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過去の記録
過去の記録 ～06/07｜本日 06/08 | 今後の予定 06/09～
講演会
16:30-18:00 数理科学研究科棟(駒場) 056号室
伊東一文 氏 (大学院数理科学研究科)
Fractional Evolution Equations and Applications 4
伊東一文 氏 (大学院数理科学研究科)
Fractional Evolution Equations and Applications 4
[ 講演概要 ]
In recent years increasing interests and considerable
researches have been given to the fractional differential equations both
in time and space variables.
These are due to the applications of the fractional calculus
to problems in a wide areas of physics and engineering science and a rapid
development of the corresponding theory. A motivating example includes
the so-called continuous time random walk process
and the Levy process model for the mathematical finance.
In this lecture we develop solution techniques based on the linear and
nonlinear semigroup theory and apply it to solve the associated inverse
and optimal control problems. The property and stability of the solutions
as well as numerical integration methods
are discussed. The lecture also covers the basis and application of the
so-called Crandall-Ligget theory and the locally quasi-dissipative
operator method developed by Kobayashi-Kobayashi-Oharu.
In recent years increasing interests and considerable
researches have been given to the fractional differential equations both
in time and space variables.
These are due to the applications of the fractional calculus
to problems in a wide areas of physics and engineering science and a rapid
development of the corresponding theory. A motivating example includes
the so-called continuous time random walk process
and the Levy process model for the mathematical finance.
In this lecture we develop solution techniques based on the linear and
nonlinear semigroup theory and apply it to solve the associated inverse
and optimal control problems. The property and stability of the solutions
as well as numerical integration methods
are discussed. The lecture also covers the basis and application of the
so-called Crandall-Ligget theory and the locally quasi-dissipative
operator method developed by Kobayashi-Kobayashi-Oharu.
複素解析幾何セミナー
10:30-12:00 数理科学研究科棟(駒場) 128号室
Colin Guillarmou 氏 (Ecole Normale Superieure)
Eta invariant and Selberg Zeta function of odd type over convex co-compact hyperbolic manifolds
Colin Guillarmou 氏 (Ecole Normale Superieure)
Eta invariant and Selberg Zeta function of odd type over convex co-compact hyperbolic manifolds
代数幾何学セミナー
16:40-18:10 数理科学研究科棟(駒場) 126号室
權業 善範 氏 (東大数理)
On weak Fano varieties with log canonical singularities
權業 善範 氏 (東大数理)
On weak Fano varieties with log canonical singularities
[ 講演概要 ]
We prove that the anti-canonical divisors of weak Fano
3-folds with log canonical singularities are semiample. Moreover, we consider
semiampleness of the anti-log canonical divisor of any weak log Fano pair
with log canonical singularities. We show semiampleness dose not hold in
general by constructing several examples. Based on those examples, we propose
sufficient conditions which seem to be the best possible and we prove
semiampleness under such conditions. In particular we derive semiampleness of the
anti-canonical divisors of log canonical weak Fano 4-folds whose lc centers
are at most 1-dimensional. We also investigate the Kleiman-Mori cones of
weak log Fano pairs with log canonical singularities.
We prove that the anti-canonical divisors of weak Fano
3-folds with log canonical singularities are semiample. Moreover, we consider
semiampleness of the anti-log canonical divisor of any weak log Fano pair
with log canonical singularities. We show semiampleness dose not hold in
general by constructing several examples. Based on those examples, we propose
sufficient conditions which seem to be the best possible and we prove
semiampleness under such conditions. In particular we derive semiampleness of the
anti-canonical divisors of log canonical weak Fano 4-folds whose lc centers
are at most 1-dimensional. We also investigate the Kleiman-Mori cones of
weak log Fano pairs with log canonical singularities.
