a submanifold of a Ricci-flat Lorentz metric on a manifold of dimension n+2, which is now called the ambient space. Using this correspondence, one can construct many examples of conformal invariants and conformally invariant operators. However, if n is even, their construction of the ambient space is obstructed at the jet of order n/2 and thereby the application of the ambient space was limited. In this talk, I'll recall basic ideas of the ambient space and then explain how to avoid the difficulty and go beyond the obstruction. This is a joint work with Robin Graham.
In 1985, Charles Fefferman and Robin Graham gave a method for realizing a conformal manifold of dimension n as a submanifold of a Ricci-flat Lorentz metric on a manifold of dimension n+2, which is now called the ambient space. Using this correspondence, one can construct many examples of conformal invariants and conformally invariant operators. However, if n is even, their construction of the ambient space is obstructed at the jet of order n/2 and thereby the application of the ambient space was limited. In this talk, I'll recall basic ideas of the ambient space and then explain how to avoid the difficulty and go beyond the obstruction. This is a joint work with Robin Graham.
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
下村 明洋 氏 (首都大学東京)
非線型消散項を伴うシュレディンガー方程式の任意の大きさの初期データに対する解の漸近挙動(北直泰氏との共同研究)
下村 明洋 氏 (首都大学東京)
非線型消散項を伴うシュレディンガー方程式の任意の大きさの初期データに対する解の漸近挙動(北直泰氏との共同研究)
2009年04月27日(月)
代数幾何学セミナー
15:30-18:00 数理科学研究科棟(駒場) 122号室
Prof. Alessandra Sarti 氏 (Universite de Poitier) 15:30-16:30
Automorphism groups of K3 surfaces
) 17:00-18:00
The cohomological crepant resolution conjecture
Prof. Alessandra Sarti 氏 (Universite de Poitier) 15:30-16:30
Automorphism groups of K3 surfaces
[ 講演概要 ]
I will present recent progress in the study of prime order automorphisms of K3 surfaces.
An automorphism is called (non-) symplectic if the induced
operation on the global nowhere vanishing holomorphic two form
is (non-) trivial. After a short survey on the topic, I will
describe the topological structure of the fixed locus, the
geometry of these K3 surfaces and their moduli spaces.
Prof. Samuel Boissier 氏 (Universite de NiceI will present recent progress in the study of prime order automorphisms of K3 surfaces.
An automorphism is called (non-) symplectic if the induced
operation on the global nowhere vanishing holomorphic two form
is (non-) trivial. After a short survey on the topic, I will
describe the topological structure of the fixed locus, the
geometry of these K3 surfaces and their moduli spaces.
) 17:00-18:00
The cohomological crepant resolution conjecture
[ 講演概要 ]
The cohomological crepant resolution conjecture is one
form of Ruan's conjecture concerning the relation between the
geometry of a quotient singularity X/G - where X is a smooth
complex variety and G a finite group of automorphisms - and the
geometry of a crepant resolution of singularities of X/G ; it
generalizes the classical McKay correspondence. Following the
examples of the Hilbert schemes of points on surfaces and the
weighted projective spaces, I will present some of the recents
developments of the subject.
The cohomological crepant resolution conjecture is one
form of Ruan's conjecture concerning the relation between the
geometry of a quotient singularity X/G - where X is a smooth
complex variety and G a finite group of automorphisms - and the
geometry of a crepant resolution of singularities of X/G ; it
generalizes the classical McKay correspondence. Following the
examples of the Hilbert schemes of points on surfaces and the
weighted projective spaces, I will present some of the recents
developments of the subject.
2009年04月23日(木)
作用素環セミナー
16:30-18:00 数理科学研究科棟(駒場) 128号室
内藤克利 氏 (首都大)
Entire Cyclic Cohomology of Noncommutative 2-Tori
内藤克利 氏 (首都大)
Entire Cyclic Cohomology of Noncommutative 2-Tori
2009年04月22日(水)
PDE実解析研究会
10:30-11:30 数理科学研究科棟(駒場) 128号室
いつもとは会場が異なります。
Wilhelm Klingenberg 氏 (University of Durham)
From Codazzi-Mainardi to Cauchy-Riemann
いつもとは会場が異なります。
Wilhelm Klingenberg 氏 (University of Durham)
From Codazzi-Mainardi to Cauchy-Riemann
[ 講演概要 ]
In joint work with Brendan Guilfoyle we established an upper bound for the winding number of the principal curvature foliation at any isolated umbilic of a surface in Euclidean three-space. In our talk, we will focus on the analytic core of the problem. Here is a model of the triaxial ellipsoid with its curvature foliation and one umbilic on the right.
