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Seminar on Geometric Complex Analysis
Seminar information archive ～05/08｜Next seminar｜Future seminars 05/09～
| Date, time & place | Monday 10:30 - 12:00 128Room #128 (Graduate School of Math. Sci. Bldg.) |
|---|---|
| Organizer(s) | Kengo Hirachi, Shigeharu Takayama |
Seminar information archive
2006/10/23
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
泊 昌孝 (日本大学文理学部)
Classification of hypersurface simple K3 singularities -- 95 and others
泊 昌孝 (日本大学文理学部)
Classification of hypersurface simple K3 singularities -- 95 and others
2006/10/16
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Sebastien Boucksom (東大数理 JSPS研究員)
Differentiability of the volume of divisors and Khovanskii-Teissier inequalities
Sebastien Boucksom (東大数理 JSPS研究員)
Differentiability of the volume of divisors and Khovanskii-Teissier inequalities
2006/07/10
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Do Duc Thai (Hanoi教育大)
Characterization of domains in $C^n$ by their noncompact automorphism groups
Do Duc Thai (Hanoi教育大)
Characterization of domains in $C^n$ by their noncompact automorphism groups
[ Abstract ]
In this talk, the characterization of domains in $C^n$ by their noncompact automorphism groups are given. By this characterization, the Bedford-Pinchuk theorem is true for any domain (not necessary bounded) in $C^n$.
In this talk, the characterization of domains in $C^n$ by their noncompact automorphism groups are given. By this characterization, the Bedford-Pinchuk theorem is true for any domain (not necessary bounded) in $C^n$.
2006/07/03
14:00-15:30 Room #128 (Graduate School of Math. Sci. Bldg.)
Jörg Winkelmann (Université Henri Poincaré Nancy)
Complex Semi-Abelian Varieties II --- Compactifications and etc.
Jörg Winkelmann (Université Henri Poincaré Nancy)
Complex Semi-Abelian Varieties II --- Compactifications and etc.
2006/06/26
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
織田孝幸 (東大数理)
Toward construction of Green current for modular cycles in modular varieties
織田孝幸 (東大数理)
Toward construction of Green current for modular cycles in modular varieties
2006/06/19
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
後藤竜司 (大阪大学)
Deformations and smoothing of (generalized) holomorphic symplectic structures
後藤竜司 (大阪大学)
Deformations and smoothing of (generalized) holomorphic symplectic structures
2006/06/12
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
赤堀隆夫 (兵庫県立大学)
The Rumin complex and Hamiltonian mechanism
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~hirachi/scv/akahori.pdf
赤堀隆夫 (兵庫県立大学)
The Rumin complex and Hamiltonian mechanism
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~hirachi/scv/akahori.pdf
2006/06/05
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Wolfram Bauer (東京理科大)
Integral formulas for infinite dimensional domains with arbitrary boundary
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~hirachi/scv/Bauer.pdf
Wolfram Bauer (東京理科大)
Integral formulas for infinite dimensional domains with arbitrary boundary
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~hirachi/scv/Bauer.pdf
2006/05/29
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Marco Brunella (Bourgogne)
Uniformisation of Holomorphic Foliations by Curves II
Marco Brunella (Bourgogne)
Uniformisation of Holomorphic Foliations by Curves II
2006/05/29
13:30-15:00 Room #128 (Graduate School of Math. Sci. Bldg.)
大沢 健夫 (名古屋大学)
Hodge theory with bounds and its application to foliations
大沢 健夫 (名古屋大学)
Hodge theory with bounds and its application to foliations
2006/05/22
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Marco Brunella (Bourgogne)
Uniformisation of Holomorphic Foliations by Curves I (Part II on May 29)
Marco Brunella (Bourgogne)
Uniformisation of Holomorphic Foliations by Curves I (Part II on May 29)
[ Abstract ]
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.
2006/05/22
15:00-16:30 Room #470 (Graduate School of Math. Sci. Bldg.)
Nessim Sibony (Paris Sud)
Laminations with Singularities by Riemann Surfaces II
Nessim Sibony (Paris Sud)
Laminations with Singularities by Riemann Surfaces II
2006/05/15
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Nessim Sibony (Paris Sud)
Laminations with Singularities by Riemann Surfaces I (Part II on May 22)
Nessim Sibony (Paris Sud)
Laminations with Singularities by Riemann Surfaces I (Part II on May 22)
[ Abstract ]
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.
2006/05/08
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
大沢 健夫 (名古屋大学)
Real-analytic Levi-flats in complex tori
大沢 健夫 (名古屋大学)
Real-analytic Levi-flats in complex tori
2006/04/24
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Jonas Wiklund (名古屋大学, JSPS fellow)
Monge-Ampére mass at the boundary on some domains with corner
Jonas Wiklund (名古屋大学, JSPS fellow)
Monge-Ampére mass at the boundary on some domains with corner
[ Abstract ]
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.
2006/04/17
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.
2006/01/30
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
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
2005/12/05
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
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
2005/11/21
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
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.
2005/11/07
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
2005/10/24
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
平地健吾 (東大数理)
Ambient metrics for even dimensional conformal structures
平地健吾 (東大数理)
Ambient metrics for even dimensional conformal structures
2005/10/17
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
吉川謙一 (東大数理)
On the discriminant of certain K3 surfaces
吉川謙一 (東大数理)
On the discriminant of certain K3 surfaces
