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Seminar information archive
Seminar information archive ～02/04｜Today's seminar 02/05 | Future seminars 02/06～
Seminar on Geometric Complex Analysis
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Katsutoshi Yamanoi (Osaka Univ.)
On pseudo Kobayashi hyperbolicity of subvarieties of abelian varieties
(Japanese)
Katsutoshi Yamanoi (Osaka Univ.)
On pseudo Kobayashi hyperbolicity of subvarieties of abelian varieties
(Japanese)
[ Abstract ]
A subvariety of an abelian variety is of general type if and only if it is pseudo Kobayashi hyperbolic. I will discuss the proof of this result.
A subvariety of an abelian variety is of general type if and only if it is pseudo Kobayashi hyperbolic. I will discuss the proof of this result.
2015/12/17
Algebraic Geometry Seminar
15:30-17:00 Room #122 (Graduate School of Math. Sci. Bldg.)
Dulip Piyaratne (IPMU)
Polarization and stability on a derived equivalent abelian variety (English)
http://db.ipmu.jp/member/personal/3989en.html
Dulip Piyaratne (IPMU)
Polarization and stability on a derived equivalent abelian variety (English)
[ Abstract ]
In this talk I will explain how one can define a polarization on a derived equivalent abelian variety by using Fourier-Mukai theory. Furthermore, we see how such a realisations is connected with stability conditions on their derived categories. Then I will discuss these ideas for abelian surfaces and abelian 3-folds in detail.
[ Reference URL ]In this talk I will explain how one can define a polarization on a derived equivalent abelian variety by using Fourier-Mukai theory. Furthermore, we see how such a realisations is connected with stability conditions on their derived categories. Then I will discuss these ideas for abelian surfaces and abelian 3-folds in detail.
http://db.ipmu.jp/member/personal/3989en.html
2015/12/16
Operator Algebra Seminars
16:45-18:15 Room #118 (Graduate School of Math. Sci. Bldg.)
Yul Otani (Univ. Tokyo)
Nuclearity in AQFT and related results
Yul Otani (Univ. Tokyo)
Nuclearity in AQFT and related results
thesis presentations
10:30-11:45 Room #122 (Graduate School of Math. Sci. Bldg.)
山本 光 (東京大学大学院数理科学研究科)
Special Lagrangian submanifolds and mean curvature flows（特殊ラグランジュ部分多様体と平均曲率流について） (JAPANESE)
山本 光 (東京大学大学院数理科学研究科)
Special Lagrangian submanifolds and mean curvature flows（特殊ラグランジュ部分多様体と平均曲率流について） (JAPANESE)
FMSP Lectures
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Yuri Luchko (University of Applied Sciences, Berlin)
Selected topics in fractional partial differential equations (ENGLISH)
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Luchko.pdf
Yuri Luchko (University of Applied Sciences, Berlin)
Selected topics in fractional partial differential equations (ENGLISH)
[ Abstract ]
In this talk, some remarkable mathematical and physical properties of solutions to the fractional diffusion equation, the alpha-fractional diffusion and alpha-fractional wave equations, the fractional reaction-diffusion equation, and the fractional Schrödinger equation are revisited. From the mathematical viewpoint, the maximum principle for the initial-boundary-value problems for the fractional diffusion equation, the scaling properties of the solutions to the alpha-fractional diffusion and alpha-fractional wave equations and the role of the Mellin integral transform technique for their analytical treatment, as well as the eigenvalue problem for the fractional Schrödinger equation are considered. Physical aspects include a discussion of a probabilistic interpretation of the fundamental solutions to the Cauchy problem for the alpha-fractional diffusion equation, their entropy and the entropy production rates, and some different concepts of the propagation velocities of the fractional wave processes.
