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Seminar information archive
Seminar information archive ～05/13｜Today's seminar 05/14 | Future seminars 05/15～
Operator Algebra Seminars
16:30-18:00 Room #052 (Graduate School of Math. Sci. Bldg.)
戸松 玲治 (東大数理・COE)
Compact Kac 環の極小作用の分類 I
戸松 玲治 (東大数理・COE)
Compact Kac 環の極小作用の分類 I
2006/04/19
Number Theory Seminar
16:30-17:30 Room #117 (Graduate School of Math. Sci. Bldg.)
谷口 隆 (東京大学大学院数理科学研究科)
Distributions of discriminants of cubic algebras
谷口 隆 (東京大学大学院数理科学研究科)
Distributions of discriminants of cubic algebras
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)
Oscillatory growth of a crystal controlled by interface kinetics and transport process
http://coe.math.sci.hokudai.ac.jp/sympo/various/005.html
横山 悦郎 (学習院大学)
Oscillatory growth of a crystal controlled by interface kinetics and transport process
[ Abstract ]
Periodic texture in a crystal -such as growth banding and growth striations- are believed to be caused by oscillatory growth. The origin of oscillatory growth falls into two categories, i.e., external and internal. Since the growth rate of a crystal depends strongly on the growth conditions, periodic changes of external conditions, such as temperature, concentration, convection etc., are common reasons for explaining oscillatory growth. On the other hand, it is thought that oscillatory growth can also have an internal cause, but there is no clear understanding. In this talk we propose the hypothesis of a hysteresis behaviour of growth rate to explain the formation of periodic structures of a growing crystal without a change of external conditions. Recently, evidence for our hypothesis is observed not only in the growth of a crystal but also in the motion of steps on the surface of crystals. Possibly such self-oscillatory growth can be controlled in experiments in near future.
[ Reference URL ]Periodic texture in a crystal -such as growth banding and growth striations- are believed to be caused by oscillatory growth. The origin of oscillatory growth falls into two categories, i.e., external and internal. Since the growth rate of a crystal depends strongly on the growth conditions, periodic changes of external conditions, such as temperature, concentration, convection etc., are common reasons for explaining oscillatory growth. On the other hand, it is thought that oscillatory growth can also have an internal cause, but there is no clear understanding. In this talk we propose the hypothesis of a hysteresis behaviour of growth rate to explain the formation of periodic structures of a growing crystal without a change of external conditions. Recently, evidence for our hypothesis is observed not only in the growth of a crystal but also in the motion of steps on the surface of crystals. Possibly such self-oscillatory growth can be controlled in experiments in near future.
http://coe.math.sci.hokudai.ac.jp/sympo/various/005.html
2006/04/18
Tuesday Seminar on Topology
16:30-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)
Vladimir Turaev (Univ. Louis Pasteur Strasbourg)
Topology of words
Vladimir Turaev (Univ. Louis Pasteur Strasbourg)
Topology of words
[ Abstract ]
There is a parallel between words, defined as finite sequences of letters, and curves on surfaces. This allows to treat words as geometric objects and to analyze them using techniques from low-dimensional topology. I will discuss basic ideas in this direction and the resulting topological invariants of words.
There is a parallel between words, defined as finite sequences of letters, and curves on surfaces. This allows to treat words as geometric objects and to analyze them using techniques from low-dimensional topology. I will discuss basic ideas in this direction and the resulting topological invariants of words.
Lie Groups and Representation Theory
16:30-18:00 Room #126 (Graduate School of Math. Sci. Bldg.)