2010年01月22日(金)
GCOE社会数理講演シリーズ
16:20-17:50 数理科学研究科棟(駒場) 117号室
中川淳一 氏 (新日本製鐵(株)技術開発本部)
数学者と企業研究者との連携
中川淳一 氏 (新日本製鐵(株)技術開発本部)
数学者と企業研究者との連携
講演会
16:30-18:00 数理科学研究科棟(駒場) 118号室
伊東一文 氏 (大学院数理科学研究科)
Fractional Evolution Equations and Applications 3
伊東一文 氏 (大学院数理科学研究科)
Fractional Evolution Equations and Applications 3
[ 講演概要 ]
In recent years increasing interests and considerable
researches have been given to the fractional differential equations both
in time and space variables.
These are due to the applications of the fractional calculus
to problems in a wide areas of physics and engineering science and a rapid
development of the corresponding theory. A motivating example includes
the so-called continuous time random walk process
and the Levy process model for the mathematical finance.
In this lecture we develop solution techniques based on the linear and
nonlinear semigroup theory and apply it to solve the associated inverse
and optimal control problems. The property and stability of the solutions
as well as numerical integration methods
are discussed. The lecture also covers the basis and application of the
so-called Crandall-Ligget theory and the locally quasi-dissipative
operator method developed by Kobayashi-Kobayashi-Oharu.
Nonlinear evolution equations, Crandall-Ligget theory,
Locally quasi-dissipative operators approach
In recent years increasing interests and considerable
researches have been given to the fractional differential equations both
in time and space variables.
These are due to the applications of the fractional calculus
to problems in a wide areas of physics and engineering science and a rapid
development of the corresponding theory. A motivating example includes
the so-called continuous time random walk process
and the Levy process model for the mathematical finance.
In this lecture we develop solution techniques based on the linear and
nonlinear semigroup theory and apply it to solve the associated inverse
and optimal control problems. The property and stability of the solutions
as well as numerical integration methods
are discussed. The lecture also covers the basis and application of the
so-called Crandall-Ligget theory and the locally quasi-dissipative
operator method developed by Kobayashi-Kobayashi-Oharu.
Nonlinear evolution equations, Crandall-Ligget theory,
Locally quasi-dissipative operators approach
2010年01月21日(木)
作用素環セミナー
16:30-18:00 数理科学研究科棟(駒場) 128号室
山下真 氏 (東大数理)
On Subfactors Arising from Asymptotic Representations of Symmetric Groups
山下真 氏 (東大数理)
On Subfactors Arising from Asymptotic Representations of Symmetric Groups
応用解析セミナー
16:00-17:30 数理科学研究科棟(駒場) 122号室
Danielle Hilhorst 氏 (パリ南大学 / CNRS)
A finite volume method on general meshes for a degenerate parabolic convection-reaction-diffusion equation
Danielle Hilhorst 氏 (パリ南大学 / CNRS)
A finite volume method on general meshes for a degenerate parabolic convection-reaction-diffusion equation
[ 講演概要 ]
We propose a finite volume method on general meshes for degenerate parabolic convection-reaction-diffusion equations. Such equations arise for instance in the modeling of contaminant transport in groundwater. After giving a convergence proof, we present the results of numerical tests.
We propose a finite volume method on general meshes for degenerate parabolic convection-reaction-diffusion equations. Such equations arise for instance in the modeling of contaminant transport in groundwater. After giving a convergence proof, we present the results of numerical tests.
2010年01月20日(水)
東京幾何セミナー
17:00-18:30 数理科学研究科棟(駒場) 122号室
場所は東大数理(駒場)、東京工業大学(大岡山)のいずれかで行います。
詳細については、上記セミナーURLよりご確認下さい。
「今後の予定」欄には、東工大で行われるセミナーは表��
Craig Van Coevering 氏 (MIT)
Asymptotically conical manifolds and the Monge-Ampere equation
場所は東大数理(駒場)、東京工業大学(大岡山)のいずれかで行います。
詳細については、上記セミナーURLよりご確認下さい。
「今後の予定」欄には、東工大で行われるセミナーは表��
Craig Van Coevering 氏 (MIT)
Asymptotically conical manifolds and the Monge-Ampere equation
[ 講演概要 ]
Some analysis is considered on manifolds with a conical end. Then we show that in the Kahler case the complex Monge-Ampere equation can be solved with the same regularity as is known in the ALE case. By considering resolutions of toric singularities and hypersurface singularities this can easily be used to produce many Calabi-Yau manifolds with a conical end.
