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Seminar information archive
Seminar information archive ～01/17｜Today's seminar 01/18 | Future seminars 01/19～
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
2009/03/12
Colloquium
15:00-17:30 Room #050 (Graduate School of Math. Sci. Bldg.)
菊地文雄 (東京大学大学院数理科学研究科) 15:00-16:00
数値解析:得られた成果と残された課題
正標数の世界に40年
菊地文雄 (東京大学大学院数理科学研究科) 15:00-16:00
数値解析:得られた成果と残された課題
[ Abstract ]
有限要素法を中心とする偏微分方程式の数値計算と数値解析に従事して長い歳月を経た。その間に偏微分方程式としては、Poisson方程式、弾性論のCauchy-Navierの方程式、非圧縮流体のStokes方程式、平板の曲げに対する重調和方程式やReissner-Mindlinの方程式、電磁気学のMaxwell方程式、プラズマ平衡のGrad-Shafranov方程式などを扱ってきたが、得られた成果もかなりある反面、残された課題も多いと思う。定年退職にあたり、少々整理と総括をしておきたい。
桂 利行 (東京大学大学院数理科学研究科) 16:30-17:30有限要素法を中心とする偏微分方程式の数値計算と数値解析に従事して長い歳月を経た。その間に偏微分方程式としては、Poisson方程式、弾性論のCauchy-Navierの方程式、非圧縮流体のStokes方程式、平板の曲げに対する重調和方程式やReissner-Mindlinの方程式、電磁気学のMaxwell方程式、プラズマ平衡のGrad-Shafranov方程式などを扱ってきたが、得られた成果もかなりある反面、残された課題も多いと思う。定年退職にあたり、少々整理と総括をしておきたい。
正標数の世界に40年
[ Abstract ]
正標数における代数幾何学には、標数0の場合とは異なる特有の現象がある。1950年代には、これらは病理的現象として捉えられ、研究している人の数も少なかった。現在では、特有の現象を扱うための手段がかなり整備され、正標数の様々な対象に対して興味ある現象が解析されている。代数多様体の単有理性、野性的ファイバーの問題、正標数特有のサイクルの構造等、これまで正標数の世界で行ってきた研究を中心に思い出を交えてお話ししたい。
正標数における代数幾何学には、標数0の場合とは異なる特有の現象がある。1950年代には、これらは病理的現象として捉えられ、研究している人の数も少なかった。現在では、特有の現象を扱うための手段がかなり整備され、正標数の様々な対象に対して興味ある現象が解析されている。代数多様体の単有理性、野性的ファイバーの問題、正標数特有のサイクルの構造等、これまで正標数の世界で行ってきた研究を中心に思い出を交えてお話ししたい。
GCOE lecture series
09:30-14:30 Room #123 (Graduate School of Math. Sci. Bldg.)
Roger Zierau (Oklahoma State University) 09:30-10:30
Dirac Cohomology
https://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html
Bernhard Krötz (Max Planck) 11:00-12:00
Harish-Chandra modules
Special unipotent representations of real reductive groups
Roger Zierau (Oklahoma State University) 09:30-10:30
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/seminar/ut-seminar.html
Bernhard Krötz (Max Planck) 11:00-12:00
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.
Peter Trapa (Utah大学) 13:30-14:30We 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.
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.
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.
2009/03/05
Tuesday Seminar on Topology
16:30-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)
Shicheng Wang (Peking University)
Extending surface automorphisms over 4-space
Shicheng Wang (Peking University)
Extending surface automorphisms over 4-space
[ Abstract ]
Let $e: M^p\\to R^{p+2}$ be a co-dimensional 2 smooth embedding
from a closed orientable manifold to the Euclidean space and $E_e$ be the subgroup of ${\\cal M}_M$, the mapping class group
of $M$, whose elements extend over $R^{p+2}$ as self-diffeomorphisms. Then there is a spin structure
on $M$ derived from the embedding which is preserved by each $\\tau \\in E_e$.
Some applications: (1) the index $[{\\cal M}_{F_g}:E_e]\\geq 2^{2g-1}+2^{g-1}$ for any embedding $e:F_g\\to R^4$, where $F_g$
is the surface of genus $g$. (2) $[{\\cal M}_{T^p}:E_e]\\geq 2^p-1$ for any unknotted embedding
$e:T^p\\to R^{p+2}$, where $T^p$ is the $p$-dimensional torus. Those two lower bounds are known to be sharp.
This is a joint work of Ding-Liu-Wang-Yao.
