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過去の記録 ～07/14｜本日 07/15 | 今後の予定 07/16～
FMSPレクチャーズ
13:30-14:30 数理科学研究科棟(駒場) 126号室
Yavar Kian 氏 (Aix-Marseille Univ.)
Determination of time-dependent coefficients for wave equations from partial data (ENGLISH)
[ 参考URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Kian.pdf
Yavar Kian 氏 (Aix-Marseille Univ.)
Determination of time-dependent coefficients for wave equations from partial data (ENGLISH)
[ 参考URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Kian.pdf
2016年04月12日(火)
Lie群論・表現論セミナー
17:00-18:30 数理科学研究科棟(駒場) 128号室
Piotr Pragacz 氏 (Institute of Mathematics, Polish Academy of Sciences)
Universal Gysin formulas for flag bundles
Piotr Pragacz 氏 (Institute of Mathematics, Polish Academy of Sciences)
Universal Gysin formulas for flag bundles
[ 講演概要 ]
We give generalizations of the formula for the push-forward of a power of the hyperplane class in a projective bundle to flag bundles of type A, B, C, D. The formulas (and also the proofs) involve only the Segre classes of the original vector bundles and characteristic classes of universal bundles. This is a joint work with Lionel Darondeau.
We give generalizations of the formula for the push-forward of a power of the hyperplane class in a projective bundle to flag bundles of type A, B, C, D. The formulas (and also the proofs) involve only the Segre classes of the original vector bundles and characteristic classes of universal bundles. This is a joint work with Lionel Darondeau.
トポロジー火曜セミナー
17:00-18:30 数理科学研究科棟(駒場) 056号室
Tea: Common Room 16:30 - 17:00
Aniceto Murillo 氏 (Universidad de Malaga)
Homotopy theory of differential graded Lie algebras (ENGLISH)
Tea: Common Room 16:30 - 17:00
Aniceto Murillo 氏 (Universidad de Malaga)
Homotopy theory of differential graded Lie algebras (ENGLISH)
[ 講演概要 ]
Having as motivation the Deligne's principle by which every deformation functor is governed by a differential graded Lie algebra, we build a homotopy theory for these algebras which extend the classical Quillen approach and let us model any (non necessarily 1-connected nor path connected) complex. This is joint work with Urtzi Buijs, Yves Félix and Daniel Tanré.
Having as motivation the Deligne's principle by which every deformation functor is governed by a differential graded Lie algebra, we build a homotopy theory for these algebras which extend the classical Quillen approach and let us model any (non necessarily 1-connected nor path connected) complex. This is joint work with Urtzi Buijs, Yves Félix and Daniel Tanré.
解析学火曜セミナー
16:50-18:20 数理科学研究科棟(駒場) 126号室
Jussi Behrndt 氏 (Graz University of Technology)
Scattering matrices and Dirichlet-to-Neumann maps (English)
Jussi Behrndt 氏 (Graz University of Technology)
Scattering matrices and Dirichlet-to-Neumann maps (English)
[ 講演概要 ]
In this talk we discuss a recent result on the representation of the scattering matrix in terms of an abstract Titchmarsh-Weyl m-function. The general result can be applied to scattering problems for Schrödinger operators with $\delta$-type interactions on curves and hypersurfaces, and scattering problems involving Neumann and Robin realizations of Schrödinger operators on unbounded domains. In both applications we obtain formulas for the corresponding scattering matrices in terms of Dirichlet-to-Neumann maps. This talk is based on joint work with Mark Malamud and Hagen Neidhardt.
In this talk we discuss a recent result on the representation of the scattering matrix in terms of an abstract Titchmarsh-Weyl m-function. The general result can be applied to scattering problems for Schrödinger operators with $\delta$-type interactions on curves and hypersurfaces, and scattering problems involving Neumann and Robin realizations of Schrödinger operators on unbounded domains. In both applications we obtain formulas for the corresponding scattering matrices in terms of Dirichlet-to-Neumann maps. This talk is based on joint work with Mark Malamud and Hagen Neidhardt.
