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複素解析幾何セミナー
過去の記録 ～12/05｜次回の予定｜今後の予定 12/06～
| 開催情報 | 月曜日 10:30～12:00 数理科学研究科棟(駒場) 128号室 |
|---|---|
| 担当者 | 平地 健吾, 高山 茂晴 |
過去の記録
2006年06月05日(月)
10:30-12:00 数理科学研究科棟(駒場) 128号室
Wolfram Bauer 氏 (東京理科大)
Integral formulas for infinite dimensional domains with arbitrary boundary
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/~hirachi/scv/Bauer.pdf
Wolfram Bauer 氏 (東京理科大)
Integral formulas for infinite dimensional domains with arbitrary boundary
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/~hirachi/scv/Bauer.pdf
2006年05月29日(月)
10:30-12:00 数理科学研究科棟(駒場) 128号室
Marco Brunella 氏 (Bourgogne)
Uniformisation of Holomorphic Foliations by Curves II
Marco Brunella 氏 (Bourgogne)
Uniformisation of Holomorphic Foliations by Curves II
2006年05月29日(月)
13:30-15:00 数理科学研究科棟(駒場) 128号室
大沢 健夫 氏 (名古屋大学)
Hodge theory with bounds and its application to foliations
大沢 健夫 氏 (名古屋大学)
Hodge theory with bounds and its application to foliations
2006年05月22日(月)
10:30-12:00 数理科学研究科棟(駒場) 128号室
Marco Brunella 氏 (Bourgogne)
Uniformisation of Holomorphic Foliations by Curves I (Part II on May 29)
Marco Brunella 氏 (Bourgogne)
Uniformisation of Holomorphic Foliations by Curves I (Part II on May 29)
[ 講演概要 ]
In the first lecture, we give a definition of "leaf" for a singular holomorphic one-dimensional foliation on a projective manifold. The definition is such that the leaves of a foliation glue together in a nice way, giving a "covering tube" which is a sort of semi-global flow box. This is, in some sense, the topological part of the theory. In the second lecture, we prove some convexity property of this covering tube. As a corollary we obtain that, when there are hyperbolic leaves, the leafwise Poincare' metric has some remarkable positivity property. In the third lecture, we study foliations all of whose leaves are parabolic. Using a suitable extension theorem for certain meromorphic maps, we show how to generalise the above positivity property to this degenerate class of foliations.
In the first lecture, we give a definition of "leaf" for a singular holomorphic one-dimensional foliation on a projective manifold. The definition is such that the leaves of a foliation glue together in a nice way, giving a "covering tube" which is a sort of semi-global flow box. This is, in some sense, the topological part of the theory. In the second lecture, we prove some convexity property of this covering tube. As a corollary we obtain that, when there are hyperbolic leaves, the leafwise Poincare' metric has some remarkable positivity property. In the third lecture, we study foliations all of whose leaves are parabolic. Using a suitable extension theorem for certain meromorphic maps, we show how to generalise the above positivity property to this degenerate class of foliations.
2006年05月22日(月)
15:00-16:30 数理科学研究科棟(駒場) 470号室
午前の部と部屋が異なります。
Nessim Sibony 氏 (Paris Sud)
Laminations with Singularities by Riemann Surfaces II
午前の部と部屋が異なります。
Nessim Sibony 氏 (Paris Sud)
Laminations with Singularities by Riemann Surfaces II
2006年05月15日(月)
10:30-12:00 数理科学研究科棟(駒場) 128号室
Nessim Sibony 氏 (Paris Sud)
Laminations with Singularities by Riemann Surfaces I (Part II on May 22)
Nessim Sibony 氏 (Paris Sud)
Laminations with Singularities by Riemann Surfaces I (Part II on May 22)
[ 講演概要 ]
The basic example of a lamination, possibly with singularites, by Riemann surfaces, is the closure of a leaf of a holomorphic foliation in the complex projective plane.There are also many examples arising from the theory of iteration of a holomorphic map. The goal is to introduce tools in order to understand the globalproperties of leaves of a holomorphic lamination, mostly in compact Kaehler manifolds. We will develop the following topics.