Some analysis is considered on manifolds with a conical end. Then we show that in the Kahler case the complex Monge-Ampere equation can be solved with the same regularity as is known in the ALE case. By considering resolutions of toric singularities and hypersurface singularities this can easily be used to produce many Calabi-Yau manifolds with a conical end.
講演会
16:30-18:00 数理科学研究科棟(駒場) 118号室
伊東一文 氏 (大学院数理科学研究科)
Fractional Evolution Equations and Applications 2
伊東一文 氏 (大学院数理科学研究科)
Fractional Evolution Equations and Applications 2
[ 講演概要 ]
In recent years increasing interests and considerable
researches have been given to the fractional differential equations both
in time and space variables.
These are due to the applications of the fractional calculus
to problems in a wide areas of physics and engineering science and a rapid
development of the corresponding theory. A motivating example includes
the so-called continuous time random walk process
and the Levy process model for the mathematical finance.
In this lecture we develop solution techniques based on the linear and
nonlinear semigroup theory and apply it to solve the associated inverse
and optimal control problems. The property and stability of the solutions
as well as numerical integration methods
are discussed. The lecture also covers the basis and application of the
so-called Crandall-Ligget theory and the locally quasi-dissipative
operator method developed by Kobayashi-Kobayashi-Oharu.
Existence and Uniqueness by C_0 semigroup theory, dissipative linear
operator
and Hille-Yoshida, Trotter-Kato theory.
In recent years increasing interests and considerable
researches have been given to the fractional differential equations both
in time and space variables.
These are due to the applications of the fractional calculus
to problems in a wide areas of physics and engineering science and a rapid
development of the corresponding theory. A motivating example includes
the so-called continuous time random walk process
and the Levy process model for the mathematical finance.
In this lecture we develop solution techniques based on the linear and
nonlinear semigroup theory and apply it to solve the associated inverse
and optimal control problems. The property and stability of the solutions
as well as numerical integration methods
are discussed. The lecture also covers the basis and application of the
so-called Crandall-Ligget theory and the locally quasi-dissipative
operator method developed by Kobayashi-Kobayashi-Oharu.
Existence and Uniqueness by C_0 semigroup theory, dissipative linear
operator
and Hille-Yoshida, Trotter-Kato theory.
数理人口学・数理生物学セミナー
14:40-16:10 数理科学研究科棟(駒場) 052号室
江島啓介 氏 (東京大学情報理工学研究科数理情報専攻修士課程)
東京都市圏パーソントリップ調査に基づく新型インフルエンザ感染拡大シミュレーション
江島啓介 氏 (東京大学情報理工学研究科数理情報専攻修士課程)
東京都市圏パーソントリップ調査に基づく新型インフルエンザ感染拡大シミュレーション
[ 講演概要 ]
新型インフルエンザの感染拡大に対する対応策として,学校施設等の閉鎖など外
出時の感染機会を減らすための措置が考えられるが,その効果は十分に明らかで
はない.そこで本研究では,individual based modelに東京都市圏パーソント
リップ調査を組み合わせることにより感染拡大モデルを構築し,数値シミュレー
ションによって外出規制および施設閉鎖の効果を検討した.外出規制に関して
は,規制日数が12日以上と長い場合には効果が大きいことがわかった.また,施
設閉鎖に関しては,閉鎖期間・閉鎖基準を厳しくすると,ピークまでの日数は変
わらないものの,累積罹患率は低下することがわかった.
新型インフルエンザの感染拡大に対する対応策として,学校施設等の閉鎖など外
出時の感染機会を減らすための措置が考えられるが,その効果は十分に明らかで
はない.そこで本研究では,individual based modelに東京都市圏パーソント
リップ調査を組み合わせることにより感染拡大モデルを構築し,数値シミュレー
ションによって外出規制および施設閉鎖の効果を検討した.外出規制に関して
は,規制日数が12日以上と長い場合には効果が大きいことがわかった.また,施
設閉鎖に関しては,閉鎖期間・閉鎖基準を厳しくすると,ピークまでの日数は変
わらないものの,累積罹患率は低下することがわかった.