伴 克馬 (東京大学大学院数理科学研究科)
Rankin-Cohen-伊吹山型の微分作用素について
伴 克馬 (東京大学大学院数理科学研究科)
Rankin-Cohen-伊吹山型の微分作用素について
[ Abstract ]
正則保型形式の正則微分は一般に保型形式ではなくなるが、それらを組み合わせることで新たな正則保型形式を与えることもできる。
楕円モジュラー形式に対するRankin-Cohen微分作用素はその最も簡単な例である。伊吹山はSiegelモジュラー形式に対するこのようなタイプの微分作用素がどのような形をしているかについて、一般的な記述を与えた。
今回のセミナーでは、伊吹山による結果を表現論的な命題として捉え直し、その命題が自然にSU(p,q)やO*(2p)上の正則保型形式にも拡張されることを説明する。
正則保型形式の正則微分は一般に保型形式ではなくなるが、それらを組み合わせることで新たな正則保型形式を与えることもできる。
楕円モジュラー形式に対するRankin-Cohen微分作用素はその最も簡単な例である。伊吹山はSiegelモジュラー形式に対するこのようなタイプの微分作用素がどのような形をしているかについて、一般的な記述を与えた。
今回のセミナーでは、伊吹山による結果を表現論的な命題として捉え直し、その命題が自然にSU(p,q)やO*(2p)上の正則保型形式にも拡張されることを説明する。
2006/04/17
Seminar on Geometric Complex Analysis
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
C. Robin Graham (University of Washington)
Dirichlet-to-Neumann map for Poincaré-Einstein metrics
C. Robin Graham (University of Washington)
Dirichlet-to-Neumann map for Poincaré-Einstein metrics
[ Abstract ]
This talk will describe an analogue of a Dirichlet to Neumann map for Poincaré-Einstein metrics, also known as asymptotically hyperbolic Einstein metrics. An explicit identification of the linearization of the map at the sphere will be given for even interior dimensions, together with applications to the structure of the map near the sphere and to the positive frequency conjecture of LeBrun which was resolved by Biquard.
This talk will describe an analogue of a Dirichlet to Neumann map for Poincaré-Einstein metrics, also known as asymptotically hyperbolic Einstein metrics. An explicit identification of the linearization of the map at the sphere will be given for even interior dimensions, together with applications to the structure of the map near the sphere and to the positive frequency conjecture of LeBrun which was resolved by Biquard.
2006/04/15
Monthly Seminar on Arithmetic of Automorphic Forms
13:30-15:45 Room #123 (Graduate School of Math. Sci. Bldg.)
軍司 圭一 (東京大学大学院数理科学研究科) 13:30-14:30
On the dimension of the space of Siegel Eisenstein series of weight one.
L-functions for $GSp(2)\\times GL(2)$: archimedean theory and applications
軍司 圭一 (東京大学大学院数理科学研究科) 13:30-14:30
On the dimension of the space of Siegel Eisenstein series of weight one.
[ Abstract ]
一般に低いweightのSiegel保型形式の空間の次元を求めるのは難しく、特にcusp形式についてはほとんど分かっていない。この講演では素数レベルの主合同部分群に対して、Siegel-Eisenstein級数と呼ぶべき、cusp形式
の補空間の一部の次元を、有限群の表現論及びSatakeコンパクト化の境界の様子を調べることによって計算する方法を与える。
森山 知則 (東京大学大学院数理科学研究科) 14:45-15:45一般に低いweightのSiegel保型形式の空間の次元を求めるのは難しく、特にcusp形式についてはほとんど分かっていない。この講演では素数レベルの主合同部分群に対して、Siegel-Eisenstein級数と呼ぶべき、cusp形式
の補空間の一部の次元を、有限群の表現論及びSatakeコンパクト化の境界の様子を調べることによって計算する方法を与える。
L-functions for $GSp(2)\\times GL(2)$: archimedean theory and applications
[ Abstract ]
$\\Pi$ を $GSp(2)$のWhittaker模型を持つ尖点保型表現で,実素点で大きい離散系列表現を生成するものとする。$\\Pi$と$\\GL(2)$の尖点保型表現$\\sigma$の組からテンソル積 L-関数が定義される。
このL-関数の関数等式を,ゼータ積分を使って証明する。
証明のいくつかの副産物($\\Pi$ のspinor L-関数への応用など)についてもお話したい。
$\\Pi$ を $GSp(2)$のWhittaker模型を持つ尖点保型表現で,実素点で大きい離散系列表現を生成するものとする。$\\Pi$と$\\GL(2)$の尖点保型表現$\\sigma$の組からテンソル積 L-関数が定義される。
このL-関数の関数等式を,ゼータ積分を使って証明する。
証明のいくつかの副産物($\\Pi$ のspinor L-関数への応用など)についてもお話したい。
Infinite Analysis Seminar Tokyo
13:30-16:00 Room #117 (Graduate School of Math. Sci. Bldg.)