-Poincare metric on a hyperbolic lamination.
-Positive cycles and positive harmonic currents directed by a lamination.
-Ahlfors construction of positive harmonic currents.
-Cohomological and geometrical intersection of positive harmonic currents.
The basic example of a lamination, possibly with singularites, by Riemann surfaces, is the closure of a leaf of a holomorphic foliation in the complex projective plane.There are also many examples arising from the theory of iteration of a holomorphic map. The goal is to introduce tools in order to understand the globalproperties of leaves of a holomorphic lamination, mostly in compact Kaehler manifolds. We will develop the following topics.
-Poincare metric on a hyperbolic lamination.
-Positive cycles and positive harmonic currents directed by a lamination.
-Ahlfors construction of positive harmonic currents.
-Cohomological and geometrical intersection of positive harmonic currents.
2006年05月08日(月)
10:30-12:00 数理科学研究科棟(駒場) 128号室
大沢 健夫 氏 (名古屋大学)
Real-analytic Levi-flats in complex tori
大沢 健夫 氏 (名古屋大学)
Real-analytic Levi-flats in complex tori
2006年04月24日(月)
10:30-12:00 数理科学研究科棟(駒場) 128号室
Jonas Wiklund 氏 (名古屋大学, JSPS fellow)
Monge-Ampére mass at the boundary on some domains with corner
Jonas Wiklund 氏 (名古屋大学, JSPS fellow)
Monge-Ampére mass at the boundary on some domains with corner
[ 講演概要 ]
The Monge-Ampére operator is a highly non-linear operator that assigns a positive measure to every plurisubharmonic function and the null-measure to every maximal plurisubharmonic measure, whenever it is well defined. We discuss the sweeping out of this measure to the boundary for functions that essentially vanish on the boundary, and show two examples that this boundary measure vanish outside the distinguished boundary. Namely for analytic polyhedrons and for the cross product of two hyperconvex domains. Some related open problems are also mentioned.
The Monge-Ampére operator is a highly non-linear operator that assigns a positive measure to every plurisubharmonic function and the null-measure to every maximal plurisubharmonic measure, whenever it is well defined. We discuss the sweeping out of this measure to the boundary for functions that essentially vanish on the boundary, and show two examples that this boundary measure vanish outside the distinguished boundary. Namely for analytic polyhedrons and for the cross product of two hyperconvex domains. Some related open problems are also mentioned.
2006年04月17日(月)
10:30-12:00 数理科学研究科棟(駒場) 128号室
C. Robin Graham 氏 (University of Washington)
Dirichlet-to-Neumann map for Poincaré-Einstein metrics
C. Robin Graham 氏 (University of Washington)
Dirichlet-to-Neumann map for Poincaré-Einstein metrics
[ 講演概要 ]
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年01月30日(月)
10:30-12:00 数理科学研究科棟(駒場) 128号室
藤木 明 氏 (大阪大学)
Compact non-kaehler threefolds associated to hyperbolic 3-manifolds