2010年01月19日(火)
解析学火曜セミナー
16:30-18:00 数理科学研究科棟(駒場) 128号室
岡田 靖則 氏 (千葉大・理)
超函数の有界性と Massera 型定理について
岡田 靖則 氏 (千葉大・理)
超函数の有界性と Massera 型定理について
作用素環セミナー
16:30-18:00 数理科学研究科棟(駒場) 126号室
高井博司 氏 (首都大学東京)
Entire Cyclic Cohomology of Noncommutative Spheres
高井博司 氏 (首都大学東京)
Entire Cyclic Cohomology of Noncommutative Spheres
トポロジー火曜セミナー
17:00-18:00 数理科学研究科棟(駒場) 056号室
Tea: 16:40 - 17:00 コモンルーム
小林 亮一 氏 (名古屋大学)
Localization via group action and its application to
the period condition of algebraic minimal surfaces
Tea: 16:40 - 17:00 コモンルーム
小林 亮一 氏 (名古屋大学)
Localization via group action and its application to
the period condition of algebraic minimal surfaces
[ 講演概要 ]
The optimal estimate for the number of exceptional
values of the Gauss map of algebraic minimal surfaces is a long
standing problem. In this lecture, I will introduce new ideas
toward the solution of this problem. The ``collective Cohn-Vossen
inequality" is the key idea. From this we have effective
Nevanlinna's lemma on logarithmic derivative for a certain class
of meromorphic functions on the disk. On the other hand, we can
construct a family holomorphic functions on the disk from the
Weierstrass data of the algebraic minimal surface under
consideration, which encodes the period condition.
Applying effective Lemma on logarithmic derivative to these
functions, we can extract an intriguing inequality.
The optimal estimate for the number of exceptional
values of the Gauss map of algebraic minimal surfaces is a long
standing problem. In this lecture, I will introduce new ideas
toward the solution of this problem. The ``collective Cohn-Vossen
inequality" is the key idea. From this we have effective
Nevanlinna's lemma on logarithmic derivative for a certain class
of meromorphic functions on the disk. On the other hand, we can
construct a family holomorphic functions on the disk from the
Weierstrass data of the algebraic minimal surface under
consideration, which encodes the period condition.
Applying effective Lemma on logarithmic derivative to these
functions, we can extract an intriguing inequality.
講演会
16:30-18:00 数理科学研究科棟(駒場) 118号室
伊東一文 氏 (大学院数理科学研究科)
Fractional Evolution Equations and Applications 1
伊東一文 氏 (大学院数理科学研究科)
Fractional Evolution Equations and Applications 1
[ 講演概要 ]
In recent years increasing interests and considerable
researches have been given to the fractional differential equations both
in time and space variables.
These are due to the applications of the fractional calculus
to problems in a wide areas of physics and engineering science and a rapid
development of the corresponding theory. A motivating example includes
the so-called continuous time random walk process
and the Levy process model for the mathematical finance.
In this lecture we develop solution techniques based on the linear and
nonlinear semigroup theory and apply it to solve the associated inverse
and optimal control problems. The property and stability of the solutions
as well as numerical integration methods
are discussed. The lecture also covers the basis and application of the
so-called Crandall-Ligget theory and the locally quasi-dissipative
operator method developed by Kobayashi-Kobayashi-Oharu.
Motivation: Continuous time random walk (CTRW) process
Fractional differential equations in time and Mittag-Leffler functions
In recent years increasing interests and considerable
researches have been given to the fractional differential equations both
in time and space variables.
These are due to the applications of the fractional calculus
to problems in a wide areas of physics and engineering science and a rapid
development of the corresponding theory. A motivating example includes
the so-called continuous time random walk process
and the Levy process model for the mathematical finance.