2016年04月11日(月)
代数幾何学セミナー
15:30-17:00 数理科学研究科棟(駒場) 122号室
Piotr Pragacz 氏 (Institute of Mathematics, Polish Academy of Sciences )
Gysin maps, duality and Schubert classes
(English)
https://www.impan.pl/~pragacz/main.htm
Piotr Pragacz 氏 (Institute of Mathematics, Polish Academy of Sciences )
Gysin maps, duality and Schubert classes
(English)
[ 講演概要 ]
We establish a Gysin formula for Schubert bundles
and a strong version of the duality theorem in Schubert calculus
on Grassmann bundles. We then combine them to compute the fundamental
classes of Schubert bundles in Grassmann bundles, which yields a new
proof of the Giambelli formula for vector bundles. This is a joint
work with Lionel Darondeau.
[ 参考URL ]We establish a Gysin formula for Schubert bundles
and a strong version of the duality theorem in Schubert calculus
on Grassmann bundles. We then combine them to compute the fundamental
classes of Schubert bundles in Grassmann bundles, which yields a new
proof of the Giambelli formula for vector bundles. This is a joint
work with Lionel Darondeau.
https://www.impan.pl/~pragacz/main.htm
作用素環セミナー
16:４５-18:15 数理科学研究科棟(駒場) 118号室
Ryszard Nest 氏 (Univ. Copenhagen)
On analytic construction of the group three-cocycles
(English)
Ryszard Nest 氏 (Univ. Copenhagen)
On analytic construction of the group three-cocycles
(English)
FMSPレクチャーズ
15:30-17:00 数理科学研究科棟(駒場) Lecture Hall, Kavli IPMU号室
全2回講演の(1)
Alan Weinstein 氏 (University of California, Berkeley)
Lecture 1: Special subspaces in symplectic vector spaces (ENGLISH)
[ 参考URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Weinstein.pdf
全2回講演の(1)
Alan Weinstein 氏 (University of California, Berkeley)
Lecture 1: Special subspaces in symplectic vector spaces (ENGLISH)
[ 参考URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Weinstein.pdf
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
足助 太郎 氏 (東京大学)
Defining the Julia sets on CP^2 (JAPANESE)
足助 太郎 氏 (東京大学)
Defining the Julia sets on CP^2 (JAPANESE)
[ 講演概要 ]
The Julia sets play a central role in the study of complex dynamical systems as well as Kleinian groups where they appear as limit sets. They are also known to be meaningful for complex foliations without singularities, however still not defined for singular ones. In this talk, I will discuss some expected properties of the Julia sets for singular foliations and difficulties for defining them.
The Julia sets play a central role in the study of complex dynamical systems as well as Kleinian groups where they appear as limit sets. They are also known to be meaningful for complex foliations without singularities, however still not defined for singular ones. In this talk, I will discuss some expected properties of the Julia sets for singular foliations and difficulties for defining them.
2016年04月08日(金)
談話会・数理科学講演会
15:30-16:30 数理科学研究科棟(駒場) 123号室
2016年度よりお茶&Coffee&お菓子の時間が変更になります 15:00〜15:30 (コモンルーム)
François Apery 氏 (l'IRMA à Strasbourg)
Using mathematical objects (ENGLISH)
2016年度よりお茶&Coffee&お菓子の時間が変更になります 15:00〜15:30 (コモンルーム)
François Apery 氏 (l'IRMA à Strasbourg)
Using mathematical objects (ENGLISH)
[ 講演概要 ]
Mathematical models are not only teaching tools or pieces of museum but can also have inspiring influence to discovering new truths in mathematics. Through some examples including the Boy surface we will show how models have played a major role in the emergence of new results.
Mathematical models are not only teaching tools or pieces of museum but can also have inspiring influence to discovering new truths in mathematics. Through some examples including the Boy surface we will show how models have played a major role in the emergence of new results.