In joint work with Brendan Guilfoyle we established an upper bound for the winding number of the principal curvature foliation at any isolated umbilic of a surface in Euclidean three-space. In our talk, we will focus on the analytic core of the problem. Here is a model of the triaxial ellipsoid with its curvature foliation and one umbilic on the right.
東京幾何セミナー
14:45-18:00 数理科学研究科棟(駒場) 122号室
場所は東大数理(駒場)、東京工業大学(大岡山)のいずれかで行います。
詳細については、上記セミナーURLよりご確認下さい。
「今後の予定」欄には、東工大で行われるセミナーは表��
中田文憲 氏 (東京工業大学理工学研究科) 14:45-16:15
Einstein-Weyl structures on 3-dimensional Severi varieties
Toric non-Abelian Hodge theory
場所は東大数理(駒場)、東京工業大学(大岡山)のいずれかで行います。
詳細については、上記セミナーURLよりご確認下さい。
「今後の予定」欄には、東工大で行われるセミナーは表��
中田文憲 氏 (東京工業大学理工学研究科) 14:45-16:15
Einstein-Weyl structures on 3-dimensional Severi varieties
[ 講演概要 ]
The space of nodal curves on a projective surface is called a Severi variety.In this talk, we show that any Severi variety of nodal rational curves on a non-singular projective surface is always equipped with a natural Einstein-Weyl structure, if the space is 3-dimensional. This is a generalization of the Einstein-Weyl structure on the space of smooth rational curves on a complex surface, given by N. Hitchin in the context of twistor theory. We will explain some properties of the Einstein-Weyl spaces given by this method, and we will also show some examples of such Einstein-Weyl spaces. (This is a joint work with Nobuhiro Honda.)
Tamas Hausel 氏 (Oxford University) 16:30-18:00The space of nodal curves on a projective surface is called a Severi variety.In this talk, we show that any Severi variety of nodal rational curves on a non-singular projective surface is always equipped with a natural Einstein-Weyl structure, if the space is 3-dimensional. This is a generalization of the Einstein-Weyl structure on the space of smooth rational curves on a complex surface, given by N. Hitchin in the context of twistor theory. We will explain some properties of the Einstein-Weyl spaces given by this method, and we will also show some examples of such Einstein-Weyl spaces. (This is a joint work with Nobuhiro Honda.)
Toric non-Abelian Hodge theory
[ 講演概要 ]
First we give an overview of the geometrical and topological aspects of the spaces in the non-Abelian Hodge theory of a curve and their connection with quiver varieties. Then by concentrating on toric hyperkaehler varieties in place of quiver varieties we construct the toric Betti, De Rham and Dolbeault spaces and prove several of the expected properties of the geometry and topology of these varieties. This is joint work with Nick Proudfoot.
First we give an overview of the geometrical and topological aspects of the spaces in the non-Abelian Hodge theory of a curve and their connection with quiver varieties. Then by concentrating on toric hyperkaehler varieties in place of quiver varieties we construct the toric Betti, De Rham and Dolbeault spaces and prove several of the expected properties of the geometry and topology of these varieties. This is joint work with Nick Proudfoot.
統計数学セミナー
15:00-16:10 数理科学研究科棟(駒場) 128号室
Arnaud DOUCET 氏 (統計数理研究所)
Interacting Markov chain Monte Carlo Methods for Solving Nonlinear Measure-Valued Equations
https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2009/02.html
Arnaud DOUCET 氏 (統計数理研究所)
Interacting Markov chain Monte Carlo Methods for Solving Nonlinear Measure-Valued Equations
[ 講演概要 ]
We present a new class of interacting Markov chain Monte Carlo algorithms for solving numerically discrete-time measure-valued equations. The associated stochastic processes belong to the class of self-interacting Markov chains. In contrast to traditional Markov chains, their time evolution depend on the occupation measure of their past values. This general methodology allows us to provide a natural way to sample from a sequence of target probability measures of increasing complexity. We develop an original theoretical analysis to analyze the behaviour of these iterative algorithms. We establish a variety of convergence results including exponential estimates and a uniform convergence theorem with respect to the number of target distributions. We also illustrate these algorithms in the context of Feynman-Kac distribution flows.
(this is joint work with Professor Pierre Del Moral)
[ 参考URL ]We present a new class of interacting Markov chain Monte Carlo algorithms for solving numerically discrete-time measure-valued equations. The associated stochastic processes belong to the class of self-interacting Markov chains. In contrast to traditional Markov chains, their time evolution depend on the occupation measure of their past values. This general methodology allows us to provide a natural way to sample from a sequence of target probability measures of increasing complexity. We develop an original theoretical analysis to analyze the behaviour of these iterative algorithms. We establish a variety of convergence results including exponential estimates and a uniform convergence theorem with respect to the number of target distributions. We also illustrate these algorithms in the context of Feynman-Kac distribution flows.