In this lecture we develop solution techniques based on the linear and
nonlinear semigroup theory and apply it to solve the associated inverse
and optimal control problems. The property and stability of the solutions
as well as numerical integration methods
are discussed. The lecture also covers the basis and application of the
so-called Crandall-Ligget theory and the locally quasi-dissipative
operator method developed by Kobayashi-Kobayashi-Oharu.
Motivation: Continuous time random walk (CTRW) process
Fractional differential equations in time and Mittag-Leffler functions
2010年01月18日(月)
複素解析幾何セミナー
10:30-12:00 数理科学研究科棟(駒場) 128号室
奥間智弘 氏 (山形大学地域教育文化学部)
スプライス商特異点について
奥間智弘 氏 (山形大学地域教育文化学部)
スプライス商特異点について
代数幾何学セミナー
16:40-18:10 数理科学研究科棟(駒場) 126号室
Anne-Sophie Kaloghiros 氏 (RIMS)
The divisor class group of terminal Gorenstein Fano 3-folds and rationality questions
Anne-Sophie Kaloghiros 氏 (RIMS)
The divisor class group of terminal Gorenstein Fano 3-folds and rationality questions
[ 講演概要 ]
Let Y be a quartic hypersurface in CP^4 with mild singularities, e.g. no worse than ordinary double points.
If Y contains a surface that is not a hyperplane section, Y is not Q-factorial and the divisor class group of Y, Cl Y, contains divisors that are not Cartier. However, the rank of Cl Y is bounded.
In this talk, I will show that in most cases, it is possible to describe explicitly the divisor class group Cl Y by running a Minimal Model Program (MMP) on X, a small Q-factorialisation of Y. In this case, the generators of Cl Y/ Pic Y are ``topological traces " of K-negative extremal contractions on X.
This has surprising consequences: it is possible to conclude that a number of families of non-factorial quartic 3-folds are rational.
In particular, I give some examples of rational quartic hypersurfaces Y_4\\subset CP^4 with rk Cl Y=2 and show that when the divisor class group of Y has sufficiently high rank, Y is always rational.
Let Y be a quartic hypersurface in CP^4 with mild singularities, e.g. no worse than ordinary double points.
If Y contains a surface that is not a hyperplane section, Y is not Q-factorial and the divisor class group of Y, Cl Y, contains divisors that are not Cartier. However, the rank of Cl Y is bounded.
In this talk, I will show that in most cases, it is possible to describe explicitly the divisor class group Cl Y by running a Minimal Model Program (MMP) on X, a small Q-factorialisation of Y. In this case, the generators of Cl Y/ Pic Y are ``topological traces " of K-negative extremal contractions on X.
This has surprising consequences: it is possible to conclude that a number of families of non-factorial quartic 3-folds are rational.
In particular, I give some examples of rational quartic hypersurfaces Y_4\\subset CP^4 with rk Cl Y=2 and show that when the divisor class group of Y has sufficiently high rank, Y is always rational.
