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過去の記録 ～04/24｜本日 04/25 | 今後の予定 04/26～
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
Błażej Szepietowski 氏 (Gdansk University)
Topological rigidity of finite cyclic group actions on compact surfaces (ENGLISH)
Tea: Common Room 16:30-17:00
Błażej Szepietowski 氏 (Gdansk University)
Topological rigidity of finite cyclic group actions on compact surfaces (ENGLISH)
[ 講演概要 ]
Two actions of a group on a surface are called topologically equivalent if they are conjugate by a homeomorphism of the surface. I will describe a method of enumeration (and classification) of topological equivalence classes of actions of a finite group on a compact surface, based on the combinatorial theory of noneuclidean crystallographic groups (NEC groups in short) and a relationship between the outer automorphism group of an NEC group and certain mapping class group. By this method we study topological equivalence of actions of a finite cyclic group on a compact surface, in the situation where the order of the group is large relative to the genus of the surface.
Two actions of a group on a surface are called topologically equivalent if they are conjugate by a homeomorphism of the surface. I will describe a method of enumeration (and classification) of topological equivalence classes of actions of a finite group on a compact surface, based on the combinatorial theory of noneuclidean crystallographic groups (NEC groups in short) and a relationship between the outer automorphism group of an NEC group and certain mapping class group. By this method we study topological equivalence of actions of a finite cyclic group on a compact surface, in the situation where the order of the group is large relative to the genus of the surface.
2016年04月18日(月)
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
Juan Orendain 氏 (UNAM/東大数理)
On the functoriality of Haagerup's $L^2$-space construction: Verticalizing decorated 2-categories
Juan Orendain 氏 (UNAM/東大数理)
On the functoriality of Haagerup's $L^2$-space construction: Verticalizing decorated 2-categories
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
小櫃 邦夫 氏 (鹿児島大学)
Weil-Petersson計量の漸近展開についての最近の進展 (JAPANESE)
小櫃 邦夫 氏 (鹿児島大学)
Weil-Petersson計量の漸近展開についての最近の進展 (JAPANESE)
[ 講演概要 ]
リーマン面のモジュライ空間上のWeil-Petersson計量の境界における漸近展開は、H. Masurが1976年に与えた結果を初めとし、その後Yamada, Wolpert, Obitsu-Wolpertによって改良された。最近、Melrose, X. Zhu, Mazzeo, Swobodaにより、その漸近展開の形が完全に決定された。彼らの仕事を紹介し、残された問題や関連する話題について解説する。
リーマン面のモジュライ空間上のWeil-Petersson計量の境界における漸近展開は、H. Masurが1976年に与えた結果を初めとし、その後Yamada, Wolpert, Obitsu-Wolpertによって改良された。最近、Melrose, X. Zhu, Mazzeo, Swobodaにより、その漸近展開の形が完全に決定された。彼らの仕事を紹介し、残された問題や関連する話題について解説する。
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
柏原崇人 氏 (東京大学大学院数理科学研究科)
滑らかな領域における有限要素法の誤差評価について (日本語)
柏原崇人 氏 (東京大学大学院数理科学研究科)
滑らかな領域における有限要素法の誤差評価について (日本語)
[ 講演概要 ]
滑らかな領域$\Omega$上の偏微分方程式を有限要素法で離散化する場合，$\Omega$をフラットな三角形で厳密に分割するのは不可能なので，$\Omega$を多角形領域$\Omega_h$で近似した上で，$\Omega_h$に対して三角形分割や有限要素空間を考えるのが一般的である．よって誤差評価を行う際には，$\Omega$と$\Omega_h$のギャップ，つまり「領域の摂動」を定量的に評価する必要が生じる．このような状況を考慮した誤差評価の結果は存在するものの，標準的な手法が体系化されているとは言えないと思われる（特に，$L^2$誤差評価に関しては驚くほど結果が少ない）．本講演では，ポアソン方程式の(1)ノイマン問題，(2)ニーチェの方法によるディリクレ問題，をモデルケースとして，「領域の摂動」を考慮した$H^1$および$L^2$誤差評価を証明する．他の方程式や境界条件への応用を見込んで，できるだけ一般的かつ標準的な証明の枠組みを提案することを目標とする．
