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過去の記録 ～04/24｜本日 04/25 | 今後の予定 04/26～
2019年10月15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
Gwénaël Massuyeau 氏 (Université de Bourgogne)
Generalized Dehn twists on surfaces and surgeries in 3-manifolds (ENGLISH)
Tea: Common Room 16:30-17:00
Gwénaël Massuyeau 氏 (Université de Bourgogne)
Generalized Dehn twists on surfaces and surgeries in 3-manifolds (ENGLISH)
[ 講演概要 ]
(Joint work with Yusuke Kuno.) Given an oriented surface S and a simple closed curve C in S, the "Dehn twist" along C is the homeomorphism of S defined by "twisting" S around C by a full twist. If the curve C is not simple, this transformation of S does not make sense anymore, but one can consider two possible generalizations: one possibility is to use the homotopy intersection form of S to "simulate" the action of a Dehn twist on the (Malcev completion of) the fundamental group of S; another possibility is to view C as a curve on the top boundary of the cylinder S×[0,1], to push it arbitrarily into the interior so as to obtain, by surgery along the resulting knot, a new 3-manifold. In this talk, we will relate two those possible generalizations of a Dehn twist and we will give explicit formulas using a "symplectic expansion" of the fundamental group of S.
(Joint work with Yusuke Kuno.) Given an oriented surface S and a simple closed curve C in S, the "Dehn twist" along C is the homeomorphism of S defined by "twisting" S around C by a full twist. If the curve C is not simple, this transformation of S does not make sense anymore, but one can consider two possible generalizations: one possibility is to use the homotopy intersection form of S to "simulate" the action of a Dehn twist on the (Malcev completion of) the fundamental group of S; another possibility is to view C as a curve on the top boundary of the cylinder S×[0,1], to push it arbitrarily into the interior so as to obtain, by surgery along the resulting knot, a new 3-manifold. In this talk, we will relate two those possible generalizations of a Dehn twist and we will give explicit formulas using a "symplectic expansion" of the fundamental group of S.
2019年10月10日(木)
情報数学セミナー
16:50-18:35 数理科学研究科棟(駒場) 122号室
AIと量子計算（暗号理論を含む）を主題とする
高島 克幸 氏 (三菱電機/九州大学)
同種写像に基づく耐量子計算機暗号技術 (Japanese)
AIと量子計算（暗号理論を含む）を主題とする
高島 克幸 氏 (三菱電機/九州大学)
同種写像に基づく耐量子計算機暗号技術 (Japanese)
[ 講演概要 ]
大規模な量子コンピュータが出現すれば，これまで広く使われてきた公開鍵暗号が破られる危険性が指摘されている．それに対する対策として，量子コンピュータでも効率的に解けない数学問題の困難性に基づいて，新しい暗号を提案する動きが活発化している．それらは，耐量子計算機暗号と呼ばれるが，格子，符号，多変数多項式，同種写像などといったそれぞれ異なる数学問題の計算困難性をよりどころにした方式が知られている．本講演では，その動向の概略と共に，私が主に取り組んでいる同種写像暗号について説明する．特にSIDH鍵共有と種数1,2のCGLハッシュ関数を紹介する．
大規模な量子コンピュータが出現すれば，これまで広く使われてきた公開鍵暗号が破られる危険性が指摘されている．それに対する対策として，量子コンピュータでも効率的に解けない数学問題の困難性に基づいて，新しい暗号を提案する動きが活発化している．それらは，耐量子計算機暗号と呼ばれるが，格子，符号，多変数多項式，同種写像などといったそれぞれ異なる数学問題の計算困難性をよりどころにした方式が知られている．本講演では，その動向の概略と共に，私が主に取り組んでいる同種写像暗号について説明する．特にSIDH鍵共有と種数1,2のCGLハッシュ関数を紹介する．
FMSPレクチャーズ
13:00-15:05 数理科学研究科棟(駒場) 002号室
全6回：9/26～10/31の毎週（木）13:00-15:05
Chung-jun Tsai 氏 (National Taiwan University)
Topic on minimal submanifolds (3/6) (ENGLISH)
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Tsai.pdf
全6回：9/26～10/31の毎週（木）13:00-15:05
Chung-jun Tsai 氏 (National Taiwan University)
Topic on minimal submanifolds (3/6) (ENGLISH)
[ 講演概要 ]
The main theme of these lectures will be theory about minimal submanifolds, which are higher dimensional generalizations of geodesics. A naive motivation is that one tries to understand the geometry from its special submanifolds (minimal, etc.).
For minimal submanifolds, the equations are no longer ODEs, but elliptic PDEs. This increases the difficulties. The study are very good examples for the application of methods from PDEs and calculus of variations. We will try to explain some important results in this theory, which stimulate many of the researches today.
Here are some specific materials we plan to cover: Simon’s work based on the second variational formula, Sacks - Uhlenback theorem on the existence of minimal 2-spheres, the theory of stable minimal hypersurfaces by Schoen-Simon-Yau.
[ 参考URL ]The main theme of these lectures will be theory about minimal submanifolds, which are higher dimensional generalizations of geodesics. A naive motivation is that one tries to understand the geometry from its special submanifolds (minimal, etc.).
For minimal submanifolds, the equations are no longer ODEs, but elliptic PDEs. This increases the difficulties. The study are very good examples for the application of methods from PDEs and calculus of variations. We will try to explain some important results in this theory, which stimulate many of the researches today.
Here are some specific materials we plan to cover: Simon’s work based on the second variational formula, Sacks - Uhlenback theorem on the existence of minimal 2-spheres, the theory of stable minimal hypersurfaces by Schoen-Simon-Yau.