2010年01月15日(金)
GCOE社会数理講演シリーズ
16:20-17:50 数理科学研究科棟(駒場) 117号室
中川淳一 氏 (新日本製鐵(株)技術開発本部)
製鐵プロセスにおける数学
中川淳一 氏 (新日本製鐵(株)技術開発本部)
製鐵プロセスにおける数学
2010年01月14日(木)
作用素環セミナー
16:30-18:00 数理科学研究科棟(駒場) 128号室
Marius Junge 氏 (Univ. Illinois, Urbana-Champaign)
Applications of operator algebras in Quantum information theory
Marius Junge 氏 (Univ. Illinois, Urbana-Champaign)
Applications of operator algebras in Quantum information theory
2010年01月13日(水)
講演会
16:45-17:45 数理科学研究科棟(駒場) 128号室
Felix Rubin 氏 (Zurich 大学)
Scaled limit for the largest eigenvalue from the generalized Cauchy ensemble
Felix Rubin 氏 (Zurich 大学)
Scaled limit for the largest eigenvalue from the generalized Cauchy ensemble
講演会
15:30-16:30 数理科学研究科棟(駒場) 128号室
Michael Allman 氏 (Warwick 大学)
Breaking the chain: slow versus fast pulling
Michael Allman 氏 (Warwick 大学)
Breaking the chain: slow versus fast pulling
2010年01月12日(火)
Lie群論・表現論セミナー
16:30-18:00 数理科学研究科棟(駒場) 126号室
西岡斉治 氏 (東京大学大学院数理科学研究科博士課程)
代数的差分方程式の可解性と既約性
https://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar2010.html#20100112nishioka
西岡斉治 氏 (東京大学大学院数理科学研究科博士課程)
代数的差分方程式の可解性と既約性
[ 講演概要 ]
差分代数の理論を使って,代数的差分方程式の代数函数解や超幾
何函数解の非存在や,存在する場合の特殊解の分類をする。
[ 参考URL ]差分代数の理論を使って,代数的差分方程式の代数函数解や超幾
何函数解の非存在や,存在する場合の特殊解の分類をする。
https://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar2010.html#20100112nishioka
トポロジー火曜セミナー
16:30-18:30 数理科学研究科棟(駒場) 056号室
Tea: 16:00 - 16:30 コモンルーム
篠原 克寿 氏 (東京大学大学院数理科学研究科) 16:30-17:30
Index problem for generically-wild homoclinic classes in dimension three
On a generalized suspension theorem for directed Fukaya categories
Tea: 16:00 - 16:30 コモンルーム
篠原 克寿 氏 (東京大学大学院数理科学研究科) 16:30-17:30
Index problem for generically-wild homoclinic classes in dimension three
[ 講演概要 ]
In the sphere of non-hyperbolic differentiable dynamical systems, one can construct an example of a homolinic class which does not admit any kind of dominated splittings (a weak form of hyperbolicity) in a robust way. In this talk, we discuss the index (dimension of the unstable manifold) of the periodic points inside such homoclinic classes from a $C^1$-generic viewpoint.
二木 昌宏 氏 (東京大学大学院数理科学研究科) 17:30-18:30In the sphere of non-hyperbolic differentiable dynamical systems, one can construct an example of a homolinic class which does not admit any kind of dominated splittings (a weak form of hyperbolicity) in a robust way. In this talk, we discuss the index (dimension of the unstable manifold) of the periodic points inside such homoclinic classes from a $C^1$-generic viewpoint.
On a generalized suspension theorem for directed Fukaya categories
[ 講演概要 ]
The directed Fukaya category $\\mathrm{Fuk} W$ of exact Lefschetz
fibration $W : X \\to \\mathbb{C}$ proposed by Kontsevich is a
categorification of the Milnor lattice of $W$. This is defined as the
directed $A_\\infty$-category $\\mathrm{Fuk} W = \\mathrm{Fuk}^\\to
\\mathbb{V}$ generated by a distinguished basis $\\mathbb{V}$ of
vanishing cycles.
Recently Seidel has proved that this is stable under the suspension $W
+ u^2$ as a consequence of his foundational work on the directed
Fukaya category. We generalize his suspension theorem to the $W + u^d$
case by considering partial tensor product $\\mathrm{Fuk} W \\otimes'
\\mathcal{A}_{d-1}$, where $\\mathcal{A}_{d-1}$ is the category
corresponding to the $A_n$-type quiver. This also generalizes a recent
work by the author with Kazushi Ueda.
The directed Fukaya category $\\mathrm{Fuk} W$ of exact Lefschetz
fibration $W : X \\to \\mathbb{C}$ proposed by Kontsevich is a
categorification of the Milnor lattice of $W$. This is defined as the
directed $A_\\infty$-category $\\mathrm{Fuk} W = \\mathrm{Fuk}^\\to
\\mathbb{V}$ generated by a distinguished basis $\\mathbb{V}$ of
vanishing cycles.
Recently Seidel has proved that this is stable under the suspension $W
+ u^2$ as a consequence of his foundational work on the directed
Fukaya category. We generalize his suspension theorem to the $W + u^d$
case by considering partial tensor product $\\mathrm{Fuk} W \\otimes'
\\mathcal{A}_{d-1}$, where $\\mathcal{A}_{d-1}$ is the category
corresponding to the $A_n$-type quiver. This also generalizes a recent
work by the author with Kazushi Ueda.