[ Reference URL ]In this talk, some remarkable mathematical and physical properties of solutions to the fractional diffusion equation, the alpha-fractional diffusion and alpha-fractional wave equations, the fractional reaction-diffusion equation, and the fractional Schrödinger equation are revisited. From the mathematical viewpoint, the maximum principle for the initial-boundary-value problems for the fractional diffusion equation, the scaling properties of the solutions to the alpha-fractional diffusion and alpha-fractional wave equations and the role of the Mellin integral transform technique for their analytical treatment, as well as the eigenvalue problem for the fractional Schrödinger equation are considered. Physical aspects include a discussion of a probabilistic interpretation of the fundamental solutions to the Cauchy problem for the alpha-fractional diffusion equation, their entropy and the entropy production rates, and some different concepts of the propagation velocities of the fractional wave processes.
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Luchko.pdf
2015/12/15
Tuesday Seminar on Topology
17:00-18:30 Room #056 (Graduate School of Math. Sci. Bldg.)
Constantin Teleman (University of California, Berkeley)
The Curved Cartan Complex (ENGLISH)
Constantin Teleman (University of California, Berkeley)
The Curved Cartan Complex (ENGLISH)
[ Abstract ]
The Cartan model computes the equivariant cohomology of a smooth manifold X with
differentiable action of a compact Lie group G, from the invariant polynomial
functions on the Lie algebra with values in differential forms and a deformation
of the de Rham differential. Before extracting invariants, the Cartan differential
does not square to zero and is apparently meaningless. Unrecognised was the fact
that the full complex is a curved algebra, computing the quotient by G of the
algebra of differential forms on X. This generates, for example, a gauged version of
string topology. Another instance of the construction, applied to deformation
quantisation of symplectic manifolds, gives the BRST construction of the symplectic
quotient. Finally, the theory for a X point with an additional quadratic curving
computes the representation category of the compact group G, and this generalises
to the loop group of G and even to real semi-simple groups.
The Cartan model computes the equivariant cohomology of a smooth manifold X with
differentiable action of a compact Lie group G, from the invariant polynomial
functions on the Lie algebra with values in differential forms and a deformation
of the de Rham differential. Before extracting invariants, the Cartan differential
does not square to zero and is apparently meaningless. Unrecognised was the fact
that the full complex is a curved algebra, computing the quotient by G of the
algebra of differential forms on X. This generates, for example, a gauged version of
string topology. Another instance of the construction, applied to deformation
quantisation of symplectic manifolds, gives the BRST construction of the symplectic
quotient. Finally, the theory for a X point with an additional quadratic curving
computes the representation category of the compact group G, and this generalises
to the loop group of G and even to real semi-simple groups.
2015/12/14
Seminar on Geometric Complex Analysis
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Fuminori Nakata (Fukushima Univ.)
Twistor correspondence for associative Grassmanniann
Fuminori Nakata (Fukushima Univ.)
Twistor correspondence for associative Grassmanniann
[ Abstract ]
It is well known that the 6-dimensional sphere has a non-integrable almost complex structure which is introduced from the (right) multiplication of imaginary octonians. On this 6-sphere, there is a family of psuedo-holomorphic $\mathbb{C}\mathbb{P}^1$ parameterised by the associative Grassmannian, where the associative Grassmaniann is an 8-dimensional quaternion Kaehler manifold defined as the set of associative 3-planes in the 7-dimensional real vector space of the imaginary octonians. In the talk, we show that this story is quite analogous to the Penrose's twistor correspondence and that the geometric structures on the associative Grassmaniann nicely fit to this construction. This is a joint work with H. Hashimoto, K. Mashimo and M. Ohashi.
It is well known that the 6-dimensional sphere has a non-integrable almost complex structure which is introduced from the (right) multiplication of imaginary octonians. On this 6-sphere, there is a family of psuedo-holomorphic $\mathbb{C}\mathbb{P}^1$ parameterised by the associative Grassmannian, where the associative Grassmaniann is an 8-dimensional quaternion Kaehler manifold defined as the set of associative 3-planes in the 7-dimensional real vector space of the imaginary octonians. In the talk, we show that this story is quite analogous to the Penrose's twistor correspondence and that the geometric structures on the associative Grassmaniann nicely fit to this construction. This is a joint work with H. Hashimoto, K. Mashimo and M. Ohashi.
Algebraic Geometry Seminar
15:30-17:00 Room #122 (Graduate School of Math. Sci. Bldg.)