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Tsai.pdf
離散数理モデリングセミナー
17:00-18:00 数理科学研究科棟(駒場) 056号室
Boris Konopelchenko 氏 (INFN, sezione di Lecce, Lecce, Italy)
Universal parabolic regularization of gradient catastrophes for the Burgers-Hopf equation and singularities of the plane into plane mappings of parabolic type (English)
Boris Konopelchenko 氏 (INFN, sezione di Lecce, Lecce, Italy)
Universal parabolic regularization of gradient catastrophes for the Burgers-Hopf equation and singularities of the plane into plane mappings of parabolic type (English)
[ 講演概要 ]
Two intimately connected topics, namely, regularization of gradient catastrophes of all orders for the Burgers-Hopf equation via the Jordan chain and the singularities of the plane into plane mappings
associated with two-component hydrodynamic type systems of parabolic type are discussed.
It is shown that the regularization of all gradient catastrophes (generic and higher orders) for the Burgers-Hopf equation is achieved by the step by step embedding of the Burgers-Hopf equation into multi-component parabolic systems of quasilinear PDEs with the most degenerate Jordan blocks. Infinite parabolic Jordan chain provides us with the complete regularization. This chain contains Burgers and KdV equations as particular reductions.
It is demonstrated that the singularities of the plane into planes mappings associated with the two-component system of quasilinear PDEs of parabolic type are quite different from those in hyperbolic and elliptic cases. Impediments arising in the application of the original Whitney's approach to such case are discussed. It is shown that flex is the lowest singularity while higher singularities are given by ( k+1,k+2) curves which are of cusp type for k=2n+1, n=1,2,...,. Regularization of these singularities is discussed.
Presentation is based on two publications:
1. B. Konopelchenko and G. Ortenzi, Parabolic regularization of the gradient catastrophes for the Burgers-Hopf equation and Jordan chain, J. Phys. A: Math. Theor., 51 (2018) 275201.
2. B.G. Konopelchenko and G. Ortenzi, On the plane into plane mappings of hydrodynamic type. Parabolic case. Rev. Math. Phys.,32 (2020) 2020006. Online access. arXiv:1904.00901.
Two intimately connected topics, namely, regularization of gradient catastrophes of all orders for the Burgers-Hopf equation via the Jordan chain and the singularities of the plane into plane mappings
associated with two-component hydrodynamic type systems of parabolic type are discussed.
It is shown that the regularization of all gradient catastrophes (generic and higher orders) for the Burgers-Hopf equation is achieved by the step by step embedding of the Burgers-Hopf equation into multi-component parabolic systems of quasilinear PDEs with the most degenerate Jordan blocks. Infinite parabolic Jordan chain provides us with the complete regularization. This chain contains Burgers and KdV equations as particular reductions.
It is demonstrated that the singularities of the plane into planes mappings associated with the two-component system of quasilinear PDEs of parabolic type are quite different from those in hyperbolic and elliptic cases. Impediments arising in the application of the original Whitney's approach to such case are discussed. It is shown that flex is the lowest singularity while higher singularities are given by ( k+1,k+2) curves which are of cusp type for k=2n+1, n=1,2,...,. Regularization of these singularities is discussed.
Presentation is based on two publications:
1. B. Konopelchenko and G. Ortenzi, Parabolic regularization of the gradient catastrophes for the Burgers-Hopf equation and Jordan chain, J. Phys. A: Math. Theor., 51 (2018) 275201.
2. B.G. Konopelchenko and G. Ortenzi, On the plane into plane mappings of hydrodynamic type. Parabolic case. Rev. Math. Phys.,32 (2020) 2020006. Online access. arXiv:1904.00901.
2019年10月09日(水)
作用素環セミナー
16:45-18:15 数理科学研究科棟(駒場) 126号室
窪田陽介 氏 (理研)
Relative K-homology group of $C^*$-algebras and almost flat vector bundle on manifolds with boundary
窪田陽介 氏 (理研)
Relative K-homology group of $C^*$-algebras and almost flat vector bundle on manifolds with boundary
代数学コロキウム
17:00-18:00 数理科学研究科棟(駒場) 056号室
Yuanqing Cai 氏 (京都大学)
Twisted doubling integrals for classical groups (ENGLISH)
Yuanqing Cai 氏 (京都大学)
Twisted doubling integrals for classical groups (ENGLISH)
[ 講演概要 ]
In the 1980s, Piatetski-Shapiro and Rallis discovered a family of Rankin-Selberg integrals for the classical groups that did not rely on Whittaker models. This is the so-called doubling method. It grew out of Rallis' work on the inner products of theta lifts -- the Rallis inner product formula.
In this talk, we present a family of Rankin-Selberg integrals (the twisted doubling method, in joint work with Friedberg, Ginzburg, and Kaplan) for the tensor product L-function of a pair of automorphic cuspidal representations, one of a classical group, the other of a general linear group. This can be viewed as a generalization of the doubling integrals of Piatetski-Shapiro and Rallis. Time permitting, we will discuss the twisted doubling integrals for Brylinski-Deligne covers of classical groups.
In the 1980s, Piatetski-Shapiro and Rallis discovered a family of Rankin-Selberg integrals for the classical groups that did not rely on Whittaker models. This is the so-called doubling method. It grew out of Rallis' work on the inner products of theta lifts -- the Rallis inner product formula.
In this talk, we present a family of Rankin-Selberg integrals (the twisted doubling method, in joint work with Friedberg, Ginzburg, and Kaplan) for the tensor product L-function of a pair of automorphic cuspidal representations, one of a classical group, the other of a general linear group. This can be viewed as a generalization of the doubling integrals of Piatetski-Shapiro and Rallis. Time permitting, we will discuss the twisted doubling integrals for Brylinski-Deligne covers of classical groups.
