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Seminar information archive
Seminar information archive ～05/20｜Today's seminar 05/21 | Future seminars 05/22～
2009/04/28
Tuesday Seminar on Topology
16:30-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)
平地 健吾 (東京大学大学院数理科学研究科)
The ambient metric in conformal geometry
平地 健吾 (東京大学大学院数理科学研究科)
The ambient metric in conformal geometry
[ Abstract ]
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.
Tuesday Seminar of Analysis
16:30-18:00 Room #128 (Graduate School of Math. Sci. Bldg.)
下村 明洋 (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 (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)
2009/04/27
Algebraic Geometry Seminar
15:30-18:00 Room #122 (Graduate School of Math. Sci. Bldg.)
Prof. Alessandra Sarti (Universite de Poitier) 15:30-16:30
Automorphism groups of K3 surfaces
) 17:00-18:00
The cohomological crepant resolution conjecture
Prof. Alessandra Sarti (Universite de Poitier) 15:30-16:30
Automorphism groups of K3 surfaces
[ Abstract ]
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 (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
[ Abstract ]
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.
2009/04/23
Operator Algebra Seminars
16:30-18:00 Room #128 (Graduate School of Math. Sci. Bldg.)
内藤克利 (首都大)
Entire Cyclic Cohomology of Noncommutative 2-Tori
内藤克利 (首都大)
Entire Cyclic Cohomology of Noncommutative 2-Tori
2009/04/22
PDE Real Analysis Seminar
10:30-11:30 Room #128 (Graduate School of Math. Sci. Bldg.)
Wilhelm Klingenberg (University of Durham)
From Codazzi-Mainardi to Cauchy-Riemann
Wilhelm Klingenberg (University of Durham)
From Codazzi-Mainardi to Cauchy-Riemann
[ Abstract ]
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.
Geometry Seminar
14:45-18:00 Room #122 (Graduate School of Math. Sci. Bldg.)
中田文憲 (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
中田文憲 (東京工業大学理工学研究科) 14:45-16:15
Einstein-Weyl structures on 3-dimensional Severi varieties
[ Abstract ]
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 (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
[ Abstract ]
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.
Seminar on Probability and Statistics
15:00-16:10 Room #128 (Graduate School of Math. Sci. Bldg.)
Arnaud DOUCET (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 (統計数理研究所)
Interacting Markov chain Monte Carlo Methods for Solving Nonlinear Measure-Valued Equations
[ Abstract ]
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)
[ Reference 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
2009/04/21
Tuesday Seminar on Topology
16:30-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)
Ivan Marin (Univ. Paris VII)
Some algebraic aspects of KZ systems
Ivan Marin (Univ. Paris VII)
Some algebraic aspects of KZ systems
[ Abstract ]
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.
2009/04/20
Seminar on Geometric Complex Analysis
10:30-12:00 Room #126 (Graduate School of Math. Sci. Bldg.)
鎌田博行 (宮城教育大学)
Indefinite Kähler surfaces of constant scalar curvature
鎌田博行 (宮城教育大学)
Indefinite Kähler surfaces of constant scalar curvature
2009/04/18
Infinite Analysis Seminar Tokyo
11:00-14:30 Room #117 (Graduate School of Math. Sci. Bldg.)
Vladimir Dobrev (Institute for Nuclear Reserch and Nuclear Energy, Sofia, Bulgaria) 11:00-12:00
Invariant Differential Operators for Non-Compact Lie Groups
TBA
Vladimir Dobrev (Institute for Nuclear Reserch and Nuclear Energy, Sofia, Bulgaria) 11:00-12:00
Invariant Differential Operators for Non-Compact Lie Groups
[ Abstract ]
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 (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
[ Abstract ]
TBA
TBA
2009/04/16
Operator Algebra Seminars
16:30-18:00 Room #128 (Graduate School of Math. Sci. Bldg.)
緒方芳子 (東大数理)
Large Deviations in Quantum Spin Chains
緒方芳子 (東大数理)
Large Deviations in Quantum Spin Chains
2009/04/15
Lectures
15:30-17:00 Room #470 (Graduate School of Math. Sci. Bldg.)
Wilhelm Stannat (Darmstadt 工科大学)
Invariant measures for stochastic partial differential equations: new a priori estimates and applications
Wilhelm Stannat (Darmstadt 工科大学)
Invariant measures for stochastic partial differential equations: new a priori estimates and applications
Seminar on Probability and Statistics
16:20-17:30 Room #128 (Graduate School of Math. Sci. Bldg.)
Jean JACOD (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 (Universite Paris VI)
Estimating the successive Blumenthal-Getoor indices for a discretely observed process
[ Abstract ]
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)
[ Reference 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
Seminar on Probability and Statistics
15:00-16:10 Room #128 (Graduate School of Math. Sci. Bldg.)
Jean JACOD (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 (Universite Paris VI)
A survey on realized p-variations for semimartingales
[ Abstract ]
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 $p$.
[ Reference 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
2009/04/14
Lectures
16:30-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)
Klaus Niederkruger (Ecole normale superieure de Lyon)
Resolution of symplectic orbifolds obtained from reduction
Klaus Niederkruger (Ecole normale superieure de Lyon)
Resolution of symplectic orbifolds obtained from reduction
[ Abstract ]
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.
2009/04/13
Seminar on Geometric Complex Analysis
10:30-12:00 Room #126 (Graduate School of Math. Sci. Bldg.)