(this is joint work with Professor Pierre Del Moral)
https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2009/02.html
2009年04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
Ivan Marin 氏 (Univ. Paris VII)
Some algebraic aspects of KZ systems
Tea: 16:00 - 16:30 コモンルーム
Ivan Marin 氏 (Univ. Paris VII)
Some algebraic aspects of KZ systems
[ 講演概要 ]
Knizhnik-Zamolodchikov (KZ) systems enables one
to construct representations of (generalized)
braid groups. While this geometric construction is
now very well understood, it still brings to
attention, or helps constructing, new algebraic objects.
In this talk, we will present some of them, including an
infinitesimal version of Iwahori-Hecke algebras and a
generalization of the Krammer representations of the usual
braid groups.
Knizhnik-Zamolodchikov (KZ) systems enables one
to construct representations of (generalized)
braid groups. While this geometric construction is
now very well understood, it still brings to
attention, or helps constructing, new algebraic objects.
In this talk, we will present some of them, including an
infinitesimal version of Iwahori-Hecke algebras and a
generalization of the Krammer representations of the usual
braid groups.
2009年04月20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) 126号室
鎌田博行 氏 (宮城教育大学)
Indefinite Kähler surfaces of constant scalar curvature
鎌田博行 氏 (宮城教育大学)
Indefinite Kähler surfaces of constant scalar curvature
2009年04月18日(土)
東京無限可積分系セミナー
11:00-14:30 数理科学研究科棟(駒場) 117号室
Vladimir Dobrev 氏 (Institute for Nuclear Reserch and Nuclear Energy, Sofia, Bulgaria) 11:00-12:00
Invariant Differential Operators for Non-Compact Lie Groups
TBA
Vladimir Dobrev 氏 (Institute for Nuclear Reserch and Nuclear Energy, Sofia, Bulgaria) 11:00-12:00
Invariant Differential Operators for Non-Compact Lie Groups
[ 講演概要 ]
We present a canonical procedure for the explicit construction of
invariant differential operators. The exposition is for semi-simple
Lie algebras, but is easily generalized to the supersymmetric and
quantum group settings. Especially important is a narrow class of
algebras, which we call 'conformal Lie algebras', which have very
similar properties to the conformal algebras of n-dimensional
Minkowski space-time. Examples are given in detail, including diagrams of
intertwining operators, or equivalently, multiplets of elementary
representations (generalized Verma modules).
笠谷昌弘 氏 (東大数理) 13:30-14:30We present a canonical procedure for the explicit construction of
invariant differential operators. The exposition is for semi-simple
Lie algebras, but is easily generalized to the supersymmetric and
quantum group settings. Especially important is a narrow class of
algebras, which we call 'conformal Lie algebras', which have very
similar properties to the conformal algebras of n-dimensional
Minkowski space-time. Examples are given in detail, including diagrams of
intertwining operators, or equivalently, multiplets of elementary
representations (generalized Verma modules).
TBA
[ 講演概要 ]
TBA
TBA
2009年04月16日(木)
作用素環セミナー
16:30-18:00 数理科学研究科棟(駒場) 128号室
緒方芳子 氏 (東大数理)
Large Deviations in Quantum Spin Chains
緒方芳子 氏 (東大数理)
Large Deviations in Quantum Spin Chains
2009年04月15日(水)
講演会
15:30-17:00 数理科学研究科棟(駒場) 470号室
Wilhelm Stannat 氏 (Darmstadt 工科大学)
Invariant measures for stochastic partial differential equations: new a priori estimates and applications
Wilhelm Stannat 氏 (Darmstadt 工科大学)
Invariant measures for stochastic partial differential equations: new a priori estimates and applications
統計数学セミナー
16:20-17:30 数理科学研究科棟(駒場) 128号室
Jean JACOD 氏 (Universite Paris VI)
Estimating the successive Blumenthal-Getoor indices for a discretely observed process
https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2009/00.html
Jean JACOD 氏 (Universite Paris VI)
Estimating the successive Blumenthal-Getoor indices for a discretely observed process
[ 講演概要 ]
Letting F be a Levy measure whose "tail" $F ([-x, x])$ admits an expansion $\\sigma_{i\\ge 1} a_i/x^\\beta$ as $x \\rightarrow 0$, we call $\\beta_1 > \\beta_2 >...$ the successive Blumenthal-Getoor indices, since $\\beta_1$ is in this case the usual Blumenthal-Getoor index. This notion may be extended to more general semimartingale. We propose here a method to estimate the $\\beta_i$'s and the coefficients $a_i$'s, or rather their extension for semimartingales, when the underlying semimartingale $X$ is observed at discrete times, on fixed time interval. The asymptotic is when the time-lag goes to $0$. It is then possible to construct consistent estimators for $\\beta_i$ and $a_i$ for those $i$'s such that $\\beta_i > \\beta_1 /2$, whereas it is impossible to do so (even when $X$ is a Levy process) for those $i$'s such that $\\beta_i < \\beta_1 /2$. On the other hand, a central limit theorem for $\\beta_1$ is available only when $\\beta_i < \\beta_1 /2$: consequently, when we can actually consistently estimate some $\\beta_i$'s besides $\\beta_1$ , then no central limit theorem can hold, and correlatively the rates of convergence become quite slow (although one know them explicitly): so the results have some theoretical interest in the sense that they set up bounds on what is actually possible to achieve, but the practical applications are probably quite thin.