Atsushi Kanazawa (Harvard)
Extending Hori-Vafa toric mirror symmetry via SYZ and modular forms (English)
Atsushi Kanazawa (Harvard)
Extending Hori-Vafa toric mirror symmetry via SYZ and modular forms (English)
[ Abstract ]
In this talk, I will introduce partial compactification for a class of toric Calabi-Yau manifolds. A fundamental question is how the Hori-Vafa toric mirror symmetry extends to this new class of Calabi-Yau manifolds. The answer leads us to a new connection between SYZ mirror symmetry and modular forms. If time permits, I will also discuss higher dimensional analogues of the Yau-Zaslow formula (for an elliptic K3 surface) in terms of Siegel modular forms. This talk is based on a joint work with Siu-Cheong Lau.
In this talk, I will introduce partial compactification for a class of toric Calabi-Yau manifolds. A fundamental question is how the Hori-Vafa toric mirror symmetry extends to this new class of Calabi-Yau manifolds. The answer leads us to a new connection between SYZ mirror symmetry and modular forms. If time permits, I will also discuss higher dimensional analogues of the Yau-Zaslow formula (for an elliptic K3 surface) in terms of Siegel modular forms. This talk is based on a joint work with Siu-Cheong Lau.
2015/12/09
Operator Algebra Seminars
16:45-18:15 Room #118 (Graduate School of Math. Sci. Bldg.)
David E. Evans (Cardiff Univ.)
K-theory in subfactors and conformal field theory
David E. Evans (Cardiff Univ.)
K-theory in subfactors and conformal field theory
Number Theory Seminar
18:00-19:00 Room #056 (Graduate School of Math. Sci. Bldg.)
Ted Chinburg (University of Pennsylvania & IHES)
Chern classes in Iwasawa theory (English)
Ted Chinburg (University of Pennsylvania & IHES)
Chern classes in Iwasawa theory (English)
[ Abstract ]
Many of the main conjectures in Iwasawa theory can be phrased as saying that the first Chern class of an Iwasawa module is generated by a p-adic L-series. In this talk I will describe how higher Chern classes pertain to the higher codimension behavior of Iwasawa modules. I'll then describe a template for conjectures which would link such higher Chern classes to elements in the K-theory of Iwasawa algebras which are constructed from tuples of Katz p-adic L-series. I will finally describe an instance in which a result of this kind, for the second Chern class of an unramified Iwasawa module, can be proved over an imaginary quadratic field. This is joint work with F. Bleher, R. Greenberg, M. Kakde, G. Pappas, R. Sharifi and M. J. Taylor.
Many of the main conjectures in Iwasawa theory can be phrased as saying that the first Chern class of an Iwasawa module is generated by a p-adic L-series. In this talk I will describe how higher Chern classes pertain to the higher codimension behavior of Iwasawa modules. I'll then describe a template for conjectures which would link such higher Chern classes to elements in the K-theory of Iwasawa algebras which are constructed from tuples of Katz p-adic L-series. I will finally describe an instance in which a result of this kind, for the second Chern class of an unramified Iwasawa module, can be proved over an imaginary quadratic field. This is joint work with F. Bleher, R. Greenberg, M. Kakde, G. Pappas, R. Sharifi and M. J. Taylor.
2015/12/08
Tuesday Seminar on Topology
17:00-18:30 Room #056 (Graduate School of Math. Sci. Bldg.)
Yuichi Yamada (The Univ. of Electro-Comm.)
Lens space surgery and Kirby calculus of 4-manifolds (JAPANESE)
Yuichi Yamada (The Univ. of Electro-Comm.)
Lens space surgery and Kirby calculus of 4-manifolds (JAPANESE)
[ Abstract ]
The problem asking "Which knot yields a lens space by Dehn surgery" is
called "lens space surgery". Berge's list ('90) is believed to be the
complete list, but it is still unproved, even after some progress by
Heegaard Floer Homology.
This problem seems to enter a new aspect: study using 4-manifolds, lens
space surgery from lens spaces, checking hyperbolicity by computer.
In the talk, we review the structure of Berge's list and talk on our
study on pairs of distinct knots but yield same lens spaces, and
4-maniolds constructed from such pairs. This is joint work with Motoo
Tange (Tsukuba University).