千葉優作 (東大数理)
A new method to generalize the Nevanlinna theory to several complex variables
千葉優作 (東大数理)
A new method to generalize the Nevanlinna theory to several complex variables
2009/04/09
Operator Algebra Seminars
16:30-18:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Dietmar Bisch (Vanderbilt University)
Bimodules, planarity and freeness
Dietmar Bisch (Vanderbilt University)
Bimodules, planarity and freeness
2009/04/08
Seminar on Mathematics for various disciplines
10:30-11:30 Room #056 (Graduate School of Math. Sci. Bldg.)
横山悦郎 (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 (学習院大学)
Growth of an Ice Disk from Supercooled Water: Theory and Space Experiment in Kibo of International Space Station
[ Abstract ]
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.
2009/03/25
GCOE lecture series
16:00-17:30 Room #128 (Graduate School of Math. Sci. Bldg.)
Mark Gross (University of California, San Diego)
The Strominger-Yau-Zaslow conjecture and mirror symmetry via degenerations II
Mark Gross (University of California, San Diego)
The Strominger-Yau-Zaslow conjecture and mirror symmetry via degenerations II
[ Abstract ]
The second half of the lecture.
The second half of the lecture.
2009/03/24
GCOE lecture series
16:00-17:30 Room #128 (Graduate School of Math. Sci. Bldg.)
Mark Gross (University of California, San Diego)
The Strominger-Yau-Zaslow conjecture and mirror symmetry via degenerations I
Mark Gross (University of California, San Diego)
The Strominger-Yau-Zaslow conjecture and mirror symmetry via degenerations I
[ Abstract ]
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.
2009/03/21
Infinite Analysis Seminar Tokyo
11:00-14:30 Room #117 (Graduate School of Math. Sci. Bldg.)
梶原 康史 (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 (神戸理) 11:00-12:00
On classes of transformations for bilinear sum of
(basic) hypergeometric series and multivariate generalizations.
[ Abstract ]
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 (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
[ Abstract ]
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) $.
2009/03/17
GCOE lecture series
10:00-17:30 Room #123 (Graduate School of Math. Sci. Bldg.)
Roger Zierau (Oklahoma State University) 11:00-12:00
Dirac Cohomology
Salah Mehdi (Metz University) 13:30-14:30
Enright-Varadarajan modules and harmonic spinors
Bernhard Krötz
(Max Planck Institute) 15:00-16:00
Harish-Chandra modules
Peter Trapa (Utah) 16:30-17:30
Special unipotent representations of real reductive groups
Roger Zierau (Oklahoma State University) 11:00-12:00
Dirac Cohomology
Salah Mehdi (Metz University) 13:30-14:30
Enright-Varadarajan modules and harmonic spinors
Bernhard Krötz
(Max Planck Institute) 15:00-16:00
Harish-Chandra modules
Peter Trapa (Utah) 16:30-17:30
Special unipotent representations of real reductive groups
2009/03/16
GCOE lecture series
10:00-16:20 Room #123 (Graduate School of Math. Sci. Bldg.)
Bernhard Krötz
(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 (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 (Oklahoma State University) 13:30-14:30
Dirac Cohomology
https://www.ms.u-tokyo.ac.jp/~toshi/index.files/springschooltokyo200903.html#zierau
Salah Mehdi (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
Bernhard Krötz
(Max Planck Institute) 10:00-11:00
Harish-Chandra modules
[ Abstract ]
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.
[ Reference 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 (Utah) 11:15-12:15
Special unipotent representations of real reductive groups
[ Abstract ]
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.
[ Reference 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 (Oklahoma State University) 13:30-14:30
Dirac Cohomology
[ Abstract ]
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.
[ Reference 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 (Metz University) 15:20-16:20
Enright-Varadarajan modules and harmonic spinors
[ Abstract ]
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.
[ Reference 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
2009/03/14
GCOE lecture series
09:00-14:00 Room #123 (Graduate School of Math. Sci. Bldg.)
Roger Zierau (Oklahoma State University) 09:00-10:00
Dirac cohomology
Salah Mehdi (Metz University) 10:15-11:15
Enright-Varadarajan modules and harmonic spinors
Bernhard Krötz (Max Planck Institute) 11:45-12:45
Harish-Chandra modules
Peter Trapa (Utah University) 13:00-14:00
Special unipotent representations of real reductive groups
Roger Zierau (Oklahoma State University) 09:00-10:00
Dirac cohomology
Salah Mehdi (Metz University) 10:15-11:15
Enright-Varadarajan modules and harmonic spinors
Bernhard Krötz (Max Planck Institute) 11:45-12:45
Harish-Chandra modules
Peter Trapa (Utah University) 13:00-14:00
Special unipotent representations of real reductive groups
2009/03/13
GCOE lecture series
09:30-16:30 Room #123 (Graduate School of Math. Sci. Bldg.)
Salah Mehdi (Metz) 09:30-10:30
Enright-Varadarajan modules and harmonic spinors
Special unipotent representations of real reductive groups
Bernhard Krötz
(Max Planck Institute) 13:30-14:30
Harish-Chandra modules
Roger Zierau (Oklahoma State University) 15:00-16:00
Dirac Cohomology
Salah Mehdi (Metz) 09:30-10:30
Enright-Varadarajan modules and harmonic spinors
[ Abstract ]
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 (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
(Max Planck Institute) 13:30-14:30
Harish-Chandra modules
Roger Zierau (Oklahoma State University) 15:00-16:00
Dirac Cohomology
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