滑らかな領域$\Omega$上の偏微分方程式を有限要素法で離散化する場合，$\Omega$をフラットな三角形で厳密に分割するのは不可能なので，$\Omega$を多角形領域$\Omega_h$で近似した上で，$\Omega_h$に対して三角形分割や有限要素空間を考えるのが一般的である．よって誤差評価を行う際には，$\Omega$と$\Omega_h$のギャップ，つまり「領域の摂動」を定量的に評価する必要が生じる．このような状況を考慮した誤差評価の結果は存在するものの，標準的な手法が体系化されているとは言えないと思われる（特に，$L^2$誤差評価に関しては驚くほど結果が少ない）．本講演では，ポアソン方程式の(1)ノイマン問題，(2)ニーチェの方法によるディリクレ問題，をモデルケースとして，「領域の摂動」を考慮した$H^1$および$L^2$誤差評価を証明する．他の方程式や境界条件への応用を見込んで，できるだけ一般的かつ標準的な証明の枠組みを提案することを目標とする．
東京確率論セミナー
16:50-18:20 数理科学研究科棟(駒場) 128号室
李 嘉衣 氏 (東京大学大学院数理科学研究科)
Sharp interface limit for one-dimensional stochastic Allen-Cahn equation with Dirichlet boundary condition
李 嘉衣 氏 (東京大学大学院数理科学研究科)
Sharp interface limit for one-dimensional stochastic Allen-Cahn equation with Dirichlet boundary condition
[ 講演概要 ]
本講演では、確率反応拡散方程式に対する鋭敏な界面極限を扱う。具体的にはディリクレ境界条件を持つ1次元確率アレン・カーン方程式を考察する。この方程式は界面の挙動を記述し、十分小さいパラメータ$\varepsilon > 0$により界面の幅が特徴付けられる。特に$\varepsilon$を限りなく小さくした時の解の挙動に興味がある。この場合、ディリクレ境界条件のため極限における界面の運動は反射壁を持つブラウン運動になることが予想される。そこで解を$L^2$-値のマルコフ過程とみなし、それに対応するディリクレ形式のモスコ収束により、極限での界面の挙動を特定する。
本講演では、確率反応拡散方程式に対する鋭敏な界面極限を扱う。具体的にはディリクレ境界条件を持つ1次元確率アレン・カーン方程式を考察する。この方程式は界面の挙動を記述し、十分小さいパラメータ$\varepsilon > 0$により界面の幅が特徴付けられる。特に$\varepsilon$を限りなく小さくした時の解の挙動に興味がある。この場合、ディリクレ境界条件のため極限における界面の運動は反射壁を持つブラウン運動になることが予想される。そこで解を$L^2$-値のマルコフ過程とみなし、それに対応するディリクレ形式のモスコ収束により、極限での界面の挙動を特定する。
2016年04月14日(木)
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(2)
Alan Weinstein 氏 (University of California, Berkeley)
Lecture 2: Geometric and algebraic Poisson modules (ENGLISH)
[ 参考URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Weinstein.pdf
全2回講演の(2)
Alan Weinstein 氏 (University of California, Berkeley)
Lecture 2: Geometric and algebraic Poisson modules (ENGLISH)
[ 参考URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Weinstein.pdf
2016年04月13日(水)
代数学コロキウム
17:30-18:30 数理科学研究科棟(駒場) 056号室
玉川安騎男 氏 (京都大学数理解析研究所)
Semisimplicity of geometric monodromy on etale cohomology (joint work with Anna Cadoret and Chun Yin Hui)
(English)
玉川安騎男 氏 (京都大学数理解析研究所)
Semisimplicity of geometric monodromy on etale cohomology (joint work with Anna Cadoret and Chun Yin Hui)
(English)
[ 講演概要 ]
Let K be a function field over an algebraically closed field of characteritic p \geq 0, X a proper smooth K-scheme, and l a prime distinct from p. Deligne proved that the Q_l-coefficient etale cohomology groups of the geometric fiber of X --> K are always semisimple as G_K-modules. In this talk, we consider a similar problem for the F_l-coefficient etale cohomology groups. Among other things, we show that if p=0 (resp. in general), they are semisimple for all but finitely many l's (resp. for all l's in a set of density 1).
(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.)
Let K be a function field over an algebraically closed field of characteritic p \geq 0, X a proper smooth K-scheme, and l a prime distinct from p. Deligne proved that the Q_l-coefficient etale cohomology groups of the geometric fiber of X --> K are always semisimple as G_K-modules. In this talk, we consider a similar problem for the F_l-coefficient etale cohomology groups. Among other things, we show that if p=0 (resp. in general), they are semisimple for all but finitely many l's (resp. for all l's in a set of density 1).
(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.)
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.
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