The problem asking "Which knot yields a lens space by Dehn surgery" is
called "lens space surgery". Berge's list ('90) is believed to be the
complete list, but it is still unproved, even after some progress by
Heegaard Floer Homology.
This problem seems to enter a new aspect: study using 4-manifolds, lens
space surgery from lens spaces, checking hyperbolicity by computer.
In the talk, we review the structure of Berge's list and talk on our
study on pairs of distinct knots but yield same lens spaces, and
4-maniolds constructed from such pairs. This is joint work with Motoo
Tange (Tsukuba University).
2015/12/07
Tokyo Probability Seminar
16:50-18:20 Room #128 (Graduate School of Math. Sci. Bldg.)
Jean-Dominique Deuschel (TU Berlin)
Quenched invariance principle for random walks in time-dependent balanced random environment
Jean-Dominique Deuschel (TU Berlin)
Quenched invariance principle for random walks in time-dependent balanced random environment
[ Abstract ]
We prove an almost sure functional limit theorem for a random walk in an space-time ergodic balanced environment under certain moment conditions. The proof is based on the maximal principle for parabolic difference operators. We also deal with the non-elliptic case, where the corresponding limiting diffusion matrix can be random in higher dimensions. This is a joint work with N. Berger, X. Guo and A. Ramirez.
We prove an almost sure functional limit theorem for a random walk in an space-time ergodic balanced environment under certain moment conditions. The proof is based on the maximal principle for parabolic difference operators. We also deal with the non-elliptic case, where the corresponding limiting diffusion matrix can be random in higher dimensions. This is a joint work with N. Berger, X. Guo and A. Ramirez.
Seminar on Geometric Complex Analysis
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Tatsuki Hayama (Senshu Univ.)
Cycle connectivity and pseudoconcavity of flag domains (Japanese)
Tatsuki Hayama (Senshu Univ.)
Cycle connectivity and pseudoconcavity of flag domains (Japanese)
[ Abstract ]
We consider an open real group orbit in a complex flag variety which has no non-constant function. We introduce Huckleberry's results on cycle connectivity and show that it is pseudoconcave if it satisfies a certain condition on the root system of the Lie algebra. In Hodge theory, we are mainly interested in the case where it is a Mumford-Tate domain. We also discuss Hodge theoretical meanings of this work.
We consider an open real group orbit in a complex flag variety which has no non-constant function. We introduce Huckleberry's results on cycle connectivity and show that it is pseudoconcave if it satisfies a certain condition on the root system of the Lie algebra. In Hodge theory, we are mainly interested in the case where it is a Mumford-Tate domain. We also discuss Hodge theoretical meanings of this work.
Algebraic Geometry Seminar
15:30-17:00 Room #122 (Graduate School of Math. Sci. Bldg.)
Alexey Bondal (IPMU)
Flops and spherical functors (English)
Alexey Bondal (IPMU)
Flops and spherical functors (English)
[ Abstract ]
I will describe various functors on derived categories of coherent sheaves
related to flops and relations between these functors. A categorical
version of deformation theory of systems of objects in abelian categories
will be outlined and its relation to flop spherical functors will be
presented.
I will describe various functors on derived categories of coherent sheaves
related to flops and relations between these functors. A categorical
version of deformation theory of systems of objects in abelian categories
will be outlined and its relation to flop spherical functors will be
presented.
2015/12/04
Colloquium
16:50-17:50 Room #123 (Graduate School of Math. Sci. Bldg.)
Makiko Sasada (Graduate School of Mathematical Sciences, University of Tokyo)
Exact forms and closed forms on some infinite product spaces appearing in the study of probability theory
(JAPANESE)
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/teacher/sasada.html
Makiko Sasada (Graduate School of Mathematical Sciences, University of Tokyo)
Exact forms and closed forms on some infinite product spaces appearing in the study of probability theory
(JAPANESE)
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/teacher/sasada.html
Geometry Colloquium
10:00-11:30 Room #126 (Graduate School of Math. Sci. Bldg.)