(joint with Yacine Ait-Sahalia)
[ 参考URL ]Letting F be a Levy measure whose "tail" $F ([-x, x])$ admits an expansion $\\sigma_{i\\ge 1} a_i/x^\\beta$ as $x \\rightarrow 0$, we call $\\beta_1 > \\beta_2 >...$ the successive Blumenthal-Getoor indices, since $\\beta_1$ is in this case the usual Blumenthal-Getoor index. This notion may be extended to more general semimartingale. We propose here a method to estimate the $\\beta_i$'s and the coefficients $a_i$'s, or rather their extension for semimartingales, when the underlying semimartingale $X$ is observed at discrete times, on fixed time interval. The asymptotic is when the time-lag goes to $0$. It is then possible to construct consistent estimators for $\\beta_i$ and $a_i$ for those $i$'s such that $\\beta_i > \\beta_1 /2$, whereas it is impossible to do so (even when $X$ is a Levy process) for those $i$'s such that $\\beta_i < \\beta_1 /2$. On the other hand, a central limit theorem for $\\beta_1$ is available only when $\\beta_i < \\beta_1 /2$: consequently, when we can actually consistently estimate some $\\beta_i$'s besides $\\beta_1$ , then no central limit theorem can hold, and correlatively the rates of convergence become quite slow (although one know them explicitly): so the results have some theoretical interest in the sense that they set up bounds on what is actually possible to achieve, but the practical applications are probably quite thin.
(joint with Yacine Ait-Sahalia)
https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2009/00.html
統計数学セミナー
15:00-16:10 数理科学研究科棟(駒場) 128号室
Jean JACOD 氏 (Universite Paris VI)
A survey on realized p-variations for semimartingales
https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2009/00.html
Jean JACOD 氏 (Universite Paris VI)
A survey on realized p-variations for semimartingales
[ 講演概要 ]
Let $X$ be a process which is observed at the times $i\\Delta_n$ for $i=0,1,\\ldots,$. If $p>0$ the realized $p$-variation over the time interval $[0, t]$ is
V^n(p)_t=\\sum_{i=1}^{[t/\\Delta_n]}|X_{i\\Delta_n}-X_{(i-1)\\Delta_n}|^p.
The behavior of these $p$-variations when $\\Delta_n ightarrow 0$ (and t is fixed) is now well understood, from the point of view of limits in probability (these are basically old results due to Lepingle) and also for the associated central limit theorem.
The aim of this talk is to review those results, as well as a few extensions (multipower variations, truncated variations). We will put some emphasis on the assumptions on $X$ which are needed, depending on the value of $p$.
[ 参考URL ]Let $X$ be a process which is observed at the times $i\\Delta_n$ for $i=0,1,\\ldots,$. If $p>0$ the realized $p$-variation over the time interval $[0, t]$ is
V^n(p)_t=\\sum_{i=1}^{[t/\\Delta_n]}|X_{i\\Delta_n}-X_{(i-1)\\Delta_n}|^p.
The behavior of these $p$-variations when $\\Delta_n ightarrow 0$ (and t is fixed) is now well understood, from the point of view of limits in probability (these are basically old results due to Lepingle) and also for the associated central limit theorem.
The aim of this talk is to review those results, as well as a few extensions (multipower variations, truncated variations). We will put some emphasis on the assumptions on $X$ which are needed, depending on the value of $p$.
https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2009/00.html
2009年04月14日(火)
講演会
16:30-18:00 数理科学研究科棟(駒場) 056号室
Klaus Niederkruger 氏 (Ecole normale superieure de Lyon)
Resolution of symplectic orbifolds obtained from reduction
Klaus Niederkruger 氏 (Ecole normale superieure de Lyon)
Resolution of symplectic orbifolds obtained from reduction
[ 講演概要 ]
We present a method to obtain resolutions of symplectic orbifolds arising from symplectic reduction of a Hamiltonian S1-manifold at a regular value. As an application, we show that all isolated cyclic singularities of a symplectic orbifold admit a resolution and that pre-quantizations of symplectic orbifolds are symplectically fillable by a smooth manifold.