Let $e: M^p\\to R^{p+2}$ be a co-dimensional 2 smooth embedding
from a closed orientable manifold to the Euclidean space and $E_e$ be the subgroup of ${\\cal M}_M$, the mapping class group
of $M$, whose elements extend over $R^{p+2}$ as self-diffeomorphisms. Then there is a spin structure
on $M$ derived from the embedding which is preserved by each $\\tau \\in E_e$.
Some applications: (1) the index $[{\\cal M}_{F_g}:E_e]\\geq 2^{2g-1}+2^{g-1}$ for any embedding $e:F_g\\to R^4$, where $F_g$
is the surface of genus $g$. (2) $[{\\cal M}_{T^p}:E_e]\\geq 2^p-1$ for any unknotted embedding
$e:T^p\\to R^{p+2}$, where $T^p$ is the $p$-dimensional torus. Those two lower bounds are known to be sharp.
This is a joint work of Ding-Liu-Wang-Yao.
GCOE Seminars
10:15-11:15 Room #270 (Graduate School of Math. Sci. Bldg.)
V. Isakov (Wichita State Univ.)
Carleman type estimates with two large parameters and applications to elasticity theory woth residual stress
V. Isakov (Wichita State Univ.)
Carleman type estimates with two large parameters and applications to elasticity theory woth residual stress
[ Abstract ]
We give Carleman estimates with two large parameters for general second order partial differential operators with real-valued coefficients.
We outline proofs based on differential quadratic forms and Fourier analysis. As an application, we give Carleman estimates for (anisotropic)elasticity system with residual stress and discuss applications to control theory and inverse problems.
We give Carleman estimates with two large parameters for general second order partial differential operators with real-valued coefficients.
We outline proofs based on differential quadratic forms and Fourier analysis. As an application, we give Carleman estimates for (anisotropic)elasticity system with residual stress and discuss applications to control theory and inverse problems.
GCOE Seminars
11:15-12:15 Room #270 (Graduate School of Math. Sci. Bldg.)
J. Ralston (UCLA)
Determining moving boundaries from Cauchy data on remote surfaces
J. Ralston (UCLA)
Determining moving boundaries from Cauchy data on remote surfaces
[ Abstract ]
We consider wave equations in domains with time-dependent boundaries (moving obstacles) contained in a fixed cylinder for all time. We give sufficient conditions for the determination of the moving boundary from the Cauchy data on part of the boundary of the cylinder. We also study the related problem of reachability of the moving boundary by time-like curves from the boundary of the cylinder.
We consider wave equations in domains with time-dependent boundaries (moving obstacles) contained in a fixed cylinder for all time. We give sufficient conditions for the determination of the moving boundary from the Cauchy data on part of the boundary of the cylinder. We also study the related problem of reachability of the moving boundary by time-like curves from the boundary of the cylinder.
2009/03/04
GCOE Seminars
15:00-16:00 Room #270 (Graduate School of Math. Sci. Bldg.)
P. Gaitan (with H. Isozaki and O. Poisson) (Univ. Marseille)
Probing for inclusions for the heat equation with complex
spherical waves
P. Gaitan (with H. Isozaki and O. Poisson) (Univ. Marseille)
Probing for inclusions for the heat equation with complex
spherical waves
GCOE Seminars
16:15-17:15 Room #270 (Graduate School of Math. Sci. Bldg.)
M. Cristofol (Univ. Marseille)
Coefficient reconstruction from partial measurements in a heterogeneous
equation of FKPP type
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/gcoe/activity/documents/abstractTokyo.pdf
M. Cristofol (Univ. Marseille)
Coefficient reconstruction from partial measurements in a heterogeneous
equation of FKPP type
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/gcoe/activity/documents/abstractTokyo.pdf
2009/03/03
GCOE Seminars
16:15-17:15 Room #270 (Graduate School of Math. Sci. Bldg.)
O. Poisson (Univ. Marseille)
Carleman estimates for the heat equation with discontinuous diffusion coefficients and applications
O. Poisson (Univ. Marseille)
Carleman estimates for the heat equation with discontinuous diffusion coefficients and applications
[ Abstract ]
We consider a heat equation in a bounded domain. We assume that the coefficient depends on the spatial variable and admits a discontinuity across an interface. We prove a Carleman estimate for the solution of the above heat equation without assumptions on signs of the jump of the coefficient.
We consider a heat equation in a bounded domain. We assume that the coefficient depends on the spatial variable and admits a discontinuity across an interface. We prove a Carleman estimate for the solution of the above heat equation without assumptions on signs of the jump of the coefficient.
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