Yoshihiro Takeyama (Graduate School of Pure and Applied Sciences, University of Tsukuba)
The q-Boson system and a deformation of the affine Hecke algebra (Japanese)
Yoshihiro Takeyama (Graduate School of Pure and Applied Sciences, University of Tsukuba)
The q-Boson system and a deformation of the affine Hecke algebra (Japanese)
[ Abstract ]
The q-Boson system due to Sasamoto and Wadati is a one-dimensional "integrable" stochastic particle model. Its Q-matrix is constructed in the framework of the quantum inverse scattering method and we obtain the eigenvectors by means of the algebraic Bethe ansatz method. Recently it is found that the q-Boson model can be derived also from a representation of a deformation of the affine Hecke algebra and its representation. In this formulation we get the eigenvectors of the transpose of the Q-matrix which were constructed by the technique called the coordinate Bethe ansatz. In this talk I review the above results and discuss the relationship between the two methods.
The q-Boson system due to Sasamoto and Wadati is a one-dimensional "integrable" stochastic particle model. Its Q-matrix is constructed in the framework of the quantum inverse scattering method and we obtain the eigenvectors by means of the algebraic Bethe ansatz method. Recently it is found that the q-Boson model can be derived also from a representation of a deformation of the affine Hecke algebra and its representation. In this formulation we get the eigenvectors of the transpose of the Q-matrix which were constructed by the technique called the coordinate Bethe ansatz. In this talk I review the above results and discuss the relationship between the two methods.
2015/12/03
Seminar on Probability and Statistics
16:40-18:00 Room #123 (Graduate School of Math. Sci. Bldg.)
Arnak Dalalyan (ENSAE ParisTech)
Learning theory and sparsity ～ Sparsity and low rank matrix learning ～
Arnak Dalalyan (ENSAE ParisTech)
Learning theory and sparsity ～ Sparsity and low rank matrix learning ～
[ Abstract ]
In this third lecture, we will present extensions of the previously introduced sparse recovery techniques to the problems of machine learning and statistics in which a large matrix should be learned from data. The analogue of the sparsity, in this context, is the low-rankness of the matrix. We will show that such matrices can be effectively learned by minimizing the empirical risk penalized by the nuclear norm. The resulting problem is a problem of semi-definite programming and can be solved efficiently even when the dimension is large. Theoretical guarantees for this method will be established in the case of matrix completion with known sampling distribution.
In this third lecture, we will present extensions of the previously introduced sparse recovery techniques to the problems of machine learning and statistics in which a large matrix should be learned from data. The analogue of the sparsity, in this context, is the low-rankness of the matrix. We will show that such matrices can be effectively learned by minimizing the empirical risk penalized by the nuclear norm. The resulting problem is a problem of semi-definite programming and can be solved efficiently even when the dimension is large. Theoretical guarantees for this method will be established in the case of matrix completion with known sampling distribution.
FMSP Lectures
16:40-18:00 Room #123 (Graduate School of Math. Sci. Bldg.)
Arnak Dalalyan (ENSAE ParisTech)
(3)Sparsity and low rank matrix learning. (ENGLISH)
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Dalalyan.pdf
Arnak Dalalyan (ENSAE ParisTech)
(3)Sparsity and low rank matrix learning. (ENGLISH)
[ Abstract ]
In this third lecture, we will present extensions of the previously introduced sparse recovery techniques to the problems of machine learning and statistics in which a large matrix should be learned from data. The analogue of the sparsity, in this context, is the low-rankness of the matrix. We will show that such matrices can be effectively learned by minimizing the empirical risk penalized by the nuclear norm. The resulting problem is a problem of semi-definite programming and can be solved efficiently even when the dimension is large. Theoretical guarantees for this method will be established in the case of matrix completion with known sampling distribution.
[ Reference URL ]In this third lecture, we will present extensions of the previously introduced sparse recovery techniques to the problems of machine learning and statistics in which a large matrix should be learned from data. The analogue of the sparsity, in this context, is the low-rankness of the matrix. We will show that such matrices can be effectively learned by minimizing the empirical risk penalized by the nuclear norm. The resulting problem is a problem of semi-definite programming and can be solved efficiently even when the dimension is large. Theoretical guarantees for this method will be established in the case of matrix completion with known sampling distribution.