We present a method to obtain resolutions of symplectic orbifolds arising from symplectic reduction of a Hamiltonian S1-manifold at a regular value. As an application, we show that all isolated cyclic singularities of a symplectic orbifold admit a resolution and that pre-quantizations of symplectic orbifolds are symplectically fillable by a smooth manifold.
2009年04月13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) 126号室
千葉優作 氏 (東大数理)
A new method to generalize the Nevanlinna theory to several complex variables
千葉優作 氏 (東大数理)
A new method to generalize the Nevanlinna theory to several complex variables
2009年04月09日(木)
作用素環セミナー
16:30-18:00 数理科学研究科棟(駒場) 128号室
Dietmar Bisch 氏 (Vanderbilt University)
Bimodules, planarity and freeness
Dietmar Bisch 氏 (Vanderbilt University)
Bimodules, planarity and freeness
2009年04月08日(水)
諸分野のための数学研究会
10:30-11:30 数理科学研究科棟(駒場) 056号室
横山悦郎 氏 (学習院大学)
Growth of an Ice Disk from Supercooled Water: Theory and Space Experiment in Kibo of International Space Station
横山悦郎 氏 (学習院大学)
Growth of an Ice Disk from Supercooled Water: Theory and Space Experiment in Kibo of International Space Station
[ 講演概要 ]
We present a model of the time evolution of a disk crystal of ice with radius $R$ and thickness $h$ growing from supercooled water and discuss its morphological stability. Disk thickening, {\\it i.e.}, growth along the $c$ axis of ice, is governed by slow molecular rearrangements on the basal faces. Growth of the radius, {\\it i.e.}, growth parallel to the basal plane, is controlled by transport of latent heat. Our analysis is used to understand the symmetry breaking obtained experimentally by Shimada and Furukawa under the one-G condition. We also introduce that the space experiment of the morphological instability on the ice growing in supercooled water, which was carried out on the Japanese Experiment Module "Kibo" of International Space Station from December 2008 and February 2009.
http://kibo.jaxa.jp/experiment/theme/first/ice_crystal_end.html
We show the experimental results under the micro-G condition and discuss the feature on the "Kibo" experoments.
We present a model of the time evolution of a disk crystal of ice with radius $R$ and thickness $h$ growing from supercooled water and discuss its morphological stability. Disk thickening, {\\it i.e.}, growth along the $c$ axis of ice, is governed by slow molecular rearrangements on the basal faces. Growth of the radius, {\\it i.e.}, growth parallel to the basal plane, is controlled by transport of latent heat. Our analysis is used to understand the symmetry breaking obtained experimentally by Shimada and Furukawa under the one-G condition. We also introduce that the space experiment of the morphological instability on the ice growing in supercooled water, which was carried out on the Japanese Experiment Module "Kibo" of International Space Station from December 2008 and February 2009.
http://kibo.jaxa.jp/experiment/theme/first/ice_crystal_end.html
We show the experimental results under the micro-G condition and discuss the feature on the "Kibo" experoments.
2009年03月25日(水)
GCOEレクチャーズ
16:00-17:30 数理科学研究科棟(駒場) 128号室
Mark Gross 氏 (University of California, San Diego)
The Strominger-Yau-Zaslow conjecture and mirror symmetry via degenerations II
Mark Gross 氏 (University of California, San Diego)
The Strominger-Yau-Zaslow conjecture and mirror symmetry via degenerations II
[ 講演概要 ]
The second half of the lecture.
The second half of the lecture.
2009年03月24日(火)
GCOEレクチャーズ
16:00-17:30 数理科学研究科棟(駒場) 128号室
Mark Gross 氏 (University of California, San Diego)
The Strominger-Yau-Zaslow conjecture and mirror symmetry via degenerations I
Mark Gross 氏 (University of California, San Diego)
The Strominger-Yau-Zaslow conjecture and mirror symmetry via degenerations I
[ 講演概要 ]
I will discuss the SYZ conjecture which attempts to explain mirror symmetry via the existence of dual torus fibrations on mirror pairs of Calabi-Yau manifolds. After reviewing some older work on this subject, I will explain how it leads to an algebro-geometric version of this conjecture and will discuss recent work with Bernd Siebert. This recent work gives a mirror construction along with far more detailed information about the B-model side of mirror symmetry, leading to new mirror symmetry predictions.
I will discuss the SYZ conjecture which attempts to explain mirror symmetry via the existence of dual torus fibrations on mirror pairs of Calabi-Yau manifolds. After reviewing some older work on this subject, I will explain how it leads to an algebro-geometric version of this conjecture and will discuss recent work with Bernd Siebert. This recent work gives a mirror construction along with far more detailed information about the B-model side of mirror symmetry, leading to new mirror symmetry predictions.