2016年04月05日(火)
トポロジー火曜セミナー
17:00-18:30 数理科学研究科棟(駒場) 056号室
Tea: Common Room 16:30-17:00
北山 貴裕 氏 (東京大学大学院数理科学研究科)
Torsion invariants and representation varieties for non-positively curved cube complexes (JAPANESE)
Tea: Common Room 16:30-17:00
北山 貴裕 氏 (東京大学大学院数理科学研究科)
Torsion invariants and representation varieties for non-positively curved cube complexes (JAPANESE)
[ 講演概要 ]
Applications of torsion invariants and representation varieties have been extensively studied for 3-manifolds. Twisted Alexander polynomials are known to detect the Thurston norm and fiberedness of a 3-manifold. Ideal points of character varieties are known to detect essential surfaces in a 3-manifold in a certain extension of Culler-Shalen theory. In view of cubulation of 3-manifolds one can expect that these results naturally extend to a wider framework and, in particular, the case of virtually special cube complexes. We formulate and discuss such analogous questions for non-positively curved cube complexes.
Applications of torsion invariants and representation varieties have been extensively studied for 3-manifolds. Twisted Alexander polynomials are known to detect the Thurston norm and fiberedness of a 3-manifold. Ideal points of character varieties are known to detect essential surfaces in a 3-manifold in a certain extension of Culler-Shalen theory. In view of cubulation of 3-manifolds one can expect that these results naturally extend to a wider framework and, in particular, the case of virtually special cube complexes. We formulate and discuss such analogous questions for non-positively curved cube complexes.
2016年04月04日(月)
数値解析セミナー
16:30-18:00 数理科学研究科棟(駒場) 056号室
Eric Chung 氏 (Chinese University of Hong Kong)
Staggered discontinuous Galerkin methods for the incompressible Navier-Stokes equations (English)
Eric Chung 氏 (Chinese University of Hong Kong)
Staggered discontinuous Galerkin methods for the incompressible Navier-Stokes equations (English)
[ 講演概要 ]
In this talk, we present a staggered discontinuous Galerkin method for the approximation of the incompressible Navier-Stokes equations. Our new method combines the advantages of discontinuous Galerkin methods and staggered meshes, and results in many good properties, namely local and global conservations, optimal convergence and superconvergence through the use of a local postprocessing technique. Another key feature is that our method provides a skew-symmetric discretization of the convection term, with the aim of giving a better conservation property compared with existing discretizations. We also analyze the stability and convergence of the method. In addition, we will present some numerical results to show the performance of the proposed method.
In this talk, we present a staggered discontinuous Galerkin method for the approximation of the incompressible Navier-Stokes equations. Our new method combines the advantages of discontinuous Galerkin methods and staggered meshes, and results in many good properties, namely local and global conservations, optimal convergence and superconvergence through the use of a local postprocessing technique. Another key feature is that our method provides a skew-symmetric discretization of the convection term, with the aim of giving a better conservation property compared with existing discretizations. We also analyze the stability and convergence of the method. In addition, we will present some numerical results to show the performance of the proposed method.
2016年03月29日(火)
代数学コロキウム
17:30-18:30 数理科学研究科棟(駒場) 002号室
曜日・部屋がいつもと異なりますのでご注意ください．
Matthew Morrow 氏 (Universität Bonn)
Motivic cohomology of formal schemes in characteristic p
(English)
曜日・部屋がいつもと異なりますのでご注意ください．
Matthew Morrow 氏 (Universität Bonn)
Motivic cohomology of formal schemes in characteristic p
(English)
[ 講演概要 ]
The logarithmic Hodge-Witt sheaves of Illusie, Milne, Kato, et al. of a smooth variety in characteristic p provide a concrete realisation of its p-adic motivic cohomology, thanks to results of Geisser-Levine and Bloch-Kato-Gabber which link them to algebraic K-theory. I will explain an analogous theory for formal schemes, as well as applications to algebraic cycles, such as a weak Lefschetz theorem for formal Chow groups.
(本講演は「東京北京パリ数論幾何セミナー」として, インターネットによる東大数理, Morningside Center of MathematicsとIHESの双方向同時中継で行います.)