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Dalalyan.pdf
2015/12/02
Operator Algebra Seminars
16:45-18:15 Room #118 (Graduate School of Math. Sci. Bldg.)
Makoto Yamashita (Ochanomizu Univ.)
Drinfeld center and representation theory for monoidal categories
Makoto Yamashita (Ochanomizu Univ.)
Drinfeld center and representation theory for monoidal categories
Seminar on Probability and Statistics
14:55-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)
Arnak Dalalyan (ENSAE ParisTech)
Learning theory and sparsity ～ Lasso, Dantzig selector and their statistical properties ～
Arnak Dalalyan (ENSAE ParisTech)
Learning theory and sparsity ～ Lasso, Dantzig selector and their statistical properties ～
[ Abstract ]
In this second lecture, we will focus on the problem of high dimensional linear regression under the sparsity assumption and discuss the three main statistical problems: denoising, prediction and model selection. We will prove that convex programming based predictors such as the lasso and the Dantzig selector are provably consistent as soon as the dictionary elements are normalized and an appropriate upper bound on the noise-level is available. We will also show that under additional assumptions on the dictionary elements, the aforementioned methods are rate-optimal and model-selection consistent.
In this second lecture, we will focus on the problem of high dimensional linear regression under the sparsity assumption and discuss the three main statistical problems: denoising, prediction and model selection. We will prove that convex programming based predictors such as the lasso and the Dantzig selector are provably consistent as soon as the dictionary elements are normalized and an appropriate upper bound on the noise-level is available. We will also show that under additional assumptions on the dictionary elements, the aforementioned methods are rate-optimal and model-selection consistent.
FMSP Lectures
14:55-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)
Arnak Dalalyan (ENSAE ParisTech)
(2)Lasso, Dantzig selector and their statistical properties. (ENGLISH)
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Dalalyan.pdf
Arnak Dalalyan (ENSAE ParisTech)
(2)Lasso, Dantzig selector and their statistical properties. (ENGLISH)
[ Abstract ]
In this second lecture, we will focus on the problem of high dimensional linear regression under the sparsity assumption and discuss the three main statistical problems: denoising, prediction and model selection. We will prove that convex programming based predictors such as the lasso and the Dantzig selector are provably consistent as soon as the dictionary elements are normalized and an appropriate upper bound on the noise-level is available. We will also show that under additional assumptions on the dictionary elements, the aforementioned methods are rate-optimal and model-selection consistent.
[ Reference URL ]In this second lecture, we will focus on the problem of high dimensional linear regression under the sparsity assumption and discuss the three main statistical problems: denoising, prediction and model selection. We will prove that convex programming based predictors such as the lasso and the Dantzig selector are provably consistent as soon as the dictionary elements are normalized and an appropriate upper bound on the noise-level is available. We will also show that under additional assumptions on the dictionary elements, the aforementioned methods are rate-optimal and model-selection consistent.
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Dalalyan.pdf
Mathematical Biology Seminar
14:55-16:40 Room #128 (Graduate School of Math. Sci. Bldg.)
Kenta Yajima ( The Graduate University for Advanced Studies (Sokendai), School of Advanced Sciences)
Network centrality measure based on sensitivity analysis of the basic reproductive ratio
[ Reference URL ]
http://www.soken.ac.jp/
Kenta Yajima ( The Graduate University for Advanced Studies (Sokendai), School of Advanced Sciences)
Network centrality measure based on sensitivity analysis of the basic reproductive ratio
[ Reference URL ]
http://www.soken.ac.jp/
2015/12/01
Tuesday Seminar of Analysis
16:50-18:20 Room #126 (Graduate School of Math. Sci. Bldg.)