2009年03月21日(土)
東京無限可積分系セミナー
11:00-14:30 数理科学研究科棟(駒場) 117号室
梶原 康史 氏 (神戸理) 11:00-12:00
On classes of transformations for bilinear sum of
(basic) hypergeometric series and multivariate generalizations.
On explicit formulas for Whittaker functions on real semisimple Lie groups
梶原 康史 氏 (神戸理) 11:00-12:00
On classes of transformations for bilinear sum of
(basic) hypergeometric series and multivariate generalizations.
[ 講演概要 ]
In this talk, I will present classes of bilinear transformation
formulas for basic hypergeometric series and Milne's multivariate
basic hypergeometric series associated with the root system of
type $A$. Our construction is similar to one of elementary
proof of Sears-Whipple transformation formula for terminating
balanced ${}_4 \\phi_3$ series while we use multiple Euler
transformation formula with different dimensions which has
obtained in our previous work.
石井 卓 氏 (成蹊大理工) 13:30-14:30In this talk, I will present classes of bilinear transformation
formulas for basic hypergeometric series and Milne's multivariate
basic hypergeometric series associated with the root system of
type $A$. Our construction is similar to one of elementary
proof of Sears-Whipple transformation formula for terminating
balanced ${}_4 \\phi_3$ series while we use multiple Euler
transformation formula with different dimensions which has
obtained in our previous work.
On explicit formulas for Whittaker functions on real semisimple Lie groups
[ 講演概要 ]
will report explicit formulas
for Whittaker functions related to principal series
reprensetations on real semisimple Lie groups $G$ of
classical type.
Our explicit formulas are recursive formulas with
respect to the real rank of $G$, and in some lower rank
cases they are related to generalized
hypergeometric series $ {}_3F_2(1) $ and $ {}_4F_3(1) $.
will report explicit formulas
for Whittaker functions related to principal series
reprensetations on real semisimple Lie groups $G$ of
classical type.
Our explicit formulas are recursive formulas with
respect to the real rank of $G$, and in some lower rank
cases they are related to generalized
hypergeometric series $ {}_3F_2(1) $ and $ {}_4F_3(1) $.
2009年03月17日(火)
GCOEレクチャーズ
10:00-17:30 数理科学研究科棟(駒場) 123号室
GCOE Spring School on Representation Theory
Roger Zierau 氏 (Oklahoma State University) 11:00-12:00
Dirac Cohomology
Salah Mehdi 氏 (Metz University) 13:30-14:30
Enright-Varadarajan modules and harmonic spinors
Bernhard Krötz
氏 (Max Planck Institute) 15:00-16:00
Harish-Chandra modules
Peter Trapa 氏 (Utah) 16:30-17:30
Special unipotent representations of real reductive groups
GCOE Spring School on Representation Theory
Roger Zierau 氏 (Oklahoma State University) 11:00-12:00
Dirac Cohomology
Salah Mehdi 氏 (Metz University) 13:30-14:30
Enright-Varadarajan modules and harmonic spinors
Bernhard Krötz
氏 (Max Planck Institute) 15:00-16:00
Harish-Chandra modules
Peter Trapa 氏 (Utah) 16:30-17:30
Special unipotent representations of real reductive groups
2009年03月16日(月)
GCOEレクチャーズ
10:00-16:20 数理科学研究科棟(駒場) 123号室
GCOE Spring School on Representation Theory
Bernhard Krötz
氏 (Max Planck Institute) 10:00-11:00
Harish-Chandra modules
https://www.ms.u-tokyo.ac.jp/~toshi/index.files/springschooltokyo200903.html#kroetz
Peter Trapa 氏 (Utah) 11:15-12:15
Special unipotent representations of real reductive groups
https://www.ms.u-tokyo.ac.jp/~toshi/index.files/springschooltokyo200903.html#trapa
Roger Zierau 氏 (Oklahoma State University) 13:30-14:30
Dirac Cohomology
https://www.ms.u-tokyo.ac.jp/~toshi/index.files/springschooltokyo200903.html#zierau
Salah Mehdi 氏 (Metz University) 15:20-16:20
Enright-Varadarajan modules and harmonic spinors
https://www.ms.u-tokyo.ac.jp/~toshi/index.files/springschooltokyo200903.html#mehdi
GCOE Spring School on Representation Theory
Bernhard Krötz
氏 (Max Planck Institute) 10:00-11:00
Harish-Chandra modules
[ 講演概要 ]
We plan to give a course on the various types of topological globalizations of Harish-Chandra modules. It is intended to cover the following topics:
1.Topological representation theory on various types of locally convex vector spaces.
2.Basic algebraic theory of Harish-Chandra modules
3. Unique globalization versus lower bounds for matrix coefficients
4. Dirac type sequences for representations
5. Deformation theory of Harish-Chandra modules
The new material presented was obtained in collaboration with Joseph Bernstein and Henrik Schlichtkrull. A first reference is the recent preprint "Smooth Frechet Globalizations of Harish-Chandra Modules" by J. Bernstein and myself, downloadable at arXiv:0812.1684v1.