The logarithmic Hodge-Witt sheaves of Illusie, Milne, Kato, et al. of a smooth variety in characteristic p provide a concrete realisation of its p-adic motivic cohomology, thanks to results of Geisser-Levine and Bloch-Kato-Gabber which link them to algebraic K-theory. I will explain an analogous theory for formal schemes, as well as applications to algebraic cycles, such as a weak Lefschetz theorem for formal Chow groups.
(本講演は「東京北京パリ数論幾何セミナー」として, インターネットによる東大数理, Morningside Center of MathematicsとIHESの双方向同時中継で行います.)
2016年03月22日(火)
談話会・数理科学講演会
16:50-17:50 数理科学研究科棟(駒場) 大講義室号室
お茶会の場所はいつもと異なる、大講義室前ホワイエです。
石井志保子 氏 (東京大学大学院数理科学研究科)
Singularities and Jet schemes (JAPANESE)
http://faculty.ms.u-tokyo.ac.jp/~shihoko/
お茶会の場所はいつもと異なる、大講義室前ホワイエです。
石井志保子 氏 (東京大学大学院数理科学研究科)
Singularities and Jet schemes (JAPANESE)
[ 講演概要 ]
特異点を記述するためにいろいろな不変数が考えられていますがその中で比較的最近登場した Mather-Jacobian discrepancy と，特異点の上の jet schemes の関係を先ず紹介します．
この関係は多様体の基礎体の標数が０の場合には，このdiscrepancy 導入当初から知られており，
正標数の場合には最近証明されました．
これにより，特異点解消の存在がまだ証明されていない正標数の体上の特異点についても jet schemes を用いて
研究が進むことが期待されます．
本講演では，低次元の場合にそれがうまく機能することを紹介し，任意次元で機能するための課題を紹介します．
[ 参考URL ]特異点を記述するためにいろいろな不変数が考えられていますがその中で比較的最近登場した Mather-Jacobian discrepancy と，特異点の上の jet schemes の関係を先ず紹介します．
この関係は多様体の基礎体の標数が０の場合には，このdiscrepancy 導入当初から知られており，
正標数の場合には最近証明されました．
これにより，特異点解消の存在がまだ証明されていない正標数の体上の特異点についても jet schemes を用いて
研究が進むことが期待されます．
本講演では，低次元の場合にそれがうまく機能することを紹介し，任意次元で機能するための課題を紹介します．
http://faculty.ms.u-tokyo.ac.jp/~shihoko/
FMSPレクチャーズ
10:00-11:00 数理科学研究科棟(駒場) 118号室
Fatiha Alabau 氏 (Université de Lorraine)
Control and stabilization of degenerate wave equations (ENGLISH)
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Alabau.pdf
Fatiha Alabau 氏 (Université de Lorraine)
Control and stabilization of degenerate wave equations (ENGLISH)
[ 講演概要 ]
The control of degenerate PDE's arise in many applications such as cloaking, climatology, population genetics, and vision.
For such models, the diffusion operator degenerates on some subset of the spatial domain. We present some recent results on observability, control and stabilization of these equations.
This is a joint work with Piermarco Cannarsa (University di Roma Tor Vergata, Italy) and G\"unter Leugering (Friedrich-Alexander-Universit\"at Erlangen-N\"urnberg, Erlangen, Germany).
[ 参考URL ]The control of degenerate PDE's arise in many applications such as cloaking, climatology, population genetics, and vision.
For such models, the diffusion operator degenerates on some subset of the spatial domain. We present some recent results on observability, control and stabilization of these equations.
This is a joint work with Piermarco Cannarsa (University di Roma Tor Vergata, Italy) and G\"unter Leugering (Friedrich-Alexander-Universit\"at Erlangen-N\"urnberg, Erlangen, Germany).
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Alabau.pdf
FMSPレクチャーズ
11:00-12:00 数理科学研究科棟(駒場) 118号室
Mourad Bellassoued 氏 (Université de Tunis El Manar)
Stable determination of coefficients in the dynamical Schrödinger equation in a magnetic field (ENGLISH)
[ 参考URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Bellassoued.pdf
Mourad Bellassoued 氏 (Université de Tunis El Manar)
Stable determination of coefficients in the dynamical Schrödinger equation in a magnetic field (ENGLISH)
[ 参考URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Bellassoued.pdf
2016年03月19日(土)
FMSPレクチャーズ
11:00-12:00 数理科学研究科棟(駒場) 370号室
Oleg Emanouilov 氏 (Colorado State Univ.)
