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過去の記録 ～09/14｜本日 09/15 | 今後の予定 09/16～
2018年10月31日(水)
FMSPレクチャーズ
15:00-16:30 数理科学研究科棟(駒場) 122号室
Paul Baum 氏 (The Pennsylvania State University)
K-THEORY AND THE DIRAC OPERATOR (4/4)
Lecture 4. BEYOND ELLIPTICITY or K-HOMOLOGY AND INDEX THEORY ON CONTACT MANIFOLDS (ENGLISH)
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Baum.pdf
Paul Baum 氏 (The Pennsylvania State University)
K-THEORY AND THE DIRAC OPERATOR (4/4)
Lecture 4. BEYOND ELLIPTICITY or K-HOMOLOGY AND INDEX THEORY ON CONTACT MANIFOLDS (ENGLISH)
[ 講演概要 ]
K-homology is the dual theory to K-theory. The BD (Baum-Douglas) isomorphism of Atiyah-Kasparov K-homology and K-cycle K-homology provides a framework within which the Atiyah-Singer index theorem can be extended to certain differential operators which are hypoelliptic but not elliptic. This talk will consider such a class of differential operators on compact contact manifolds. These operators have been studied by a number of mathematicians (e.g. C.Epstein and R.Melrose).
Operators with similar analytical properties have also been studied (e.g. by Alain Connes and Henri Moscovici --- also Michel Hilsum and Georges Skandalis). Working within the BD framework, the index problem will be solved for these differential operators on compact contact manifolds.
This is joint work with Erik van Erp.
[ 参考URL ]K-homology is the dual theory to K-theory. The BD (Baum-Douglas) isomorphism of Atiyah-Kasparov K-homology and K-cycle K-homology provides a framework within which the Atiyah-Singer index theorem can be extended to certain differential operators which are hypoelliptic but not elliptic. This talk will consider such a class of differential operators on compact contact manifolds. These operators have been studied by a number of mathematicians (e.g. C.Epstein and R.Melrose).
Operators with similar analytical properties have also been studied (e.g. by Alain Connes and Henri Moscovici --- also Michel Hilsum and Georges Skandalis). Working within the BD framework, the index problem will be solved for these differential operators on compact contact manifolds.
This is joint work with Erik van Erp.
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Baum.pdf
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
早瀬友裕 氏 (東大数理)
Strong Tools in Free Probability Theory
早瀬友裕 氏 (東大数理)
Strong Tools in Free Probability Theory
2018年10月30日(火)
解析学火曜セミナー
16:50-18:20 数理科学研究科棟(駒場) 128号室
宮西吉久 氏 (大阪大学)
Spectral structure of the Neumann-Poincaré operator in three dimensions: Willmore energy and surface geometry (日本語)
宮西吉久 氏 (大阪大学)
Spectral structure of the Neumann-Poincaré operator in three dimensions: Willmore energy and surface geometry (日本語)
[ 講演概要 ]
The Neumann-Poincaré operator (abbreviated by NP) is a boundary integral operator naturally arising when solving classical boundary value problems using layer potentials. If the boundary of the domain, on which the NP operator is defined, is $C^{1, \alpha}$ smooth, then the NP operator is compact. Thus, the Fredholm integral equation, which appears when solving Dirichlet or Neumann problems, can be solved using the Fredholm index theory.
Regarding spectral properties of the NP operator, the spectrum consists of eigenvalues converging to $0$ for $C^{1, \alpha}$ smooth boundaries. Our main purpose here is to deduce eigenvalue asymptotics of the NP operators in three dimensions. This formula is the so-called Weyl's law for eigenvalue problems of NP operators. Then we discuss relationships among the Weyl's law, the Euler characteristic and the Willmore energy on the boundary surface.
The Neumann-Poincaré operator (abbreviated by NP) is a boundary integral operator naturally arising when solving classical boundary value problems using layer potentials. If the boundary of the domain, on which the NP operator is defined, is $C^{1, \alpha}$ smooth, then the NP operator is compact. Thus, the Fredholm integral equation, which appears when solving Dirichlet or Neumann problems, can be solved using the Fredholm index theory.