[ 参考URL ]We plan to give a course on the various types of topological globalizations of Harish-Chandra modules. It is intended to cover the following topics:
1.Topological representation theory on various types of locally convex vector spaces.
2.Basic algebraic theory of Harish-Chandra modules
3. Unique globalization versus lower bounds for matrix coefficients
4. Dirac type sequences for representations
5. Deformation theory of Harish-Chandra modules
The new material presented was obtained in collaboration with Joseph Bernstein and Henrik Schlichtkrull. A first reference is the recent preprint "Smooth Frechet Globalizations of Harish-Chandra Modules" by J. Bernstein and myself, downloadable at arXiv:0812.1684v1.
https://www.ms.u-tokyo.ac.jp/~toshi/index.files/springschooltokyo200903.html#kroetz
Peter Trapa 氏 (Utah) 11:15-12:15
Special unipotent representations of real reductive groups
[ 講演概要 ]
These lectures are aimed at beginning graduate students interested in the representation theory of real Lie groups. A familiarity with the theory of compact Lie groups and the basics of Harish-Chandra modules will be assumed. The goal of the lecture series is to give an exposition (with many examples) of the algebraic and geometric theory of special unipotent representations. These representations are of considerable interest; in particular, they are predicted to be the building blocks of all representation which can contribute to spaces of automorphic forms. They admit many beautiful characterizations, but their construction and unitarizability still remain mysterious.
The following topics are planned:
1.Algebraic definition of special unipotent representations and examples.
2.Localization and duality for Harish-Chandra modules.
3. Geometric definition of special unipotent representations.
[ 参考URL ]These lectures are aimed at beginning graduate students interested in the representation theory of real Lie groups. A familiarity with the theory of compact Lie groups and the basics of Harish-Chandra modules will be assumed. The goal of the lecture series is to give an exposition (with many examples) of the algebraic and geometric theory of special unipotent representations. These representations are of considerable interest; in particular, they are predicted to be the building blocks of all representation which can contribute to spaces of automorphic forms. They admit many beautiful characterizations, but their construction and unitarizability still remain mysterious.
The following topics are planned:
1.Algebraic definition of special unipotent representations and examples.
2.Localization and duality for Harish-Chandra modules.
3. Geometric definition of special unipotent representations.
https://www.ms.u-tokyo.ac.jp/~toshi/index.files/springschooltokyo200903.html#trapa
Roger Zierau 氏 (Oklahoma State University) 13:30-14:30
Dirac Cohomology
[ 講演概要 ]
Dirac operators have played an important role in representation theory. An early example is the construction of discrete series representations as spaces of L2 harmonic spinors on symmetric spaces G/K. More recently a very natural Dirac operator has been discovered by Kostant; it is referred to as the cubic Dirac operator. There are algebraic and geometric versions. Suppose G/H is a reductive homogeneous space and $\\mathfrak g = \\mathfrak h + \\mathfrak q$. Let S\\mathfrak q be the restriction of the spin representation of SO(\\mathfrak q) to H ⊂ SO(\\mathfrak q). The algebraic cubic Dirac operator is an H-homomorphism \\mathcal D: V \\otimes S\\mathfrak q → V \\otimes S\\mathfrak q, where V is an $\\mathfrak g$-module. The geometric geometric version is a differential operator acting on smooth sections of vector bundles of spinors on G/H. The algebraic cubic Dirac operator leads to a notion of Dirac cohomology, generalizing $\\mathfrak n$-cohomology. The lectures will roughly contain the following.
1.Construction of the spin representations of \\widetilde{SO}(n).
2.The algebraic cubic Dirac operator \\mathcal D: V \\otimes S\\mathfrak q → V \\otimes S\\mathfrak q will be defined and some properties, including a formula for the square, will be given.
3. Of special interest is the case when H=K, a maximal compact subgroup of G and V is a unitarizable $(\\mathfrak g,K)$-module. This case will be discussed.
4.The Dirac cohomology of a finite dimensional representation will be computed. We will see how this is related to $\\mathfrak n$-cohomology of V.
5. The relationship between the algebraic and geometric cubic Dirac operators will be described. A couple of open questions will then be discussed.
The lectures will be fairly elementary.