坂本 玲峰 (東大理) 13:30-14:30
Crystal interpretation of Kerov-Kirillov-Reshetikhin bijection.
ダブルアファインヘッケ代数と楕円ヘッケ代数について
坂本 玲峰 (東大理) 13:30-14:30
Crystal interpretation of Kerov-Kirillov-Reshetikhin bijection.
[ Abstract ]
Kerov-Kirillov-Reshetikhin bijection とは、フェルミ型公式の 証明に関して 1986 年に導入された組み合わせ的な写像であり、 rigged configurations と highest paths の間の全単射を与える。 この写像を、結晶基底の組み合わせ R 行列のみを用いた代数的な 形式に書き直すことができる [1,2]。証明には、アフィン組み合わせ R 行列の構造を rigged configurations に導入することが必要となる。 これらの結果は箱玉系と呼ばれるソリトンセルオートマトンの 逆散乱形式ともなっている。
REFERENCE:
[1] A.Kuniba, M.Okado, R.Sakamoto, T.Takagi, Y.Yamada, "Crystal interpretation of Kerov-Kirillov-Reshetikhin bijection" Nuclear Physics B 740 (2006) 299-327, math.QA/0601630.
[2] R.Sakamoto, "Crystal interpretation of Kerov-Kirillov-Reshetikhin bijection II. Proof for sl_n case", math.QA/0601697.
塩田 翠 (東大数理) 15:00-16:00Kerov-Kirillov-Reshetikhin bijection とは、フェルミ型公式の 証明に関して 1986 年に導入された組み合わせ的な写像であり、 rigged configurations と highest paths の間の全単射を与える。 この写像を、結晶基底の組み合わせ R 行列のみを用いた代数的な 形式に書き直すことができる [1,2]。証明には、アフィン組み合わせ R 行列の構造を rigged configurations に導入することが必要となる。 これらの結果は箱玉系と呼ばれるソリトンセルオートマトンの 逆散乱形式ともなっている。
REFERENCE:
[1] A.Kuniba, M.Okado, R.Sakamoto, T.Takagi, Y.Yamada, "Crystal interpretation of Kerov-Kirillov-Reshetikhin bijection" Nuclear Physics B 740 (2006) 299-327, math.QA/0601630.
[2] R.Sakamoto, "Crystal interpretation of Kerov-Kirillov-Reshetikhin bijection II. Proof for sl_n case", math.QA/0601697.
ダブルアファインヘッケ代数と楕円ヘッケ代数について
[ Abstract ]
ダブルアファインヘッケ代数と楕円ヘッケ代数の比較について話します。 楕円ヘッケ代数は、マーキング付き楕円ルート系のディンキン図形から 生成元と関係式を読み取って定義される代数です。マーキング付き楕円 ルート系は、2つのアファインルート系を部分ルート系として含むので そのヘッケ代数がダブルアファインヘッケ代数と何かしらの関係がある ことは想像がつきます。ここでは、楕円ヘッケ代数がダブルアファイン ヘッケ代数の部分代数になっていること、およびダブルアファインヘッケ 代数を楕円ヘッケ代数上の加群と見たときの自由基底について説明します。
ダブルアファインヘッケ代数と楕円ヘッケ代数の比較について話します。 楕円ヘッケ代数は、マーキング付き楕円ルート系のディンキン図形から 生成元と関係式を読み取って定義される代数です。マーキング付き楕円 ルート系は、2つのアファインルート系を部分ルート系として含むので そのヘッケ代数がダブルアファインヘッケ代数と何かしらの関係がある ことは想像がつきます。ここでは、楕円ヘッケ代数がダブルアファイン ヘッケ代数の部分代数になっていること、およびダブルアファインヘッケ 代数を楕円ヘッケ代数上の加群と見たときの自由基底について説明します。
2006/04/13
Operator Algebra Seminars
16:30-18:00 Room #118 (Graduate School of Math. Sci. Bldg.)