2019年10月08日(火)
トポロジー火曜セミナー
17:30-18:30 数理科学研究科棟(駒場) 056号室
Tea: Common Room 17:00-17:30
塚本 真輝 氏 (九州大学)
いかにして双曲的力学系を群作用に拡張するか？ (JAPANESE)
Tea: Common Room 17:00-17:30
塚本 真輝 氏 (九州大学)
いかにして双曲的力学系を群作用に拡張するか？ (JAPANESE)
[ 講演概要 ]
双曲性は通常の力学系（1パラメータ群作用の研究）において最も基本的な重要性を持つ概念です．それは，十分な豊かさ（拡大性や正エントロピー）を持ちながらも，同時に制御可能（安定性や適切な意味での良い測度の一意性）な力学系の例を与えます．ではこれを群作用に拡張できるでしょうか？
ナイーブには困難です．例えば $Z^2$ の作用を考えましょう（つまり可換な 2 パラメータ作用）・簡単にわかるのは，有限次元のコンパクト多様体に $Z^2$ が可微分に作用するとき，その $Z^2$ 作用としてのエントロピーはゼロになります．つまり，通常の有限次元の状況には，豊かな $Z^2$ 作用は存在しません．言い換えると，十分に豊かな群作用を得るためには無限次元の世界に行かざるを得ません．しかし，無限次元の世界でどのような構造を見出せばよいのでしょうか？
この講演では，このような方向性にアプローチする際に，平均次元と呼ばれる量が大きな役割を果たす可能性を説明します．特に，次のような原理についてお話します：
$Z^k$（可換な $k$ パラメータ群）が空間 $X$ に何らかの「双曲性」を持って作用するとき，$Z^k$ のランク $k-1$ の部分群 $G$ の部分作用に対する平均次元が制御できる．
この講演はTom Meyerovitch，篠田万穂との共同研究に基づきます．
双曲性は通常の力学系（1パラメータ群作用の研究）において最も基本的な重要性を持つ概念です．それは，十分な豊かさ（拡大性や正エントロピー）を持ちながらも，同時に制御可能（安定性や適切な意味での良い測度の一意性）な力学系の例を与えます．ではこれを群作用に拡張できるでしょうか？
ナイーブには困難です．例えば $Z^2$ の作用を考えましょう（つまり可換な 2 パラメータ作用）・簡単にわかるのは，有限次元のコンパクト多様体に $Z^2$ が可微分に作用するとき，その $Z^2$ 作用としてのエントロピーはゼロになります．つまり，通常の有限次元の状況には，豊かな $Z^2$ 作用は存在しません．言い換えると，十分に豊かな群作用を得るためには無限次元の世界に行かざるを得ません．しかし，無限次元の世界でどのような構造を見出せばよいのでしょうか？
この講演では，このような方向性にアプローチする際に，平均次元と呼ばれる量が大きな役割を果たす可能性を説明します．特に，次のような原理についてお話します：
$Z^k$（可換な $k$ パラメータ群）が空間 $X$ に何らかの「双曲性」を持って作用するとき，$Z^k$ のランク $k-1$ の部分群 $G$ の部分作用に対する平均次元が制御できる．
この講演はTom Meyerovitch，篠田万穂との共同研究に基づきます．
2019年10月07日(月)
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
千葉 優作 氏 (お茶の水女子大学)
Cohomology of vector bundles and non-pluriharmonic loci (Japanese)
千葉 優作 氏 (お茶の水女子大学)
Cohomology of vector bundles and non-pluriharmonic loci (Japanese)
[ 講演概要 ]
We study cohomology groups of vector bundles on neighborhoods of a non-pluriharmonic locus in Stein manifolds and in projective manifolds. By using our results, we show variants of the Lefschetz hyperplane theorem. We especially study the examples of non-pluriharmonic loci in smooth toric varieties. I would like to explain the relation of non-pluriharmonic loci and polytopes.
We study cohomology groups of vector bundles on neighborhoods of a non-pluriharmonic locus in Stein manifolds and in projective manifolds. By using our results, we show variants of the Lefschetz hyperplane theorem. We especially study the examples of non-pluriharmonic loci in smooth toric varieties. I would like to explain the relation of non-pluriharmonic loci and polytopes.
2019年10月04日(金)
離散数理モデリングセミナー
17:30-18:30 数理科学研究科棟(駒場) 118号室
Anton Dzhamay 氏 (University of Northern Colorado)
Recurrence coefficients for discrete orthogonal polynomials with hypergeometric weight and discrete Painlevé equations (English)
Anton Dzhamay 氏 (University of Northern Colorado)
Recurrence coefficients for discrete orthogonal polynomials with hypergeometric weight and discrete Painlevé equations (English)
[ 講演概要 ]
Over the last decade it became clear that the role of discrete Painlevé equations in applications has been steadily growing. Thus, the question of recognizing a certain non-autonomous recurrence as a discrete Painlevé equation and understanding its position in Sakai’s classification scheme, recognizing whether it is equivalent to some known (model) example, and especially finding an explicit change of coordinates transforming it to such example, becomes one of the central ones. Fortunately, Sakai’s geometric theory provides an almost algorithmic procedure of answering this question.
In this work we illustrate this procedure by studying an example coming from the theory of discrete orthogonal polynomials. There are many connections between orthogonal polynomials and Painlevé equations, both differential and discrete. In particular, often the coefficients of three-term recurrence relations for orthogonal polynomials can be expressed in terms of solutions of some discrete Painlevé equation. In this work we study orthogonal polynomials with general hypergeometric weight and show that their recurrence coefficients satisfy, after some change of variables, the standard discrete Painlevé-V equation. We also provide an explicit change of variables transforming this equation to the standard form.