Regarding spectral properties of the NP operator, the spectrum consists of eigenvalues converging to $0$ for $C^{1, \alpha}$ smooth boundaries. Our main purpose here is to deduce eigenvalue asymptotics of the NP operators in three dimensions. This formula is the so-called Weyl's law for eigenvalue problems of NP operators. Then we discuss relationships among the Weyl's law, the Euler characteristic and the Willmore energy on the boundary surface.
PDE実解析研究会
10:30-11:30 数理科学研究科棟(駒場) 056号室
Piotr Rybka 氏 (University of Warsaw)
The least gradient problem in the plain (English)
Piotr Rybka 氏 (University of Warsaw)
The least gradient problem in the plain (English)
[ 講演概要 ]
The least gradient problem arises in many application, e.g. in the free material design. We show existence of solutions in bounded, strictly convex planar regions, when the data are functions on bounded variation.
Our main goal is to show existence of solution in convex, but not necessarily strictly convex planar regions. In order to avoid technicalities we consider only continuous data, but BV data will do to. We formulate a set of admissibility conditions. We show that they are sufficient for existence.
This is a joint project with Wojciech Górny and Ahmad Sabra.
The least gradient problem arises in many application, e.g. in the free material design. We show existence of solutions in bounded, strictly convex planar regions, when the data are functions on bounded variation.
Our main goal is to show existence of solution in convex, but not necessarily strictly convex planar regions. In order to avoid technicalities we consider only continuous data, but BV data will do to. We formulate a set of admissibility conditions. We show that they are sufficient for existence.
This is a joint project with Wojciech Górny and Ahmad Sabra.
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
志賀 啓成 氏 (東京工業大学)
The quasiconformal equivalence of Riemann surfaces and a universality of Schottky spaces (JAPANESE)
Tea: Common Room 16:30-17:00
志賀 啓成 氏 (東京工業大学)
The quasiconformal equivalence of Riemann surfaces and a universality of Schottky spaces (JAPANESE)
[ 講演概要 ]
In the theory of Teichmüller space of Riemann surfaces, we consider the set of Riemann surfaces which are quasiconformally equivalent. For topologically finite Riemann surfaces, it is quite easy to examine if they are quasiconformally equivalent or not. On the other hand, for Riemann surfaces of topologically infinite type, the situation is rather complicated.
In this talk, after constructing an example which shows the complexity of the problem, we give some geometric conditions for Riemann surfaces to be quasiconformally equivalent. Our argument enables us to see a universality of Schottky spaces.
In the theory of Teichmüller space of Riemann surfaces, we consider the set of Riemann surfaces which are quasiconformally equivalent. For topologically finite Riemann surfaces, it is quite easy to examine if they are quasiconformally equivalent or not. On the other hand, for Riemann surfaces of topologically infinite type, the situation is rather complicated.
In this talk, after constructing an example which shows the complexity of the problem, we give some geometric conditions for Riemann surfaces to be quasiconformally equivalent. Our argument enables us to see a universality of Schottky spaces.
統計数学セミナー
15:30-16:40 数理科学研究科棟(駒場) 126号室
Ciprian A. Tudor 氏 (Université de Lille 1, Université de Panthéon-Sorbonne Paris 1)
Asymptotic expansion for random vectors
Ciprian A. Tudor 氏 (Université de Lille 1, Université de Panthéon-Sorbonne Paris 1)
Asymptotic expansion for random vectors
[ 講演概要 ]
We develop the asymptotic expansion theory for vector-valued sequences $F_{N}$ of random variables. We find the second-order term in the expansion of the density of $F_{N}$, based on assumptions in terms of the convergence of the Stein-Malliavin matrix associated to the sequence $F_{N}$ . Our approach combines the classical Fourier approach and the recent theory on Stein method and Malliavin calculus. We find the second order term of the asymptotic expansion of the density of $F_{N}$ and we discuss the main ideas on higher order asymptotic expansion. We illustrate our results by several examples.
We develop the asymptotic expansion theory for vector-valued sequences $F_{N}$ of random variables. We find the second-order term in the expansion of the density of $F_{N}$, based on assumptions in terms of the convergence of the Stein-Malliavin matrix associated to the sequence $F_{N}$ . Our approach combines the classical Fourier approach and the recent theory on Stein method and Malliavin calculus. We find the second order term of the asymptotic expansion of the density of $F_{N}$ and we discuss the main ideas on higher order asymptotic expansion. We illustrate our results by several examples.