勝良 健史 (北大理・学振SPD)
A construction of finite group actions on Kirchberg algebras
勝良 健史 (北大理・学振SPD)
A construction of finite group actions on Kirchberg algebras
2006/04/12
Geometry Seminar
14:40-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)
三鍋 聡司 (名古屋大学大学院多元数理科学研究科) 14:40-16:10
Topological Vertex とその応用
Kerr Black Holes and Compact Einstein Manifolds
三鍋 聡司 (名古屋大学大学院多元数理科学研究科) 14:40-16:10
Topological Vertex とその応用
[ Abstract ]
この講演の内容は小西由紀子さんとの共同研究に基づきます.
まず,3次元 toric Calabi--Yau 多様体の Gromov--Witten 不変量の分配関数を計算する Topological Vertex と呼ばれる方法について説明します.その応用として,分配関数のフロップに関する不変性や,3次曲面の局所 Gromov--Witten 不変量の分配関数の公式が求められることを説明したいと思います.
安井 幸則 (大阪市立大学物理学科) 16:30-18:00この講演の内容は小西由紀子さんとの共同研究に基づきます.
まず,3次元 toric Calabi--Yau 多様体の Gromov--Witten 不変量の分配関数を計算する Topological Vertex と呼ばれる方法について説明します.その応用として,分配関数のフロップに関する不変性や,3次曲面の局所 Gromov--Witten 不変量の分配関数の公式が求められることを説明したいと思います.
Kerr Black Holes and Compact Einstein Manifolds
[ Abstract ]
1978 年 Page は,4次元 AdS Kerr ブラックホール解からある種の極限操作を使って S^2 上の S^2 束に inhomogeneous Einstein 計量を構成しました.この計量はコンパクトな空間上の inhomogeneous Einstein 計量として顕に書き下された最初の例です.ここでは、Page の手法を高次元に拡張することにより,Hawking たちによって発見された5次元 AdS Kerr ブラックホール解から,S^2 上の S^3 束に無限個のアインシュタイ ン計量を誘導します.関連する話題として, 5次元佐々木アインシュタイン計量および AdS/CFT 対応についても言及したいと思います.
1978 年 Page は,4次元 AdS Kerr ブラックホール解からある種の極限操作を使って S^2 上の S^2 束に inhomogeneous Einstein 計量を構成しました.この計量はコンパクトな空間上の inhomogeneous Einstein 計量として顕に書き下された最初の例です.ここでは、Page の手法を高次元に拡張することにより,Hawking たちによって発見された5次元 AdS Kerr ブラックホール解から,S^2 上の S^3 束に無限個のアインシュタイ ン計量を誘導します.関連する話題として, 5次元佐々木アインシュタイン計量および AdS/CFT 対応についても言及したいと思います.
2006/04/11
Tuesday Seminar on Topology
16:30-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)
Martin Arkowitz (Dartmouth College)
Homotopy actions, cyclic maps and their Eckmann-Hilton duals.
Martin Arkowitz (Dartmouth College)
Homotopy actions, cyclic maps and their Eckmann-Hilton duals.