This is joint work with Galina Filipuk (University of Warsaw, Poland) and Alexander Stokes (University College, London, UK)
Over the last decade it became clear that the role of discrete Painlevé equations in applications has been steadily growing. Thus, the question of recognizing a certain non-autonomous recurrence as a discrete Painlevé equation and understanding its position in Sakai’s classification scheme, recognizing whether it is equivalent to some known (model) example, and especially finding an explicit change of coordinates transforming it to such example, becomes one of the central ones. Fortunately, Sakai’s geometric theory provides an almost algorithmic procedure of answering this question.
In this work we illustrate this procedure by studying an example coming from the theory of discrete orthogonal polynomials. There are many connections between orthogonal polynomials and Painlevé equations, both differential and discrete. In particular, often the coefficients of three-term recurrence relations for orthogonal polynomials can be expressed in terms of solutions of some discrete Painlevé equation. In this work we study orthogonal polynomials with general hypergeometric weight and show that their recurrence coefficients satisfy, after some change of variables, the standard discrete Painlevé-V equation. We also provide an explicit change of variables transforming this equation to the standard form.
This is joint work with Galina Filipuk (University of Warsaw, Poland) and Alexander Stokes (University College, London, UK)
2019年10月03日(木)
FMSPレクチャーズ
13:00-15:05 数理科学研究科棟(駒場) 002号室
全6回：9/26～10/31の毎週（木）13:00-15:05
Chung-jun Tsai 氏 (National Taiwan University)
Topic on minimal submanifolds (2/6) (ENGLISH)
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Tsai.pdf
全6回：9/26～10/31の毎週（木）13:00-15:05
Chung-jun Tsai 氏 (National Taiwan University)
Topic on minimal submanifolds (2/6) (ENGLISH)
[ 講演概要 ]
The main theme of these lectures will be theory about minimal submanifolds, which are higher dimensional generalizations of geodesics. A naive motivation is that one tries to understand the geometry from its special submanifolds (minimal, etc.).
For minimal submanifolds, the equations are no longer ODEs, but elliptic PDEs. This increases the difficulties. The study are very good examples for the application of methods from PDEs and calculus of variations. We will try to explain some important results in this theory, which stimulate many of the researches today.
Here are some specific materials we plan to cover: Simon’s work based on the second variational formula, Sacks - Uhlenback theorem on the existence of minimal 2-spheres, the theory of stable minimal hypersurfaces by Schoen-Simon-Yau.
[ 参考URL ]The main theme of these lectures will be theory about minimal submanifolds, which are higher dimensional generalizations of geodesics. A naive motivation is that one tries to understand the geometry from its special submanifolds (minimal, etc.).
For minimal submanifolds, the equations are no longer ODEs, but elliptic PDEs. This increases the difficulties. The study are very good examples for the application of methods from PDEs and calculus of variations. We will try to explain some important results in this theory, which stimulate many of the researches today.
Here are some specific materials we plan to cover: Simon’s work based on the second variational formula, Sacks - Uhlenback theorem on the existence of minimal 2-spheres, the theory of stable minimal hypersurfaces by Schoen-Simon-Yau.
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Tsai.pdf
2019年10月02日(水)
作用素環セミナー
16:45-18:15 数理科学研究科棟(駒場) 126号室
David E. Evans 氏 (Cardiff University)
Subfactors, K-theory and Equivariant Higher Twists (English)
David E. Evans 氏 (Cardiff University)
Subfactors, K-theory and Equivariant Higher Twists (English)
2019年10月01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
村上 順 氏 (早稲田大学)
Quantized SL(2) representations of knot groups (JAPANESE)
Tea: Common Room 16:30-17:00
村上 順 氏 (早稲田大学)
Quantized SL(2) representations of knot groups (JAPANESE)
[ 講演概要 ]
Let K be a knot and G be a group. The representation space of K for the group G means the space of homomorphisms from the knot group to G and is defined by using the group ring C[G], where C[G] is the ring of functions on G and has a commutative Hopf algebra structure. This construction can be generalized to any commutative Hopf algebras.
In this talk, we extend this construction to any braided Hopf algebras with braided commutativity. A typical example is BSL(2), which is the braided SL(2) introduced by S. Majid. Applying the above construction to BSL(2), we get the space of BSL(2) representations, which provides a quantization of SL(2) representations of a knot. This is joint work with Roloand van der Veen.
Let K be a knot and G be a group. The representation space of K for the group G means the space of homomorphisms from the knot group to G and is defined by using the group ring C[G], where C[G] is the ring of functions on G and has a commutative Hopf algebra structure. This construction can be generalized to any commutative Hopf algebras.
In this talk, we extend this construction to any braided Hopf algebras with braided commutativity. A typical example is BSL(2), which is the braided SL(2) introduced by S. Majid. Applying the above construction to BSL(2), we get the space of BSL(2) representations, which provides a quantization of SL(2) representations of a knot. This is joint work with Roloand van der Veen.
2019年09月30日(月)
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
濱野 佐知子 氏 (大阪市立大学)
Rigidity of the directional moduli on pseudoconvex domains fibered by open Riemann surfaces
濱野 佐知子 氏 (大阪市立大学)
Rigidity of the directional moduli on pseudoconvex domains fibered by open Riemann surfaces
[ 講演概要 ]
G. Schmieder-M. Shiba observed conformal embeddings of a fixed open Riemann surface of positive finite genus into closed Riemann surfaces of the same genus, and they showed the range of each diagonal element of the period matrices. Now we shall consider a smooth deformation of open Riemann surfaces with a complex parameter. In this talk, we show the rigidity of directional moduli induced by elements of the period matrices on pseudoconvex domains fibered by open Riemann surfaces of the same topological type.