Stéphane Malek (Université de Lille, France)
On complex singularity analysis for some linear partial differential equations
Stéphane Malek (Université de Lille, France)
On complex singularity analysis for some linear partial differential equations
[ Abstract ]
We investigate the existence of local holomorphic solutions Y of linear partial differential equations in three complex variables whose coefficients are holomorphic on some polydisc outside some singular set S. The coefficients are written as linear combinations of powers of a solution X of some first order nonlinear partial differential equation following an idea :we have initiated in a previous joint work with C. Stenger. The solutions Y are shown to develop singularities along the singular set S with estimates of exponential type depending on the growth's rate of X near the singular set. We construct these solutions with the help of series of functions with infinitely many variables which involve derivatives of all orders of X in one variable. Convergence and bounds estimates of these series are studied using a majorant series method which leads to an auxiliary functional equation that contains differential operators in infinitely many variables. Using a fixed point argument, we show that these functional equations actually have solutions in some Banach spaces of formal power series. (Joint work with A. Lastra and C. Stenger).
We investigate the existence of local holomorphic solutions Y of linear partial differential equations in three complex variables whose coefficients are holomorphic on some polydisc outside some singular set S. The coefficients are written as linear combinations of powers of a solution X of some first order nonlinear partial differential equation following an idea :we have initiated in a previous joint work with C. Stenger. The solutions Y are shown to develop singularities along the singular set S with estimates of exponential type depending on the growth's rate of X near the singular set. We construct these solutions with the help of series of functions with infinitely many variables which involve derivatives of all orders of X in one variable. Convergence and bounds estimates of these series are studied using a majorant series method which leads to an auxiliary functional equation that contains differential operators in infinitely many variables. Using a fixed point argument, we show that these functional equations actually have solutions in some Banach spaces of formal power series. (Joint work with A. Lastra and C. Stenger).
Tuesday Seminar on Topology
17:00-18:30 Room #056 (Graduate School of Math. Sci. Bldg.)
Takayuki Okuda (The University of Tokyo)
Monodromies of splitting families for singular fibers (JAPANESE)
Takayuki Okuda (The University of Tokyo)
Monodromies of splitting families for singular fibers (JAPANESE)
[ Abstract ]
A degeneration of Riemann surfaces is a family of complex curves
over a disk allowed to have a singular fiber.
A singular fiber may split into several simpler singular fibers
under a deformation family of such families,
which is called a splitting family for the singular fiber.
We are interested in the topology of splitting families.
For the topological types of degenerations of Riemann surfaces,
it is known that there is a good relationship with
the surface mapping classes, via topological monodromy.
In this talk,
we introduce the "topological monodromies of splitting families",
and give a description of those of certain splitting families.
A degeneration of Riemann surfaces is a family of complex curves
over a disk allowed to have a singular fiber.
A singular fiber may split into several simpler singular fibers
under a deformation family of such families,
which is called a splitting family for the singular fiber.
We are interested in the topology of splitting families.
For the topological types of degenerations of Riemann surfaces,
it is known that there is a good relationship with
the surface mapping classes, via topological monodromy.
In this talk,
we introduce the "topological monodromies of splitting families",
and give a description of those of certain splitting families.
2015/11/30
Seminar on Geometric Complex Analysis
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Jean-Pierre Demailly (Univ. de Grenoble I)
Extension of holomorphic functions defined on non reduced analytic subvarieties (English)
Jean-Pierre Demailly (Univ. de Grenoble I)
Extension of holomorphic functions defined on non reduced analytic subvarieties (English)
[ Abstract ]
The goal of this talk will be to discuss $L^2$ extension properties of holomorphic sections of vector bundles satisfying weak semi-positivity properties. Using techniques borrowed from recent proofs of the Ohsawa-Takegoshi extension theorem, we obtain several new surjectivity results for the restriction morphism to a non necessarily reduced subvariety, provided the latter is defined as the zero variety of a multiplier ideal sheaf. These extension results are derived from $L^2$ approximation techniques, and they hold under (probably) optimal curvature conditions.
The goal of this talk will be to discuss $L^2$ extension properties of holomorphic sections of vector bundles satisfying weak semi-positivity properties. Using techniques borrowed from recent proofs of the Ohsawa-Takegoshi extension theorem, we obtain several new surjectivity results for the restriction morphism to a non necessarily reduced subvariety, provided the latter is defined as the zero variety of a multiplier ideal sheaf. These extension results are derived from $L^2$ approximation techniques, and they hold under (probably) optimal curvature conditions.
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