About the Landis conjecture (ENGLISH)
[ 参考URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Emanouilov160319.pdf
Oleg Emanouilov 氏 (Colorado State Univ.)
About the Landis conjecture (ENGLISH)
[ 参考URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Emanouilov160319.pdf
2016年03月18日(金)
FMSPレクチャーズ
14:30-15:30 数理科学研究科棟(駒場) 118号室
Piermarco Cannarsa 氏 (Università degli Studi di Roma Tor Vergata)
Control of degenerate parabolic equations: old and new (ENGLISH)
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Cannarsa.pdf
Piermarco Cannarsa 氏 (Università degli Studi di Roma Tor Vergata)
Control of degenerate parabolic equations: old and new (ENGLISH)
[ 講演概要 ]
This talk will survey the main results obtained in the last fifteen years or so for the null controllability of degenerate parabolic operators.
We shall describe the state of the art for operators which degenerate at the boundary as well as for certain classes of interior degeneracy of hypoelliptic type.
[ 参考URL ]This talk will survey the main results obtained in the last fifteen years or so for the null controllability of degenerate parabolic operators.
We shall describe the state of the art for operators which degenerate at the boundary as well as for certain classes of interior degeneracy of hypoelliptic type.
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Cannarsa.pdf
2016年03月16日(水)
PDE実解析研究会
16:00-17:00 数理科学研究科棟(駒場) 056号室
通常の曜日、時刻と異なります。
Boris Khesin 氏 (University of Toronto)
Fluids, vortex membranes, and skew-mean-curvature flows (English)
通常の曜日、時刻と異なります。
Boris Khesin 氏 (University of Toronto)
Fluids, vortex membranes, and skew-mean-curvature flows (English)
[ 講演概要 ]
We show that an approximation of the hydrodynamical Euler equation describes the skew-mean-curvature flow on vortex membranes in any dimension. This generalizes the classical binormal, or vortex filament, equation in 3D. We present a Hamiltonian framework for dynamics of higher-dimensional vortex filaments and vortex sheets as singular 2-forms (Green currents) with support of codimensions 2 and 1, respectively.
We show that an approximation of the hydrodynamical Euler equation describes the skew-mean-curvature flow on vortex membranes in any dimension. This generalizes the classical binormal, or vortex filament, equation in 3D. We present a Hamiltonian framework for dynamics of higher-dimensional vortex filaments and vortex sheets as singular 2-forms (Green currents) with support of codimensions 2 and 1, respectively.
2016年03月11日(金)
作用素環セミナー
16:45-18:15 数理科学研究科棟(駒場) 118号室
Bas Jordans 氏 (Univ. Oslo)
Convergence to the boundary for random walks on discrete quantum groups
(English)
Bas Jordans 氏 (Univ. Oslo)
Convergence to the boundary for random walks on discrete quantum groups
(English)
2016年03月08日(火)
作用素環セミナー
16:45-18:15 数理科学研究科棟(駒場) 118号室
Roberto Longo 氏 (ローマ大学)
Equilibrium and non-equilibrium states in Conformal Field Theory (英語)
Roberto Longo 氏 (ローマ大学)
Equilibrium and non-equilibrium states in Conformal Field Theory (英語)
2016年02月22日(月)
FMSPレクチャーズ
17:00-18:00 数理科学研究科棟(駒場) 118号室
Michel Cristofol 氏 (Aix-Marseille Univ.)
Inverse problems for parabolic operators : comparison of three different approaches (ENGLISH)
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Cristofol.pdf
Michel Cristofol 氏 (Aix-Marseille Univ.)