G. Schmieder-M. Shiba observed conformal embeddings of a fixed open Riemann surface of positive finite genus into closed Riemann surfaces of the same genus, and they showed the range of each diagonal element of the period matrices. Now we shall consider a smooth deformation of open Riemann surfaces with a complex parameter. In this talk, we show the rigidity of directional moduli induced by elements of the period matrices on pseudoconvex domains fibered by open Riemann surfaces of the same topological type.
2019年09月26日(木)
FMSPレクチャーズ
13:00-15:05 数理科学研究科棟(駒場) 002号室
全6回：9/26～10/31の毎週（木）13:00-15:05
Chung-jun Tsai 氏 (National Taiwan University)
Topic on minimal submanifolds (1/6) (ENGLISH)
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Tsai.pdf
全6回：9/26～10/31の毎週（木）13:00-15:05
Chung-jun Tsai 氏 (National Taiwan University)
Topic on minimal submanifolds (1/6) (ENGLISH)
[ 講演概要 ]
The main theme of these lectures will be theory about minimal submanifolds, which are higher dimensional generalizations of geodesics. A naive motivation is that one tries to understand the geometry from its special submanifolds (minimal, etc.).
For minimal submanifolds, the equations are no longer ODEs, but elliptic PDEs. This increases the difficulties. The study are very good examples for the application of methods from PDEs and calculus of variations. We will try to explain some important results in this theory, which stimulate many of the researches today.
Here are some specific materials we plan to cover: Simon’s work based on the second variational formula, Sacks - Uhlenback theorem on the existence of minimal 2-spheres, the theory of stable minimal hypersurfaces by Schoen-Simon-Yau.
[ 参考URL ]The main theme of these lectures will be theory about minimal submanifolds, which are higher dimensional generalizations of geodesics. A naive motivation is that one tries to understand the geometry from its special submanifolds (minimal, etc.).
For minimal submanifolds, the equations are no longer ODEs, but elliptic PDEs. This increases the difficulties. The study are very good examples for the application of methods from PDEs and calculus of variations. We will try to explain some important results in this theory, which stimulate many of the researches today.
Here are some specific materials we plan to cover: Simon’s work based on the second variational formula, Sacks - Uhlenback theorem on the existence of minimal 2-spheres, the theory of stable minimal hypersurfaces by Schoen-Simon-Yau.
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Tsai.pdf
2019年09月25日(水)
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
周冠宇 氏 (東京理科大学理学部)
Keller-Segel方程式の保存型の有限体積法について (Japanese)
周冠宇 氏 (東京理科大学理学部)
Keller-Segel方程式の保存型の有限体積法について (Japanese)
[ 講演概要 ]
Keller-Segel方程式に対して，有限体積法の保存型の非線形的なスキームを提案した．まず離散解の存在性を示し，半群理論を用いて誤差評価を行った．特に，1次収束を示すために必要な離散解の事前評価を示した．さらに，自明な定常解に収束する場合に適用する離散Laypunov汎関数を定義し，Laypunov不等式を証明した．最後に爆発解について，離散Laypunov汎関数やスキームの提案について少し話したい．
Keller-Segel方程式に対して，有限体積法の保存型の非線形的なスキームを提案した．まず離散解の存在性を示し，半群理論を用いて誤差評価を行った．特に，1次収束を示すために必要な離散解の事前評価を示した．さらに，自明な定常解に収束する場合に適用する離散Laypunov汎関数を定義し，Laypunov不等式を証明した．最後に爆発解について，離散Laypunov汎関数やスキームの提案について少し話したい．
2019年08月20日(火)
博士論文発表会
13:45-15:00 数理科学研究科棟(駒場) 122号室
若月 駿 氏 (東京大学大学院数理科学研究科)
Brane coproducts and their applications
(ブレーン余積とその応用)
(JAPANESE)
若月 駿 氏 (東京大学大学院数理科学研究科)
Brane coproducts and their applications
(ブレーン余積とその応用)
(JAPANESE)
2019年08月19日(月)
数値解析セミナー
13:00-17:00 数理科学研究科棟(駒場) 122号室
"Mini Workshop on Recent Developments in Discontinuous Galerkin Methods"として開催
Eric Chung 氏 (The Chinese University of Hong Kong) 13:00-14:00
Staggered hybridisation for discontinuous Galerkin methods (英語)
DG and HDG methods for the variational inequality problems (英語)
A new HDG method using a hybridized flux (英語)
Numerical approximation of the Stokes–Darcy problem using discontinuous linear elements (英語)
"Mini Workshop on Recent Developments in Discontinuous Galerkin Methods"として開催
Eric Chung 氏 (The Chinese University of Hong Kong) 13:00-14:00
Staggered hybridisation for discontinuous Galerkin methods (英語)
[ 講演概要 ]
In this talk, we present a new staggered hybridization technique for discontinuous Galerkin methods to discretize linear elastodynamic equations and nonlinear Stokes equations. The idea of hybridization is used extensively in many discontinuous Galerkin methods, but the idea of staggered hybridization is new. Our new approach offers several advantages, namely energy conservation, high-order optimal convergence, preservation of symmetry for the stress tensor, block diagonal mass matrices as well as low dispersion error. The key idea is to use two staggered hybrid variables to enforce the continuity of the velocity and the continuity of the normal component of the stress tensor on a staggered mesh. We prove the stability and the convergence of the proposed scheme in both the semi-discrete and the fully-discrete settings. Numerical results confirm the optimal rate of convergence and show that the method has a superconvergent property for dispersion.