2018年10月29日(月)
東京確率論セミナー
16:00-17:30 数理科学研究科棟(駒場) 128号室
Sunder Sethuraman 氏 (University of Arizona)
On Hydrodynamic Limits of Young Diagrams (ENGLISH)
http://math.arizona.edu/~sethuram/
Sunder Sethuraman 氏 (University of Arizona)
On Hydrodynamic Limits of Young Diagrams (ENGLISH)
[ 講演概要 ]
We consider a family of stochastic models of evolving two-dimensional Young diagrams, given in terms of certain energies, with Gibbs invariant measures. `Static' scaling limits of the shape functions, under these Gibbs measures, have been shown by several over the years. The purpose of this article is to study corresponding `dynamical' limits of which less is understood. We show that the hydrodynamic scaling limits of the diagram shape functions may be described by different types of parabolic PDEs, depending on the energy structure.
The talk will be based on the article: https://arxiv.org/abs/1809.03592
[ 参考URL ]We consider a family of stochastic models of evolving two-dimensional Young diagrams, given in terms of certain energies, with Gibbs invariant measures. `Static' scaling limits of the shape functions, under these Gibbs measures, have been shown by several over the years. The purpose of this article is to study corresponding `dynamical' limits of which less is understood. We show that the hydrodynamic scaling limits of the diagram shape functions may be described by different types of parabolic PDEs, depending on the energy structure.
The talk will be based on the article: https://arxiv.org/abs/1809.03592
http://math.arizona.edu/~sethuram/
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
松村慎一 氏 (東北大学)
On morphisms of compact Kaehler manifolds with semi-positive holomorphic sectional curvature (JAPANESE)
松村慎一 氏 (東北大学)
On morphisms of compact Kaehler manifolds with semi-positive holomorphic sectional curvature (JAPANESE)
[ 講演概要 ]
In this talk, we consider a smooth projective variety $X$ with semi-positive holomorphic "sectional" curvature, motivated by generalizing Howard-Smyth-Wu's structure theorem and Mok's result for compact Kaehler manifold with semi-positive "bisectional" curvature.
We prove that, if $X$ admits a holomorphic maximally rationally connected fibration $X ¥to Y$, then the morphism is always smooth (that is, a submersion), that the image $Y$ admits a finite ¥'etale cover $T ¥to Y$ by a complex
torus $T$, and further that all the fibers $F$ are isomorphic.
This gives a structure theorem for $X$ when $X$ is a surface.
Moreover we show that $X$ is rationally connected, if the holomorphic sectional curvature is quasi-positive.
This result gives a generalization of Yau's conjecture.
In this talk, we consider a smooth projective variety $X$ with semi-positive holomorphic "sectional" curvature, motivated by generalizing Howard-Smyth-Wu's structure theorem and Mok's result for compact Kaehler manifold with semi-positive "bisectional" curvature.
We prove that, if $X$ admits a holomorphic maximally rationally connected fibration $X ¥to Y$, then the morphism is always smooth (that is, a submersion), that the image $Y$ admits a finite ¥'etale cover $T ¥to Y$ by a complex
torus $T$, and further that all the fibers $F$ are isomorphic.
This gives a structure theorem for $X$ when $X$ is a surface.
Moreover we show that $X$ is rationally connected, if the holomorphic sectional curvature is quasi-positive.
This result gives a generalization of Yau's conjecture.