[ 参考URL ]Dirac operators have played an important role in representation theory. An early example is the construction of discrete series representations as spaces of L2 harmonic spinors on symmetric spaces G/K. More recently a very natural Dirac operator has been discovered by Kostant; it is referred to as the cubic Dirac operator. There are algebraic and geometric versions. Suppose G/H is a reductive homogeneous space and $\\mathfrak g = \\mathfrak h + \\mathfrak q$. Let S\\mathfrak q be the restriction of the spin representation of SO(\\mathfrak q) to H ⊂ SO(\\mathfrak q). The algebraic cubic Dirac operator is an H-homomorphism \\mathcal D: V \\otimes S\\mathfrak q → V \\otimes S\\mathfrak q, where V is an $\\mathfrak g$-module. The geometric geometric version is a differential operator acting on smooth sections of vector bundles of spinors on G/H. The algebraic cubic Dirac operator leads to a notion of Dirac cohomology, generalizing $\\mathfrak n$-cohomology. The lectures will roughly contain the following.
1.Construction of the spin representations of \\widetilde{SO}(n).
2.The algebraic cubic Dirac operator \\mathcal D: V \\otimes S\\mathfrak q → V \\otimes S\\mathfrak q will be defined and some properties, including a formula for the square, will be given.
3. Of special interest is the case when H=K, a maximal compact subgroup of G and V is a unitarizable $(\\mathfrak g,K)$-module. This case will be discussed.
4.The Dirac cohomology of a finite dimensional representation will be computed. We will see how this is related to $\\mathfrak n$-cohomology of V.
5. The relationship between the algebraic and geometric cubic Dirac operators will be described. A couple of open questions will then be discussed.
The lectures will be fairly elementary.
https://www.ms.u-tokyo.ac.jp/~toshi/index.files/springschooltokyo200903.html#zierau
Salah Mehdi 氏 (Metz University) 15:20-16:20
Enright-Varadarajan modules and harmonic spinors
[ 講演概要 ]
The aim of these lectures is twofold. First we would like to describe the construction of the Enright-Varadarajan modules which provide a nice algebraic characterization of discrete series representations. This construction uses several important tools of representations theory.
Then we shall use the Enright-Varadarajan modules to define a product for harmonic spinors on homogeneous spaces.
[ 参考URL ]The aim of these lectures is twofold. First we would like to describe the construction of the Enright-Varadarajan modules which provide a nice algebraic characterization of discrete series representations. This construction uses several important tools of representations theory.
Then we shall use the Enright-Varadarajan modules to define a product for harmonic spinors on homogeneous spaces.
https://www.ms.u-tokyo.ac.jp/~toshi/index.files/springschooltokyo200903.html#mehdi
2009年03月14日(土)
GCOEレクチャーズ
09:00-14:00 数理科学研究科棟(駒場) 123号室
Roger Zierau 氏 (Oklahoma State University) 09:00-10:00
Dirac cohomology
Salah Mehdi 氏 (Metz University) 10:15-11:15
Enright-Varadarajan modules and harmonic spinors
Bernhard Krötz 氏 (Max Planck Institute) 11:45-12:45
Harish-Chandra modules
Peter Trapa 氏 (Utah University) 13:00-14:00
Special unipotent representations of real reductive groups
Roger Zierau 氏 (Oklahoma State University) 09:00-10:00
Dirac cohomology
Salah Mehdi 氏 (Metz University) 10:15-11:15
Enright-Varadarajan modules and harmonic spinors
Bernhard Krötz 氏 (Max Planck Institute) 11:45-12:45
Harish-Chandra modules
Peter Trapa 氏 (Utah University) 13:00-14:00
Special unipotent representations of real reductive groups
2009年03月13日(金)
GCOEレクチャーズ
09:30-16:30 数理科学研究科棟(駒場) 123号室
Salah Mehdi 氏 (Metz) 09:30-10:30
Enright-Varadarajan modules and harmonic spinors
Special unipotent representations of real reductive groups
Bernhard Krötz
氏 (Max Planck Institute) 13:30-14:30
Harish-Chandra modules
Roger Zierau 氏 (Oklahoma State University) 15:00-16:00
Dirac Cohomology
Salah Mehdi 氏 (Metz) 09:30-10:30
Enright-Varadarajan modules and harmonic spinors
[ 講演概要 ]
The aim of these lectures is twofold. First we would like to describe the construction of the Enright-Varadarajan modules which provide a nice algebraic characterization of discrete series representations. This construction uses several important tools of representations theory. Then we shall use the Enright-Varadarajan modules to define a product for harmonic spinors on homogeneous spaces.
Peter Trapa 氏 (Utah) 11:00-12:00The aim of these lectures is twofold. First we would like to describe the construction of the Enright-Varadarajan modules which provide a nice algebraic characterization of discrete series representations. This construction uses several important tools of representations theory. Then we shall use the Enright-Varadarajan modules to define a product for harmonic spinors on homogeneous spaces.
Special unipotent representations of real reductive groups
Bernhard Krötz
氏 (Max Planck Institute) 13:30-14:30
Harish-Chandra modules
Roger Zierau 氏 (Oklahoma State University) 15:00-16:00
Dirac Cohomology
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