Feifei Jing 氏 (Northwestern Polytechnical University) 14:30-15:30In this talk, we present a new staggered hybridization technique for discontinuous Galerkin methods to discretize linear elastodynamic equations and nonlinear Stokes equations. The idea of hybridization is used extensively in many discontinuous Galerkin methods, but the idea of staggered hybridization is new. Our new approach offers several advantages, namely energy conservation, high-order optimal convergence, preservation of symmetry for the stress tensor, block diagonal mass matrices as well as low dispersion error. The key idea is to use two staggered hybrid variables to enforce the continuity of the velocity and the continuity of the normal component of the stress tensor on a staggered mesh. We prove the stability and the convergence of the proposed scheme in both the semi-discrete and the fully-discrete settings. Numerical results confirm the optimal rate of convergence and show that the method has a superconvergent property for dispersion.
DG and HDG methods for the variational inequality problems (英語)
[ 講演概要 ]
There exist many numerical methods for solving the fluid dynamics equations, the main difference between them lies in the partitions of geometric domain and the discrete forms of governing equations. Due to the discontinuous piecewise polynomial subspaces, DG and HDG methods can be easily implemented on highly unstructured meshes, e.g. general polygonal mesh, and volume integrals could be calculated on physical elements, without reference elements and mappings between physical and reference elements. In this talk, DG and HDG methods employed to a class of variational inequality problems arising in hydrodynamics are studied. Some theoretical results will be shown, as well as the implementations of these methods are also put into practice.
及川一誠 氏 (一橋大学) 16:00-16:30There exist many numerical methods for solving the fluid dynamics equations, the main difference between them lies in the partitions of geometric domain and the discrete forms of governing equations. Due to the discontinuous piecewise polynomial subspaces, DG and HDG methods can be easily implemented on highly unstructured meshes, e.g. general polygonal mesh, and volume integrals could be calculated on physical elements, without reference elements and mappings between physical and reference elements. In this talk, DG and HDG methods employed to a class of variational inequality problems arising in hydrodynamics are studied. Some theoretical results will be shown, as well as the implementations of these methods are also put into practice.
A new HDG method using a hybridized flux (英語)
[ 講演概要 ]
We propose a new hybridizable discontinuous Galerkin (HDG) method for steady-state diffusion problems. In our method, both the trace and flux of the exact solution are hybridized. The Lehrenfeld-Schöberl stabilization is implicitly included in the method, so that the orders of convergence in all variables are optimal without postprocessing and computation of any projection. Numerical results are present to show the validation of our method.
柏原崇人 氏 (東京大学) 16:30-17:00We propose a new hybridizable discontinuous Galerkin (HDG) method for steady-state diffusion problems. In our method, both the trace and flux of the exact solution are hybridized. The Lehrenfeld-Schöberl stabilization is implicitly included in the method, so that the orders of convergence in all variables are optimal without postprocessing and computation of any projection. Numerical results are present to show the validation of our method.
Numerical approximation of the Stokes–Darcy problem using discontinuous linear elements (英語)
[ 講演概要 ]
We consider the Stokes–Darcy interface problem supplemented with the Beavers– Joseph–Saffman condition on the interface separating two domains. This condition allows for discontinuity in the tangential velocities and in the pressures along the interface. To effectively express it, we propose to use discontinuous linear finite elements to approximate all of the velocities/pressures in the Stokes/Darcy regions. The continuity of velocity in the normal direction is weakly enforced by adopting either the penalty method or Nitsche’s method. We present stability and error estimates for the proposed scheme, taking into account the situation where a curved interface is approximated by a polygonal curve or polyhedral surface.
We consider the Stokes–Darcy interface problem supplemented with the Beavers– Joseph–Saffman condition on the interface separating two domains. This condition allows for discontinuity in the tangential velocities and in the pressures along the interface. To effectively express it, we propose to use discontinuous linear finite elements to approximate all of the velocities/pressures in the Stokes/Darcy regions. The continuity of velocity in the normal direction is weakly enforced by adopting either the penalty method or Nitsche’s method. We present stability and error estimates for the proposed scheme, taking into account the situation where a curved interface is approximated by a polygonal curve or polyhedral surface.
2019年08月01日(木)
数理人口学・数理生物学セミナー
15:00-16:00 数理科学研究科棟(駒場) 118号室
Yueping Dong 氏 (Central China Normal University)
Mathematical study of the inhibitory role of regulatory T cells in tumor immune response
Yueping Dong 氏 (Central China Normal University)
Mathematical study of the inhibitory role of regulatory T cells in tumor immune response
[ 講演概要 ]
The immune system against tumor is a complex dynamical process showing a dual role. On the one hand, the immune system can activate some immune cells to kill tumor cells, such as cytotoxic T lymphocytes (CTLs) and natural killer cells (NKs), but on the other hand, more evidence shows that some immune cells can help tumor escape, such as regulatory T cells (Tregs). In this talk, we propose a tumor immune interaction model based on Tregs mediated tumor immune escape mechanism. When HTCs stimulation rate by the presence of identified tumor antigens below the critical value, the interior equilibrium P* is always stable in the region of existence. When HTCs stimulation rate higher than the critical value, the Inhibition rate of ECs by Tregs can destabilize P* and cause Hopf bifurcations and produce limit cycle. This model shows that Tregs might play a crucial role in triggering the immune escape of tumor cells. Furthermore, we introduce the adoptive cellular immunotherapy (ACI) and monoclonal immunotherapy as the treatment to boost the immune system to fight against tumors. The numerical results show that ACI can control more tumor cells, while monoclonal immunotherapy can delay the inhibitory effect of Tregs on effector cells (ECs). The results also show that the combination immunotherapy can control tumor cells and reduce the inhibitory effect of Tregs better than single immunotherapy.