2010年01月08日(金)
談話会・数理科学講演会
16:30-17:30 数理科学研究科棟(駒場) 123号室
お茶&Coffee&お菓子: 16:00～16:30 (コモンルーム)
大島利雄 氏 (東京大学大学院数理科学研究科)
特殊関数とFuchs型常微分方程式
お茶&Coffee&お菓子: 16:00～16:30 (コモンルーム)
大島利雄 氏 (東京大学大学院数理科学研究科)
特殊関数とFuchs型常微分方程式
[ 講演概要 ]
岩波全書の数学公式集III「特殊関数」の大部分はGaussの超幾何関数とその特殊化のBessel関数やLegendre多項式などで占められている。この超幾何関数についての最も重要な基本結果は1での値を与えるGaussの和公式とRiemann schemeによる特徴付けとであろう。この関数は一般超幾何関数やJordan-Pochhammer方程式へ、またHeun方程式からPainleve方程式へという解析、さらにAppell,Gelfand-青本,Heckman-Opdamによる多変数化という3つの方向の発展がある。講演ではこれらを含む統一的な理解、Riemann schemeの一般化とuniversal modelの存在定理(Deligne-Katz-Simpson問題)、接続公式(Gaussの和公式の一般化)、無限次元Kac-Moody Weyl群の作用について解説し、特異点の合流、積分表示、ベキ級数表示などについても述べたい。結果は構成的 でコンピュータ・プログラムで実現できる。
岩波全書の数学公式集III「特殊関数」の大部分はGaussの超幾何関数とその特殊化のBessel関数やLegendre多項式などで占められている。この超幾何関数についての最も重要な基本結果は1での値を与えるGaussの和公式とRiemann schemeによる特徴付けとであろう。この関数は一般超幾何関数やJordan-Pochhammer方程式へ、またHeun方程式からPainleve方程式へという解析、さらにAppell,Gelfand-青本,Heckman-Opdamによる多変数化という3つの方向の発展がある。講演ではこれらを含む統一的な理解、Riemann schemeの一般化とuniversal modelの存在定理(Deligne-Katz-Simpson問題)、接続公式(Gaussの和公式の一般化)、無限次元Kac-Moody Weyl群の作用について解説し、特異点の合流、積分表示、ベキ級数表示などについても述べたい。結果は構成的 でコンピュータ・プログラムで実現できる。
2010年01月07日(木)
作用素環セミナー
16:30-18:00 数理科学研究科棟(駒場) 128号室
Luc Rey-Bellet 氏 (Univ. Massachusetts)
Large deviations, Billiards, and Non-equilibrium Statistical Mechanics
Luc Rey-Bellet 氏 (Univ. Massachusetts)
Large deviations, Billiards, and Non-equilibrium Statistical Mechanics
GCOEセミナー
16:30-18:00 数理科学研究科棟(駒場) 128号室
LucRey-Bellet 氏 (Univ. Massachusetts)
Large deviations, Billiards, and Non-equilibrium Statistical Mechanics
LucRey-Bellet 氏 (Univ. Massachusetts)
Large deviations, Billiards, and Non-equilibrium Statistical Mechanics
[ 講演概要 ]
Large deviations have applications in many aspects of statistical mechanics. New applications for the steady states of non-equilibrium statistical mechanics have emerged during the past ten years and these applications deal with the fluctuations of the entropy production. After discussing some general aspects of entropy production we turn to concrete examples, in particular billiards with and without external forces and discuss large deviations theorems for such systems.
Large deviations have applications in many aspects of statistical mechanics. New applications for the steady states of non-equilibrium statistical mechanics have emerged during the past ten years and these applications deal with the fluctuations of the entropy production. After discussing some general aspects of entropy production we turn to concrete examples, in particular billiards with and without external forces and discuss large deviations theorems for such systems.
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