Inverse problems for parabolic operators : comparison of three different approaches (ENGLISH)
[ 講演概要 ]
Basing my talk around a toy problem : reconstruction of the potential for a linear parabolic problem, I will recall the two main classical following methods : Dirichlet to Neumann map and Carleman estimates. Then I will present a different and recent approach based on pointwise observations and I will underline some points to be improved for each method. Then, I will finish my talk by a review of some results related to this technic of pointwise observations.
[ 参考URL ]Basing my talk around a toy problem : reconstruction of the potential for a linear parabolic problem, I will recall the two main classical following methods : Dirichlet to Neumann map and Carleman estimates. Then I will present a different and recent approach based on pointwise observations and I will underline some points to be improved for each method. Then, I will finish my talk by a review of some results related to this technic of pointwise observations.
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Cristofol.pdf
2016年02月19日(金)
FMSPレクチャーズ
10:30-11:30 数理科学研究科棟(駒場) 118号室
Olivier Poisson 氏 (Aix-Marseille University)
Recovering time-dependent inclusion in heat conductive bodies by a dynamical probe method (ENGLISH)
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Poisson.pdf
Olivier Poisson 氏 (Aix-Marseille University)
Recovering time-dependent inclusion in heat conductive bodies by a dynamical probe method (ENGLISH)
[ 講演概要 ]
Many articles solve a version of the Calder'on inverse problem for the heat equation. The biggest part of them assume that the unknown conductivity do not depend on time t. But they are very few results concerning the time de- pendent situation, and they are based on the computation of an ansatz for the parabolic equation:
- A reconstruction method of an unknown moving inclusion by a dynamical probe method was performed by Daido-Kang-Nakamura in 2007, but it works for the one dimensional spatial space only,
- An energy estimate for x-multidimensional convex inclusions.
In the talk I will present a dynamical probe method based on special fundamental solutions of the heat equation and basic inequalities :
this approach is very close to the probe method for the elliptic Calderon inverse problem, and does not require regularity of the inclusion.
[ 参考URL ]Many articles solve a version of the Calder'on inverse problem for the heat equation. The biggest part of them assume that the unknown conductivity do not depend on time t. But they are very few results concerning the time de- pendent situation, and they are based on the computation of an ansatz for the parabolic equation:
- A reconstruction method of an unknown moving inclusion by a dynamical probe method was performed by Daido-Kang-Nakamura in 2007, but it works for the one dimensional spatial space only,
- An energy estimate for x-multidimensional convex inclusions.
In the talk I will present a dynamical probe method based on special fundamental solutions of the heat equation and basic inequalities :
this approach is very close to the probe method for the elliptic Calderon inverse problem, and does not require regularity of the inclusion.
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Poisson.pdf
2016年02月18日(木)
FMSPレクチャーズ
10:00-11:00 数理科学研究科棟(駒場) 002号室
This lecture will be given as part of “Workshop on L^2 Extension Theorems”.
Dror Varolin 氏 (Stony Brook)
L^2 Extension and its applications: A survey (3) (ENGLISH)
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Varolin.pdf
This lecture will be given as part of “Workshop on L^2 Extension Theorems”.
Dror Varolin 氏 (Stony Brook)
L^2 Extension and its applications: A survey (3) (ENGLISH)
[ 講演概要 ]
We discuss certain aspects of the theory of L^2 extension, going back to the famous and fundamental work of Ohsawa and Takegoshi, and even further back to work of Donnelly and Fefferman.
The first of three lectures will recall a number of L^2 extension theorems, to some extent following an incomplete history (as I see it), and ending with a sketch of a proof of one of these theorems.
The second lecture will discuss a number of my favorite applications of L^2 extension, from Bergman kernels to deformation invariance of plurigenera.
The third lecture will discuss a new proof of the extension theorem, due to Berndtsson and Lempert. The key tool is a theorem of Berndtsson on the positivity of direct images, which we will review. Berndtsson's theorem permits the introduction of degeneration techniques, whose surprising application to L^2 extension represents one of the most beautiful and fundamental recent breakthroughs in the subject.