FMSPレクチャーズ
15:00-16:30 数理科学研究科棟(駒場) 117号室
Paul Baum 氏 (The Pennsylvania State University)
K-THEORY AND THE DIRAC OPERATOR (3/4)
Lecture 3. THE RIEMANN-ROCH THEOREM (ENGLISH)
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Baum.pdf
Paul Baum 氏 (The Pennsylvania State University)
K-THEORY AND THE DIRAC OPERATOR (3/4)
Lecture 3. THE RIEMANN-ROCH THEOREM (ENGLISH)
[ 講演概要 ]
Topics in this talk :
1. Classical Riemann-Roch
2. Hirzebruch-Riemann-Roch (HRR)
3. Grothendieck-Riemann-Roch (GRR)
4. RR for possibly singular varieties (Baum-Fulton-MacPherson)
[ 参考URL ]Topics in this talk :
1. Classical Riemann-Roch
2. Hirzebruch-Riemann-Roch (HRR)
3. Grothendieck-Riemann-Roch (GRR)
4. RR for possibly singular varieties (Baum-Fulton-MacPherson)
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Baum.pdf
2018年10月26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) 002号室
伊藤 健一 氏 (東京大学大学院数理科学研究科)
一般化固有関数の漸近挙動と散乱理論 (JAPANESE)
伊藤 健一 氏 (東京大学大学院数理科学研究科)
一般化固有関数の漸近挙動と散乱理論 (JAPANESE)
[ 講演概要 ]
散乱理論とは，入射波が障害物によって散乱される前後の挙動
を記述するための理論であり，物理における散乱実験などに数学的裏付けを与え
る理論である．本講演では量子散乱理論の数学的定式化について概説したのち，
講演者がErik Skibsted氏（Aarhus大学)との共同研究で得た結果の一部を紹介す
る．時間が許せば漸近的Euclid型や漸近的双曲型エンドを持つ多様体上への一般
化についても触れたい．
散乱理論とは，入射波が障害物によって散乱される前後の挙動
を記述するための理論であり，物理における散乱実験などに数学的裏付けを与え
る理論である．本講演では量子散乱理論の数学的定式化について概説したのち，
講演者がErik Skibsted氏（Aarhus大学)との共同研究で得た結果の一部を紹介す
る．時間が許せば漸近的Euclid型や漸近的双曲型エンドを持つ多様体上への一般
化についても触れたい．
2018年10月24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
森迪也 氏 (東大数理)
The Mazur-Ulam property for unital C*-algebras (English)
森迪也 氏 (東大数理)
The Mazur-Ulam property for unital C*-algebras (English)
FMSPレクチャーズ
15:00-16:30 数理科学研究科棟(駒場) 123号室
Paul Baum 氏 (The Pennsylvania State University)
K-THEORY AND THE DIRAC OPERATOR (2/4)
Lecture 2. THE DIRAC OPERATOR (ENGLISH)
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Baum.pdf
Paul Baum 氏 (The Pennsylvania State University)
K-THEORY AND THE DIRAC OPERATOR (2/4)
Lecture 2. THE DIRAC OPERATOR (ENGLISH)
[ 講演概要 ]
The Dirac operator of R^n will be defined. This is a first order elliptic differential operator with constant coefficients.
Next, the class of differentiable manifolds which come equipped with an order one differential operator which (at the symbol level)is locally isomorphic to the Dirac operator of R^n will be considered. These are the Spin-c manifolds.
Spin-c is slightly stronger than oriented, so Spin-c can be viewed as "oriented plus epsilon". Most of the oriented manifolds that occur in practice are Spin-c. The Dirac operator of a closed Spin-c manifold is the basic example for the Hirzebruch-Riemann-Roch theorem and the Atiyah-Singer index theorem.
[ 参考URL ]The Dirac operator of R^n will be defined. This is a first order elliptic differential operator with constant coefficients.
Next, the class of differentiable manifolds which come equipped with an order one differential operator which (at the symbol level)is locally isomorphic to the Dirac operator of R^n will be considered. These are the Spin-c manifolds.
Spin-c is slightly stronger than oriented, so Spin-c can be viewed as "oriented plus epsilon". Most of the oriented manifolds that occur in practice are Spin-c. The Dirac operator of a closed Spin-c manifold is the basic example for the Hirzebruch-Riemann-Roch theorem and the Atiyah-Singer index theorem.
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Baum.pdf
2018年10月23日(火)
PDE実解析研究会
10:30-11:30 数理科学研究科棟(駒場) 056号室
Jian-Guo Liu 氏 (Duke University)
Least action principle for incompressible flow with free boundary (English)
Jian-Guo Liu 氏 (Duke University)
Least action principle for incompressible flow with free boundary (English)
[ 講演概要 ]
In this talk I will describe a connection between Arnold's least-action principle for incompressible flows with free boundary and geodesic paths for Wasserstein distance. The least-action problem for geodesic distance on the "manifold" of fluid-blob shapes exhibits instability due to microdroplet formation. Using a conformal map formulation we investigate singularity formation in water-wave dynamics neglecting gravity. A connection with fluid mixture models via a variant of Brenier's relaxed least-action principle for generalized Euler flows will also be discussed.