[ Abstract ]
We study the homotopy action of a based space A on a based space X. The resulting map A--->X is called cyclic. We classify actions on an H-space which are compatible with the H-structure. In the dual case we study coactions X--->X v B and the resulting cocyclic map X--->B. We relate the cocyclicity of a map to the Lusternik-Schnirelmann category of the map.
We study the homotopy action of a based space A on a based space X. The resulting map A--->X is called cyclic. We classify actions on an H-space which are compatible with the H-structure. In the dual case we study coactions X--->X v B and the resulting cocyclic map X--->B. We relate the cocyclicity of a map to the Lusternik-Schnirelmann category of the map.
2006/04/04
Seminar on Mathematics for various disciplines
16:30-17:30 Room #128 (Graduate School of Math. Sci. Bldg.)
Maria Reznikoff (Department of Mathematics, Princeton University)
Thermally-Driven Rare Events and Action Minimization
[ Reference URL ]
http://coe.math.sci.hokudai.ac.jp/sympo/various/004.html
Maria Reznikoff (Department of Mathematics, Princeton University)
Thermally-Driven Rare Events and Action Minimization
[ Reference URL ]
http://coe.math.sci.hokudai.ac.jp/sympo/various/004.html
2006/03/30
Real and Harmonic Analysis Seminar
10:30-11:30 Room #118 (Graduate School of Math. Sci. Bldg.)
Herbert Heyer (Tuebingen University)
Heyer教授特別講演会:Polynomial hypergroups of several variables
Herbert Heyer (Tuebingen University)
Heyer教授特別講演会:Polynomial hypergroups of several variables
2006/01/30
Seminar on Geometric Complex Analysis
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
藤木 明 (大阪大学)
Compact non-kaehler threefolds associated to hyperbolic 3-manifolds
藤木 明 (大阪大学)
Compact non-kaehler threefolds associated to hyperbolic 3-manifolds
2006/01/23
Seminar on Geometric Complex Analysis
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
金子 宏 (東京理科大)
Stochastic processes and Besov spaces on local field
金子 宏 (東京理科大)
Stochastic processes and Besov spaces on local field
2006/01/18
PDE Real Analysis Seminar
10:30-11:30 Room #056 (Graduate School of Math. Sci. Bldg.)
Juergen Saal (TU Darmstadt)
Analyticity of the interface of the classical two-phase Stefan problem
http://coe.math.sci.hokudai.ac.jp/sympo/pde_ra/index.html
Juergen Saal (TU Darmstadt)
Analyticity of the interface of the classical two-phase Stefan problem
[ Abstract ]
The Stefan problem is a model for phase transitions in liquid-solid systems, as e.g. ice surrounded by water, and accounts for heat diffusion and exchange of latent heat in a homogeneous medium.
The strong formulation of this model corresponds to a free boundary problem involving a parabolic diffusion equation for each phase and a transmission condition prescribed at the interface separating the phases.
We prove that under mild regularity assumptions on the initial data the two-phase classical Stefan problem admits a unique solution that is analytic in space and time.
The result is based on $L_p$ maximal regularity for a linearized problem, which is proved first, and the implicit function theorem.
[ Reference URL ]The Stefan problem is a model for phase transitions in liquid-solid systems, as e.g. ice surrounded by water, and accounts for heat diffusion and exchange of latent heat in a homogeneous medium.
The strong formulation of this model corresponds to a free boundary problem involving a parabolic diffusion equation for each phase and a transmission condition prescribed at the interface separating the phases.
We prove that under mild regularity assumptions on the initial data the two-phase classical Stefan problem admits a unique solution that is analytic in space and time.
The result is based on $L_p$ maximal regularity for a linearized problem, which is proved first, and the implicit function theorem.
http://coe.math.sci.hokudai.ac.jp/sympo/pde_ra/index.html
2006/01/11
PDE Real Analysis Seminar
10:30-11:30 Room #056 (Graduate School of Math. Sci. Bldg.)