[ 参考URL ]We discuss certain aspects of the theory of L^2 extension, going back to the famous and fundamental work of Ohsawa and Takegoshi, and even further back to work of Donnelly and Fefferman.
The first of three lectures will recall a number of L^2 extension theorems, to some extent following an incomplete history (as I see it), and ending with a sketch of a proof of one of these theorems.
The second lecture will discuss a number of my favorite applications of L^2 extension, from Bergman kernels to deformation invariance of plurigenera.
The third lecture will discuss a new proof of the extension theorem, due to Berndtsson and Lempert. The key tool is a theorem of Berndtsson on the positivity of direct images, which we will review. Berndtsson's theorem permits the introduction of degeneration techniques, whose surprising application to L^2 extension represents one of the most beautiful and fundamental recent breakthroughs in the subject.
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Varolin.pdf
FMSPレクチャーズ
10:30-11:30 数理科学研究科棟(駒場) 118号室
Michel Cristofol 氏 (Aix-Marseille Univ.)
Inverse boundary value problem for a hyperbolic equation in an infinite guide (ENGLISH)
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Cristofol.pdf
Michel Cristofol 氏 (Aix-Marseille Univ.)
Inverse boundary value problem for a hyperbolic equation in an infinite guide (ENGLISH)
[ 講演概要 ]
We consider the multidimensional inverse problem of determining the conductivity coefficient of a hyperbolic equation in an infinite cylindrical domain, from a single boundary observation of the solution. We prove Holder stability with the aid of a Carleman estimate specially designed for hyperbolic waveguides. I will provide numerical simulations in multiple backgrounds.
[ 参考URL ]We consider the multidimensional inverse problem of determining the conductivity coefficient of a hyperbolic equation in an infinite cylindrical domain, from a single boundary observation of the solution. We prove Holder stability with the aid of a Carleman estimate specially designed for hyperbolic waveguides. I will provide numerical simulations in multiple backgrounds.
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Cristofol.pdf
2016年02月17日(水)
FMSPレクチャーズ
10:00-11:00 数理科学研究科棟(駒場) 002号室
This lecture will be given as part of “Workshop on L^2 Extension Theorems”.
Dror Varolin 氏 (Stony Brook)
L^2 Extension and its applications: A survey (2) (ENGLISH)
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Varolin.pdf
This lecture will be given as part of “Workshop on L^2 Extension Theorems”.
Dror Varolin 氏 (Stony Brook)
L^2 Extension and its applications: A survey (2) (ENGLISH)
[ 講演概要 ]
We discuss certain aspects of the theory of L^2 extension, going back to the famous and fundamental work of Ohsawa and Takegoshi, and even further back to work of Donnelly and Fefferman.
The first of three lectures will recall a number of L^2 extension theorems, to some extent following an incomplete history (as I see it), and ending with a sketch of a proof of one of these theorems.
The second lecture will discuss a number of my favorite applications of L^2 extension, from Bergman kernels to deformation invariance of plurigenera.
The third lecture will discuss a new proof of the extension theorem, due to Berndtsson and Lempert. The key tool is a theorem of Berndtsson on the positivity of direct images, which we will review. Berndtsson's theorem permits the introduction of degeneration techniques, whose surprising application to L^2 extension represents one of the most beautiful and fundamental recent breakthroughs in the subject.
[ 参考URL ]We discuss certain aspects of the theory of L^2 extension, going back to the famous and fundamental work of Ohsawa and Takegoshi, and even further back to work of Donnelly and Fefferman.
The first of three lectures will recall a number of L^2 extension theorems, to some extent following an incomplete history (as I see it), and ending with a sketch of a proof of one of these theorems.
The second lecture will discuss a number of my favorite applications of L^2 extension, from Bergman kernels to deformation invariance of plurigenera.
The third lecture will discuss a new proof of the extension theorem, due to Berndtsson and Lempert. The key tool is a theorem of Berndtsson on the positivity of direct images, which we will review. Berndtsson's theorem permits the introduction of degeneration techniques, whose surprising application to L^2 extension represents one of the most beautiful and fundamental recent breakthroughs in the subject.
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Varolin.pdf
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