In this talk I will describe a connection between Arnold's least-action principle for incompressible flows with free boundary and geodesic paths for Wasserstein distance. The least-action problem for geodesic distance on the "manifold" of fluid-blob shapes exhibits instability due to microdroplet formation. Using a conformal map formulation we investigate singularity formation in water-wave dynamics neglecting gravity. A connection with fluid mixture models via a variant of Brenier's relaxed least-action principle for generalized Euler flows will also be discussed.
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
François Fillastre 氏 (Université de Cergy-Pontoise)
Co-Minkowski space and hyperbolic surfaces (ENGLISH)
Tea: Common Room 16:30-17:00
François Fillastre 氏 (Université de Cergy-Pontoise)
Co-Minkowski space and hyperbolic surfaces (ENGLISH)
[ 講演概要 ]
There are many ways to parametrize two copies of Teichmueller space by constant curvature -1 Riemannian or Lorentzian 3d manifolds (for example the Bers double uniformization theorem). We present the co-Minkowski space (or half-pipe space), which is a constant curvature -1 degenerated 3d space, and which is related to the tangent space of Teichmueller space. As an illustration, we give a new proof of a theorem of Thurston saying that, once the space of measured geodesic laminations on a compact hyperbolic surface is identified with the tangent space of Teichmueller space via infinitesimal earthquake, then the length of laminations is an asymmetric norm. Joint work with Thierry Barbot (Avignon).
There are many ways to parametrize two copies of Teichmueller space by constant curvature -1 Riemannian or Lorentzian 3d manifolds (for example the Bers double uniformization theorem). We present the co-Minkowski space (or half-pipe space), which is a constant curvature -1 degenerated 3d space, and which is related to the tangent space of Teichmueller space. As an illustration, we give a new proof of a theorem of Thurston saying that, once the space of measured geodesic laminations on a compact hyperbolic surface is identified with the tangent space of Teichmueller space via infinitesimal earthquake, then the length of laminations is an asymmetric norm. Joint work with Thierry Barbot (Avignon).
2018年10月22日(月)
東京確率論セミナー
16:00-17:30 数理科学研究科棟(駒場) 126号室
Trinh Khanh Duy 氏 (東北大学数理科学連携研究センター)
Limit theorems for random geometric complexes in the critical regime (ENGLISH)
Trinh Khanh Duy 氏 (東北大学数理科学連携研究センター)
Limit theorems for random geometric complexes in the critical regime (ENGLISH)
[ 講演概要 ]
Geometric complexes (eg. Cech complexes or Rips complexes) are simplicial complexes defined on a finite set of points in a Euclidean space together with a radius parameter, which can be viewed as a higher dimensional generalization of geometric graphs. This talk concerns with random geometric complexes built over binomial point processes (collections of iid points). Like random geometric graphs, there are three regimes (subcritical(or dust, sparse) regime, critical (or thermodynamic) regime and supercritical regime) which are divided according the growth of the radius parameters in which the limiting behavior of random geometric complexes is totally different. This talk introduces some results on the strong law of large numbers and a central limit theorem in the critical regime.
Geometric complexes (eg. Cech complexes or Rips complexes) are simplicial complexes defined on a finite set of points in a Euclidean space together with a radius parameter, which can be viewed as a higher dimensional generalization of geometric graphs. This talk concerns with random geometric complexes built over binomial point processes (collections of iid points). Like random geometric graphs, there are three regimes (subcritical(or dust, sparse) regime, critical (or thermodynamic) regime and supercritical regime) which are divided according the growth of the radius parameters in which the limiting behavior of random geometric complexes is totally different. This talk introduces some results on the strong law of large numbers and a central limit theorem in the critical regime.
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
足立真訓 氏 (静岡大学)
On certain hyperconvex manifolds without non-constant bounded holomorphic functions (JAPANESE)
足立真訓 氏 (静岡大学)
On certain hyperconvex manifolds without non-constant bounded holomorphic functions (JAPANESE)
[ 講演概要 ]
For each compact Riemann surface of genus > 1, we can construct a Riemann sphere bundle over the given Riemann surface using the projective structure induced by its uniformization.
The total space of this bundle is divided into two 1-convex domains by a closed Levi-flat real hypersurface. Although these two domains are not biholomorphic, we see that they have several function theoretic properties in common. In this talk, I would like to explain these common properties: hyperconvexity and expressions for certain Green function, and Liouville property and growth estimates of holomorphic functions.