The immune system against tumor is a complex dynamical process showing a dual role. On the one hand, the immune system can activate some immune cells to kill tumor cells, such as cytotoxic T lymphocytes (CTLs) and natural killer cells (NKs), but on the other hand, more evidence shows that some immune cells can help tumor escape, such as regulatory T cells (Tregs). In this talk, we propose a tumor immune interaction model based on Tregs mediated tumor immune escape mechanism. When HTCs stimulation rate by the presence of identified tumor antigens below the critical value, the interior equilibrium P* is always stable in the region of existence. When HTCs stimulation rate higher than the critical value, the Inhibition rate of ECs by Tregs can destabilize P* and cause Hopf bifurcations and produce limit cycle. This model shows that Tregs might play a crucial role in triggering the immune escape of tumor cells. Furthermore, we introduce the adoptive cellular immunotherapy (ACI) and monoclonal immunotherapy as the treatment to boost the immune system to fight against tumors. The numerical results show that ACI can control more tumor cells, while monoclonal immunotherapy can delay the inhibitory effect of Tregs on effector cells (ECs). The results also show that the combination immunotherapy can control tumor cells and reduce the inhibitory effect of Tregs better than single immunotherapy.
2019年07月25日(木)
作用素環セミナー
16:45-18:15 数理科学研究科棟(駒場) 126号室
George Elliott 氏 (Univ. Toronto)
The classification of well behaved simple C*-algebras
George Elliott 氏 (Univ. Toronto)
The classification of well behaved simple C*-algebras
2019年07月24日(水)
博士論文発表会
13:15-14:30 数理科学研究科棟(駒場) 128号室
岡田 真央 氏 (東京大学大学院数理科学研究科)
Local rigidity of certain actions of solvable groups on the boundaries of rank one symmetric spaces
(階数１対称空間の境界へのある可解群の作用の局所剛性)
(JAPANESE)
岡田 真央 氏 (東京大学大学院数理科学研究科)
Local rigidity of certain actions of solvable groups on the boundaries of rank one symmetric spaces
(階数１対称空間の境界へのある可解群の作用の局所剛性)
(JAPANESE)
2019年07月23日(火)
PDE実解析研究会
13:00-14:00 数理科学研究科棟(駒場) 056号室
通常の開始時刻と異なります。
Tianling Jin 氏 (The Hong Kong University of Science and Technology)
On the isoperimetric ratio over scalar-flat conformal classes (English)
通常の開始時刻と異なります。
Tianling Jin 氏 (The Hong Kong University of Science and Technology)
On the isoperimetric ratio over scalar-flat conformal classes (English)
[ 講演概要 ]
Let $(M,g)$ be a smooth compact Riemannian manifold of dimension $n$ with smooth boundary. Suppose that $(M,g)$ admits a scalar-flat conformal metric. We prove that the supremum of the isoperimetric ratio over the scalar-flat conformal class is strictly larger than the best constant of the isoperimetric inequality on Euclidean space, and consequently is achieved, if either (i) $n \geq 12$ and the boundary has a nonumbilic point; or (ii) $n \geq 10$, the boundary is umbilic and the Weyl tensor does not vanish at some boundary point. A crucial ingredient in the proof is the expansion of solutions to the conformal Laplacian equation with blowing up Dirichlet boundary conditions.
Let $(M,g)$ be a smooth compact Riemannian manifold of dimension $n$ with smooth boundary. Suppose that $(M,g)$ admits a scalar-flat conformal metric. We prove that the supremum of the isoperimetric ratio over the scalar-flat conformal class is strictly larger than the best constant of the isoperimetric inequality on Euclidean space, and consequently is achieved, if either (i) $n \geq 12$ and the boundary has a nonumbilic point; or (ii) $n \geq 10$, the boundary is umbilic and the Weyl tensor does not vanish at some boundary point. A crucial ingredient in the proof is the expansion of solutions to the conformal Laplacian equation with blowing up Dirichlet boundary conditions.
2019年07月16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
茂手木 公彦 氏 (日本大学)
Seifert vs. slice genera of knots in twist families and a characterization of braid axes (JAPANESE)
Tea: Common Room 16:30-17:00
茂手木 公彦 氏 (日本大学)
Seifert vs. slice genera of knots in twist families and a characterization of braid axes (JAPANESE)
[ 講演概要 ]
Twisting a knot $K$ in $S^3$ along a disjoint unknot $c$ produces a twist family of knots $\{K_n\}$ indexed by the integers. Comparing the behaviors of the Seifert genus $g(K_n)$ and the slice genus $g_4(K_n)$ under twistings, we prove that if $g(K_n) - g_4(K_n) < C$ for some constant $C$ for infinitely many integers $n > 0$ or $g(K_n) / g_4(K_n)$ limits to $1$, then the winding number of $K$ about $c$ equals either zero or the wrapping number. As a key application, if $\{K_n\}$ or the mirror twist family $\{\overline{K_n}\}$ contains infinitely many tight fibered knots, then the latter must occur. This leads to the characterization that $c$ is a braid axis of $K$ if and only if both $\{K_n\}$ and $\{\overline{K_n}\}$ each contain infinitely many tight fibered knots. We also give a necessary and sufficient condition for $\{K_n\}$ to contain infinitely many L-space knots, and apply the characterization to prove that satellite L-space knots have braided patterns, which answers a question of both Baker-Moore and Hom in the positive. This result also implies an absence of essential Conway spheres for satellite L-space knots, which gives a partial answer to a conjecture of Lidman-Moore.