伊東 一文 (North Carolina State University) 10:30-11:30
On Fluid Mechanics Formulation of Monge-Kantorovich Mass Transfer Problem
http://coe.math.sci.hokudai.ac.jp/sympo/pde_ra/index.html
Oleg Yu. Imanuvilov (Colorado State University) 11:45-12:45
Local and Global Exact Controllability of Evolution Equations
http://coe.math.sci.hokudai.ac.jp/sympo/pde_ra/index.html
伊東 一文 (North Carolina State University) 10:30-11:30
On Fluid Mechanics Formulation of Monge-Kantorovich Mass Transfer Problem
[ Abstract ]
The Monge-Kantorovich mass transfer problem is equivalently formulated as an optimal control problem for the mass transport equation. The equivalency of the two problems is establish using the Lax-Hopf formula and the optimal control theory arguments. Also, it is shown that the optimal solution to the equivalent control problem is given in a gradient form in terms of the potential solution to the Monge-Kantorovich problem. It turns out
that the control formulation is a dual formulation of the Kantrovich distance problem via the Hamilton-Jacobi equations.
[ Reference URL ]The Monge-Kantorovich mass transfer problem is equivalently formulated as an optimal control problem for the mass transport equation. The equivalency of the two problems is establish using the Lax-Hopf formula and the optimal control theory arguments. Also, it is shown that the optimal solution to the equivalent control problem is given in a gradient form in terms of the potential solution to the Monge-Kantorovich problem. It turns out
that the control formulation is a dual formulation of the Kantrovich distance problem via the Hamilton-Jacobi equations.
http://coe.math.sci.hokudai.ac.jp/sympo/pde_ra/index.html
Oleg Yu. Imanuvilov (Colorado State University) 11:45-12:45
Local and Global Exact Controllability of Evolution Equations
[ Abstract ]
We discuss rcent global and local controlability results for the Navier-Stokes system and Bousinesq system. The control is acting on the part of the boundary or locally distributed over subdomain.
[ Reference URL ]We discuss rcent global and local controlability results for the Navier-Stokes system and Bousinesq system. The control is acting on the part of the boundary or locally distributed over subdomain.
http://coe.math.sci.hokudai.ac.jp/sympo/pde_ra/index.html
2005/12/05
Seminar on Geometric Complex Analysis
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Sebastien Boucksom (ParisVII / Univ. of Tokyo)
Positive cones of hyper-Keahler manifold
Sebastien Boucksom (ParisVII / Univ. of Tokyo)
Positive cones of hyper-Keahler manifold
2005/11/28
Seminar on Geometric Complex Analysis
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
上田哲生 (京都大学)
Schroeder equation and Abel equation
上田哲生 (京都大学)
Schroeder equation and Abel equation
2005/11/22
Seminar on Mathematics for various disciplines
16:30-17:30 Room #128 (Graduate School of Math. Sci. Bldg.)
Hans Heesterbeek (University of Utrecht)
Mathematics in the epidemiology and control of infectious diseases
http://coe.math.sci.hokudai.ac.jp/sympo/various/index.html
Hans Heesterbeek (University of Utrecht)
Mathematics in the epidemiology and control of infectious diseases
[ Abstract ]
In this lecture I will give examples of the way in which mathematics helps in getting insight into the spread and control of infectious diseases. I will do this by discussing the population phenomena that are observed after an infectious agent enters a population (invasion, epidemic, recurrent epidemic, endemic, regulation, control). Along the way I will also give insight into the historical development of mathematical modelling in infectious disease epidemiology. Examples will be taken from human and animal infections. Special topics treated in some detail are threshold quantities such as the basic reproduction number R_0, the importance of understanding the structure of contacts in a population, the use of R_0 to estimate control effort with vaccines. In the last part of the lecture a number of important epidemiological problems will be discussed where input of new mathematical theory is needed.