藤木 明 氏 (大阪大学)
Compact non-kaehler threefolds associated to hyperbolic 3-manifolds
2006年01月23日(月)
10:30-12:00 数理科学研究科棟(駒場) 128号室
金子 宏 氏 (東京理科大)
Stochastic processes and Besov spaces on local field
金子 宏 氏 (東京理科大)
Stochastic processes and Besov spaces on local field
2005年12月05日(月)
10:30-12:00 数理科学研究科棟(駒場) 128号室
Sebastien Boucksom 氏 (ParisVII / Univ. of Tokyo)
Positive cones of hyper-Keahler manifold
Sebastien Boucksom 氏 (ParisVII / Univ. of Tokyo)
Positive cones of hyper-Keahler manifold
2005年11月28日(月)
10:30-12:00 数理科学研究科棟(駒場) 128号室
上田哲生 氏 (京都大学)
Schroeder equation and Abel equation
上田哲生 氏 (京都大学)
Schroeder equation and Abel equation
2005年11月21日(月)
10:30-12:00 数理科学研究科棟(駒場) 128号室
Andreas Cap 氏 (Univ. of Vienna)
On CR-invariant differential operators
Andreas Cap 氏 (Univ. of Vienna)
On CR-invariant differential operators
[ 講演概要 ]
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年11月14日(月)
10:30-12:00 数理科学研究科棟(駒場) 128号室
Raphael Pong 氏 (Ohio State Univ)
New invariants for CR and contact manifolds
Raphael Pong 氏 (Ohio State Univ)
New invariants for CR and contact manifolds
[ 講演概要 ]
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年11月07日(月)
10:30-12:00 数理科学研究科棟(駒場) 128号室
難波誠 氏 (追手門学院大学)
Moduli of Galois coverings of the complex projective line
難波誠 氏 (追手門学院大学)
Moduli of Galois coverings of the complex projective line
2005年10月24日(月)
10:30-12:00 数理科学研究科棟(駒場) 128号室
平地健吾 氏 (東大数理)
Ambient metrics for even dimensional conformal structures
平地健吾 氏 (東大数理)
Ambient metrics for even dimensional conformal structures
2005年10月17日(月)
10:30-12:00 数理科学研究科棟(駒場) 128号室
吉川謙一 氏 (東大数理)
On the discriminant of certain K3 surfaces
吉川謙一 氏 (東大数理)
On the discriminant of certain K3 surfaces
2005年07月22日(金)
10:30-12:00 数理科学研究科棟(駒場) 128号室
倉西正武 氏 (コロンビア大学)
Szegö kernel の構成について
倉西正武 氏 (コロンビア大学)
Szegö kernel の構成について
2005年07月22日(金)
15:30-17:00 数理科学研究科棟(駒場) 128号室
Dan Popovici 氏 (JSPS, 名古屋大学多元数理)
Effective Local Finite Generation of Multiplier Ideal Sheaves
Dan Popovici 氏 (JSPS, 名古屋大学多元数理)
Effective Local Finite Generation of Multiplier Ideal Sheaves
2005年07月11日(月)
10:30-12:00 数理科学研究科棟(駒場) 128号室
青柳美輝 氏 (上智大理工)
学習理論のゼータ関数と特異点解消
青柳美輝 氏 (上智大理工)
学習理論のゼータ関数と特異点解消
2005年07月04日(月)
10:30-12:00 数理科学研究科棟(駒場) 128号室
辻 元 氏 (上智大理工)
Variation of Bergman kernel of projective manifolds
辻 元 氏 (上智大理工)
Variation of Bergman kernel of projective manifolds
2005年06月27日(月)
10:30-12:00 数理科学研究科棟(駒場) 128号室
相原義弘 氏 (沼津高専)
Uniqueness problem of analytic coverng spaces
相原義弘 氏 (沼津高専)
Uniqueness problem of analytic coverng spaces
2005年06月06日(月)
10:30-12:00 数理科学研究科棟(駒場) 128号室
大沢健夫 氏 (名大多元数理)
Application of Hartogs type extension theorems to Levi flats in Kaehler manifolds
大沢健夫 氏 (名大多元数理)
Application of Hartogs type extension theorems to Levi flats in Kaehler manifolds
2005年05月30日(月)
10:30-12:00 数理科学研究科棟(駒場) 128号室
宮岡礼子 氏 (九大数理)
全曲率有限な完備極小曲面のガウス写像の除外値について
宮岡礼子 氏 (九大数理)
全曲率有限な完備極小曲面のガウス写像の除外値について