For each compact Riemann surface of genus > 1, we can construct a Riemann sphere bundle over the given Riemann surface using the projective structure induced by its uniformization.
The total space of this bundle is divided into two 1-convex domains by a closed Levi-flat real hypersurface. Although these two domains are not biholomorphic, we see that they have several function theoretic properties in common. In this talk, I would like to explain these common properties: hyperconvexity and expressions for certain Green function, and Liouville property and growth estimates of holomorphic functions.
数値解析セミナー
16:50-18:20 数理科学研究科棟(駒場) 002号室
相原研輔 氏 (東京都市大学知識工学部)
短い漸化式を用いるクリロフ部分空間法に対する残差スムージング (Japanese)
相原研輔 氏 (東京都市大学知識工学部)
短い漸化式を用いるクリロフ部分空間法に対する残差スムージング (Japanese)
[ 講演概要 ]
クリロフ部分空間法は，大規模疎行列を係数に持つ連立一次方程式に有効な反復法群である．そのうち，Bi-CG法などの短い漸化式を用いる解法は，反復毎の計算量やメモリ使用量が少なく済むため，計算効率がよいが，生成される残差ノルムは振動する．残差ノルムが大きく振動すると，丸め誤差が拡大され，収束速度の低下や近似解精度の劣化に繋がる．そこで，収束性を改善するための残差スムージングについて取り上げる．古典的な残差スムージングは，残差ノルムの収束振る舞いを滑らかにするものの，丸め誤差の拡大を防ぐ効果はほとんどないことが知られている．一方，最近提案された相互作用型の残差スムージングは，丸め誤差の蓄積を抑制することができ，近似解精度が向上するなどの付加価値がある．本講演では，行列ベクトル積から発生する丸め誤差が収束性に与える影響を考察した上で，新旧の残差スムージングの効果の違いについて議論する．
クリロフ部分空間法は，大規模疎行列を係数に持つ連立一次方程式に有効な反復法群である．そのうち，Bi-CG法などの短い漸化式を用いる解法は，反復毎の計算量やメモリ使用量が少なく済むため，計算効率がよいが，生成される残差ノルムは振動する．残差ノルムが大きく振動すると，丸め誤差が拡大され，収束速度の低下や近似解精度の劣化に繋がる．そこで，収束性を改善するための残差スムージングについて取り上げる．古典的な残差スムージングは，残差ノルムの収束振る舞いを滑らかにするものの，丸め誤差の拡大を防ぐ効果はほとんどないことが知られている．一方，最近提案された相互作用型の残差スムージングは，丸め誤差の蓄積を抑制することができ，近似解精度が向上するなどの付加価値がある．本講演では，行列ベクトル積から発生する丸め誤差が収束性に与える影響を考察した上で，新旧の残差スムージングの効果の違いについて議論する．
FMSPレクチャーズ
15:00-16:30 数理科学研究科棟(駒場) 123号室
Paul Baum 氏 (The Pennsylvania State University)
K-THEORY AND THE DIRAC OPERATOR (1/4)
Lecture 1. WHAT IS K-THEORY AND WHAT IS IT GOOD FOR? (ENGLISH)
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Baum.pdf
Paul Baum 氏 (The Pennsylvania State University)
K-THEORY AND THE DIRAC OPERATOR (1/4)
Lecture 1. WHAT IS K-THEORY AND WHAT IS IT GOOD FOR? (ENGLISH)
[ 講演概要 ]
This talk will consist of four points.
1. The basic definition of K-theory
2. A brief history of K-theory
3. Algebraic versus topological K-theory
4. The unity of K-theory
[ 参考URL ]This talk will consist of four points.