[ Reference URL ]In this lecture I will give examples of the way in which mathematics helps in getting insight into the spread and control of infectious diseases. I will do this by discussing the population phenomena that are observed after an infectious agent enters a population (invasion, epidemic, recurrent epidemic, endemic, regulation, control). Along the way I will also give insight into the historical development of mathematical modelling in infectious disease epidemiology. Examples will be taken from human and animal infections. Special topics treated in some detail are threshold quantities such as the basic reproduction number R_0, the importance of understanding the structure of contacts in a population, the use of R_0 to estimate control effort with vaccines. In the last part of the lecture a number of important epidemiological problems will be discussed where input of new mathematical theory is needed.
http://coe.math.sci.hokudai.ac.jp/sympo/various/index.html
2005/11/21
Seminar on Geometric Complex Analysis
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Andreas Cap (Univ. of Vienna)
On CR-invariant differential operators
Andreas Cap (Univ. of Vienna)
On CR-invariant differential operators
[ Abstract ]
My talk will be devoted to questions about differential operators which are intrinsic to non--degenerate CR structures of hypersurface type. Restricting to the subclass of spherical CR structures, this question admits an equivalent formulation in terms of representation theory, which leads to several surprising consequences.
Guided by the ideas from representation theory and using the canonical Cartan connection which is available in this situation, one obtains a construction for a large class of such operators, which continues to work for non--spherical structures, and even for a class of almost CR structures. In the end of the talk I will discuss joint work with V. Soucek which shows that in the integrable case many of the operators obtained in this way form complexes.
My talk will be devoted to questions about differential operators which are intrinsic to non--degenerate CR structures of hypersurface type. Restricting to the subclass of spherical CR structures, this question admits an equivalent formulation in terms of representation theory, which leads to several surprising consequences.
Guided by the ideas from representation theory and using the canonical Cartan connection which is available in this situation, one obtains a construction for a large class of such operators, which continues to work for non--spherical structures, and even for a class of almost CR structures. In the end of the talk I will discuss joint work with V. Soucek which shows that in the integrable case many of the operators obtained in this way form complexes.
2005/11/14
Seminar on Geometric Complex Analysis
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Raphael Pong (Ohio State Univ)
New invariants for CR and contact manifolds
Raphael Pong (Ohio State Univ)
New invariants for CR and contact manifolds
[ Abstract ]
In this talk I will explain the construction of several new invariants for CR and contact manifolds as noncommutative residue traces of various geometric pseudodifferential projections. In the CR setting these operators arise from the ∂b-complex and include the Szegö projections. In the contact setting they stem from the generalized Szegö projections at arbitrary integer levels of Epstein-Melrose and from the contact complex of Rumin. In particular, we recover and extend recent results of Hirachi and Boutet de Monvel and answer a question of Fefferman.
In this talk I will explain the construction of several new invariants for CR and contact manifolds as noncommutative residue traces of various geometric pseudodifferential projections. In the CR setting these operators arise from the ∂b-complex and include the Szegö projections. In the contact setting they stem from the generalized Szegö projections at arbitrary integer levels of Epstein-Melrose and from the contact complex of Rumin. In particular, we recover and extend recent results of Hirachi and Boutet de Monvel and answer a question of Fefferman.
2005/11/09
PDE Real Analysis Seminar
10:30-11:30 Room #056 (Graduate School of Math. Sci. Bldg.)