This is joint work with Kenneth Baker (University of Miami).
Twisting a knot $K$ in $S^3$ along a disjoint unknot $c$ produces a twist family of knots $\{K_n\}$ indexed by the integers. Comparing the behaviors of the Seifert genus $g(K_n)$ and the slice genus $g_4(K_n)$ under twistings, we prove that if $g(K_n) - g_4(K_n) < C$ for some constant $C$ for infinitely many integers $n > 0$ or $g(K_n) / g_4(K_n)$ limits to $1$, then the winding number of $K$ about $c$ equals either zero or the wrapping number. As a key application, if $\{K_n\}$ or the mirror twist family $\{\overline{K_n}\}$ contains infinitely many tight fibered knots, then the latter must occur. This leads to the characterization that $c$ is a braid axis of $K$ if and only if both $\{K_n\}$ and $\{\overline{K_n}\}$ each contain infinitely many tight fibered knots. We also give a necessary and sufficient condition for $\{K_n\}$ to contain infinitely many L-space knots, and apply the characterization to prove that satellite L-space knots have braided patterns, which answers a question of both Baker-Moore and Hom in the positive. This result also implies an absence of essential Conway spheres for satellite L-space knots, which gives a partial answer to a conjecture of Lidman-Moore.
This is joint work with Kenneth Baker (University of Miami).
2019年07月11日(木)
情報数学セミナー
16:50-18:35 数理科学研究科棟(駒場) 128号室
高島 克幸 氏 (三菱電機/九州大学)
楕円曲線ペアリングを用いた関数型暗号 (Japanese)
高島 克幸 氏 (三菱電機/九州大学)
楕円曲線ペアリングを用いた関数型暗号 (Japanese)
[ 講演概要 ]
関数型暗号として，本セミナーでは，既に格子暗号に基づいた方式を紹介した．今回は，楕円曲線上のペアリング演算（双線形写像）を用いた関数型暗号を紹介する．ペアリングに基づく方式は，格子ベースと比べて，一般に実用的な演算速度・データサイズを実現し，そして現実的なモデルの下での安全性（適応的安全性）が証明できるという利点がある．その観点から，内積述語暗号，属性ベース暗号，およびその派生形である属性ベース署名を紹介する．
関数型暗号として，本セミナーでは，既に格子暗号に基づいた方式を紹介した．今回は，楕円曲線上のペアリング演算（双線形写像）を用いた関数型暗号を紹介する．ペアリングに基づく方式は，格子ベースと比べて，一般に実用的な演算速度・データサイズを実現し，そして現実的なモデルの下での安全性（適応的安全性）が証明できるという利点がある．その観点から，内積述語暗号，属性ベース暗号，およびその派生形である属性ベース署名を紹介する．
数理人口学・数理生物学セミナー
15:00-16:00 数理科学研究科棟(駒場) 056号室
Dipo Aldila 氏 (Universitas Indonesia)
Understanding The Seasonality of Dengue Disease Incidences From Empirical Data (ENGLISH)
Dipo Aldila 氏 (Universitas Indonesia)
Understanding The Seasonality of Dengue Disease Incidences From Empirical Data (ENGLISH)
[ 講演概要 ]
Investigating the seasonality of dengue incidences is very important in dengue surveillance in regions with periodical climatic patterns. In lieu of the paradigm about dengue incidences varying seasonally in line with meteorology, this talk seeks to determine how well standard epidemic mo-dels (SIRUV) can capture such seasonality for better forecasts and optimal futuristic interventions. Once incidence data are assimilated by a periodic model, asymptotic analysis in relation to the long-term behavior of the dengue occurrences will be performed. For a test case, we employed an SIRUV model (later become IR model with QSSA method) to assimilate weekly dengue incidence data from the city of Jakarta, Indonesia, which we present in their raw and moving-average-filtered versions. To estimate a periodic parameter toward performing the asymptotic analysis, some optimization schemes were assigned returning magnitudes of the parameter that vary insignificantly across schemes. Furthermore, the computation results combined with the analytical results indicate that if the disease surveillance in the city does not improve, then the incidence will raise to a certain positive orbit and remain cyclical.
Investigating the seasonality of dengue incidences is very important in dengue surveillance in regions with periodical climatic patterns. In lieu of the paradigm about dengue incidences varying seasonally in line with meteorology, this talk seeks to determine how well standard epidemic mo-dels (SIRUV) can capture such seasonality for better forecasts and optimal futuristic interventions. Once incidence data are assimilated by a periodic model, asymptotic analysis in relation to the long-term behavior of the dengue occurrences will be performed. For a test case, we employed an SIRUV model (later become IR model with QSSA method) to assimilate weekly dengue incidence data from the city of Jakarta, Indonesia, which we present in their raw and moving-average-filtered versions. To estimate a periodic parameter toward performing the asymptotic analysis, some optimization schemes were assigned returning magnitudes of the parameter that vary insignificantly across schemes. Furthermore, the computation results combined with the analytical results indicate that if the disease surveillance in the city does not improve, then the incidence will raise to a certain positive orbit and remain cyclical.
2019年07月10日(水)
作用素環セミナー
16:45-18:15 数理科学研究科棟(駒場) 126号室
酒匂宏樹 氏 (新潟大)
Convergence theorems on multi-dimensional homogeneous quantum walks
酒匂宏樹 氏 (新潟大)
Convergence theorems on multi-dimensional homogeneous quantum walks
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