1. The basic definition of K-theory
2. A brief history of K-theory
3. Algebraic versus topological K-theory
4. The unity of K-theory
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Baum.pdf
2018年10月16日(火)
解析学火曜セミナー
16:50-18:20 数理科学研究科棟(駒場) 128号室
土田哲生 氏 (名城大学)
直積型シュレディンガー方程式の正値解の構造 (日本語)
土田哲生 氏 (名城大学)
直積型シュレディンガー方程式の正値解の構造 (日本語)
[ 講演概要 ]
遠方で無限大になるポテンシャル関数をもつ１次元シュレディンガー作用素ふたつからなる２次元の直積型のシュレディンガー方程式を考え、マルチンの理論に基づいてマルチン境界とマルチン核を調べる。ポテンシャルの-1/2乗のべきと-3/2乗のべきが遠方で可積分かどうかに依って、正値解の構造が異なることを示す。（村田實氏（東工大）との共同研究）
遠方で無限大になるポテンシャル関数をもつ１次元シュレディンガー作用素ふたつからなる２次元の直積型のシュレディンガー方程式を考え、マルチンの理論に基づいてマルチン境界とマルチン核を調べる。ポテンシャルの-1/2乗のべきと-3/2乗のべきが遠方で可積分かどうかに依って、正値解の構造が異なることを示す。（村田實氏（東工大）との共同研究）
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
Daniel Matei 氏 (IMAR Bucharest)
Resonance varieties and matrix tree theorems (ENGLISH)
Tea: Common Room 16:30-17:00
Daniel Matei 氏 (IMAR Bucharest)
Resonance varieties and matrix tree theorems (ENGLISH)
[ 講演概要 ]
We discuss the resonance varieties, encoding vanishing of cohomology cup products, of various classes of finitely presented groups of geometric and combinatorial origin. We describe the ideals defining those varieties in terms spanning trees in a similar vein with the classical matrix tree theorem in graph theory. We present applications of this description to 3-manifold groups and Artin groups.
We discuss the resonance varieties, encoding vanishing of cohomology cup products, of various classes of finitely presented groups of geometric and combinatorial origin. We describe the ideals defining those varieties in terms spanning trees in a similar vein with the classical matrix tree theorem in graph theory. We present applications of this description to 3-manifold groups and Artin groups.
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
Tuyen Truong 氏 (Oslo)
A countable characterisation of smooth algebraic plane curves, and generalisations (English)
Tuyen Truong 氏 (Oslo)
A countable characterisation of smooth algebraic plane curves, and generalisations (English)
[ 講演概要 ]
Given a smooth algebraic curve X in C^3, I will present a way to construct a sequence of algebraic varieties (whose ideals are explicitly determined from the ideal defining X), whose solution set is non-empty iff the curve X can be algebraically embedded into C^2.
Various other questions, such as whether two given algebraic varieties are birational, can be similarly treated. Some related conjectures are stated.
Given a smooth algebraic curve X in C^3, I will present a way to construct a sequence of algebraic varieties (whose ideals are explicitly determined from the ideal defining X), whose solution set is non-empty iff the curve X can be algebraically embedded into C^2.
Various other questions, such as whether two given algebraic varieties are birational, can be similarly treated. Some related conjectures are stated.
2018年10月15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
堀田一敬 氏 (山口大学)
Recent problems on Loewner theory (JAPANESE)
堀田一敬 氏 (山口大学)
Recent problems on Loewner theory (JAPANESE)
[ 講演概要 ]
Loewner Theory, which goes back to the parametric representation of univalent functions introduced by Loewner in 1923, has recently undergone significant development in various directions, including Schramm’s stochastic version of the Loewner differential equation and the new intrinsic approach suggested by Bracci, Contreras, Diaz-Madrigal and Gumenyuk.
In this talk, we firstly review the theory of Loewner equations in classical and modern treatments. Then we discuss some recent problems on the theory:
(i) Quasiconformal extensions of Loewner chains;
(ii) Hydrodynamics of multiple SLE.
Loewner Theory, which goes back to the parametric representation of univalent functions introduced by Loewner in 1923, has recently undergone significant development in various directions, including Schramm’s stochastic version of the Loewner differential equation and the new intrinsic approach suggested by Bracci, Contreras, Diaz-Madrigal and Gumenyuk.
In this talk, we firstly review the theory of Loewner equations in classical and modern treatments. Then we discuss some recent problems on the theory:
(i) Quasiconformal extensions of Loewner chains;
(ii) Hydrodynamics of multiple SLE.