藤田安啓 (富山大学)
Asymptotic solutions and Aubry sets for Hamilton-Jacobi equations
http://coe.math.sci.hokudai.ac.jp/sympo/pde_ra/index.html
藤田安啓 (富山大学)
Asymptotic solutions and Aubry sets for Hamilton-Jacobi equations
[ Abstract ]
In this talk, we consider the asymptotic behavior of the viscosity solution of the Cauchy problem for the Hamilton-Jacobi equation $u_t + \\alpha x\\cdot Du + H(Du) =f(x)$ in ${\\rm I}\\!{\\rm R}^N \\times (0,\\infty)$, where $\\alpha$ is a positive constant and $H$ is a convex function on ${\\rm I} \\!{\\rm R}^N$. We show that, under some assumptions, $u(x,t) - ct - v(x)$ converges to $0$ locally uniformly in ${\\rm I}\\!{\\rm R}^N$ as $t \\to \\infty$, where $c$ is a constant and $v$ is a viscosity solution of the Hamilton-Jacobi equation $c + \\alpha x\\cdot Dv + H(Dv) = f(x)$ in ${\\rm I}\\!{\\rm R}^N$. A set in ${\\rm I}\\!{\\rm R}^N$, which is called the {\\it Aubry set}, gives a concrete representation of the viscosity solution $v$. We also discuss convergence rates of this asymptotic behavior. This is a joint work with Professors H. Ishii and P. Loreti.
[ Reference URL ]In this talk, we consider the asymptotic behavior of the viscosity solution of the Cauchy problem for the Hamilton-Jacobi equation $u_t + \\alpha x\\cdot Du + H(Du) =f(x)$ in ${\\rm I}\\!{\\rm R}^N \\times (0,\\infty)$, where $\\alpha$ is a positive constant and $H$ is a convex function on ${\\rm I} \\!{\\rm R}^N$. We show that, under some assumptions, $u(x,t) - ct - v(x)$ converges to $0$ locally uniformly in ${\\rm I}\\!{\\rm R}^N$ as $t \\to \\infty$, where $c$ is a constant and $v$ is a viscosity solution of the Hamilton-Jacobi equation $c + \\alpha x\\cdot Dv + H(Dv) = f(x)$ in ${\\rm I}\\!{\\rm R}^N$. A set in ${\\rm I}\\!{\\rm R}^N$, which is called the {\\it Aubry set}, gives a concrete representation of the viscosity solution $v$. We also discuss convergence rates of this asymptotic behavior. This is a joint work with Professors H. Ishii and P. Loreti.
http://coe.math.sci.hokudai.ac.jp/sympo/pde_ra/index.html
2005/11/07
Seminar on Geometric Complex Analysis
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
難波誠 (追手門学院大学)
Moduli of Galois coverings of the complex projective line
難波誠 (追手門学院大学)
Moduli of Galois coverings of the complex projective line
2005/10/26
PDE Real Analysis Seminar
10:30-11:30 Room #056 (Graduate School of Math. Sci. Bldg.)
利根川吉廣 (北海道大学)
On Mullins-Sekerka as singular limit of Cahn-Hilliard, some mathematical progress and open problems
http://coe.math.sci.hokudai.ac.jp/sympo/pde_ra/index.html
利根川吉廣 (北海道大学)
On Mullins-Sekerka as singular limit of Cahn-Hilliard, some mathematical progress and open problems
[ Abstract ]
The Cahn-Hilliard equation and its variants have been widely used in materials science community to model coarse graining phenomena in mesoscopic scale. The equation has a parameter corresponding the order of thickness of phase boundaries. When the parameter is close to zero, the phase boundary and the chemical potential field are known to evolve by the so-called Mullins-Sekerka problem. The rigorous justification for the latter statement is known only for short-time so far. I describe some recent progress as well as some difficulties on the long-time case, relateing my recent works and those by M. Roeger and R. Schaetzle.
[ Reference URL ]The Cahn-Hilliard equation and its variants have been widely used in materials science community to model coarse graining phenomena in mesoscopic scale. The equation has a parameter corresponding the order of thickness of phase boundaries. When the parameter is close to zero, the phase boundary and the chemical potential field are known to evolve by the so-called Mullins-Sekerka problem. The rigorous justification for the latter statement is known only for short-time so far. I describe some recent progress as well as some difficulties on the long-time case, relateing my recent works and those by M. Roeger and R. Schaetzle.
http://coe.math.sci.hokudai.ac.jp/sympo/pde_ra/index.html
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