数値解析セミナー
16:50-18:20 数理科学研究科棟(駒場) 002号室
長澤壯之 氏 (埼玉大学大学院理工学研究科)
MöbiusエネルギーのMöbius不変な離散化と分解 (Japanese)
長澤壯之 氏 (埼玉大学大学院理工学研究科)
MöbiusエネルギーのMöbius不変な離散化と分解 (Japanese)
[ 講演概要 ]
O'Haraによって提唱された結び目のエネルギーの一つであるMöbiusエネルギーは、Möbius不変性を持つ事がその名前の由来となっている。エネルギーは(少なくとも見かけ上は)特異性を有するエネルギー密度の積分で与えられる事もあり、エネルギー値を手計算で求める事は多くの場合困難である。そのため、結び目を多角形で近似しエネルギー値を近似的に求めるという考えが自然に浮かぶ。そのためには多角形に対するエネルギー(離散エネルギー)が必要である。実際、幾つかの離散エネルギーが提唱されているが、それらは元のエネルギーが有するMöbius不変という性質を失っている。ここでは、Möbius不変性という構造をもった離散エネルギーを提唱し、その収束性を論 じる。また、MöbiusエネルギーはMöbius不変な分解が知られている。提唱する離散エネルギーのMöbius不変分解も与える。本講演は、Simon Blatt (ザルツブルク大学) と石関 彩(千葉大学)との共同研究に基づく。
O'Haraによって提唱された結び目のエネルギーの一つであるMöbiusエネルギーは、Möbius不変性を持つ事がその名前の由来となっている。エネルギーは(少なくとも見かけ上は)特異性を有するエネルギー密度の積分で与えられる事もあり、エネルギー値を手計算で求める事は多くの場合困難である。そのため、結び目を多角形で近似しエネルギー値を近似的に求めるという考えが自然に浮かぶ。そのためには多角形に対するエネルギー(離散エネルギー)が必要である。実際、幾つかの離散エネルギーが提唱されているが、それらは元のエネルギーが有するMöbius不変という性質を失っている。ここでは、Möbius不変性という構造をもった離散エネルギーを提唱し、その収束性を論 じる。また、MöbiusエネルギーはMöbius不変な分解が知られている。提唱する離散エネルギーのMöbius不変分解も与える。本講演は、Simon Blatt (ザルツブルク大学) と石関 彩(千葉大学)との共同研究に基づく。
2018年10月11日(木)
応用解析セミナー
16:00-17:30 数理科学研究科棟(駒場) 118号室
柏原崇人 氏 (東京大学)
Navier-Stokes方程式に対する摩擦型境界条件とその周辺 (Japanese)
柏原崇人 氏 (東京大学)
Navier-Stokes方程式に対する摩擦型境界条件とその周辺 (Japanese)
[ 講演概要 ]
非圧縮流体の支配方程式であるNavier-Stokes方程式を考える際，壁面における境界条件としては滑りなし条件（斉次Dirichlet境界条件）を課すことが多い．一方で，現実の複雑な問題を数値シミュレーション等で扱う際には，滑りがある場合とない場合が共存するような状況を考えたいことがある．摩擦型境界条件はそのような状況をモデル化した非線形な境界条件であり，1994年にH. Fujitaによって導入された．本講演の前半では，定常Stokes方程式に対する摩擦型境界条件問題の数値解析（特に有限要素法による誤差評価）および，非定常Navier-Stokes方程式に対する同問題の数学解析（時間局所的な強解の存在と一意性）の結果を紹介したい．時間が許せば，現在考察中のトピックとして，Serrinの摩擦型境界条件や，摩擦型の（境界条件ではなく）interface問題の定式化について述べたい．
非圧縮流体の支配方程式であるNavier-Stokes方程式を考える際，壁面における境界条件としては滑りなし条件（斉次Dirichlet境界条件）を課すことが多い．一方で，現実の複雑な問題を数値シミュレーション等で扱う際には，滑りがある場合とない場合が共存するような状況を考えたいことがある．摩擦型境界条件はそのような状況をモデル化した非線形な境界条件であり，1994年にH. Fujitaによって導入された．本講演の前半では，定常Stokes方程式に対する摩擦型境界条件問題の数値解析（特に有限要素法による誤差評価）および，非定常Navier-Stokes方程式に対する同問題の数学解析（時間局所的な強解の存在と一意性）の結果を紹介したい．時間が許せば，現在考察中のトピックとして，Serrinの摩擦型境界条件や，摩擦型の（境界条件ではなく）interface問題の定式化について述べたい．
2018年10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
Kaijing Ling 氏 (Harbin Institute of Technology/Univ. Tokyo)
Extension modules over some conformal algebras related Virasoro algebra (English)
Kaijing Ling 氏 (Harbin Institute of Technology/Univ. Tokyo)
Extension modules over some conformal algebras related Virasoro algebra (English)
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