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過去の記録
過去の記録 ～01/17｜本日 01/18 | 今後の予定 01/19～
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
2019年07月09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
Florent Schaffhauser 氏 (Université de Strasbourg)
Mod 2 cohomology of moduli stacks of real vector bundles (ENGLISH)
Tea: Common Room 16:30-17:00
Florent Schaffhauser 氏 (Université de Strasbourg)
Mod 2 cohomology of moduli stacks of real vector bundles (ENGLISH)
[ 講演概要 ]
The rational cohomology ring of the moduli stack of holomorphic vector bundles of fixed rank and degree over a compact Riemann surface was studied by Atiyah and Bott using tools of differential geometry and algebraic topology: they found generators of that ring and computed its Poincaré series. In joint work with Chiu-Chu Melissa Liu, we study in a similar way the mod 2 cohomology ring of the moduli stack of real vector bundles of fixed topological type over a compact Riemann surface with real structure. The goal of the talk is to explain the principle of that computation, emphasizing the analogies and differences between the real and complex cases, and discuss applications of the method. In particular, we provide explicit generators of mod 2 cohomology rings of moduli stacks of vector bundles over a real algebraic curve.
The rational cohomology ring of the moduli stack of holomorphic vector bundles of fixed rank and degree over a compact Riemann surface was studied by Atiyah and Bott using tools of differential geometry and algebraic topology: they found generators of that ring and computed its Poincaré series. In joint work with Chiu-Chu Melissa Liu, we study in a similar way the mod 2 cohomology ring of the moduli stack of real vector bundles of fixed topological type over a compact Riemann surface with real structure. The goal of the talk is to explain the principle of that computation, emphasizing the analogies and differences between the real and complex cases, and discuss applications of the method. In particular, we provide explicit generators of mod 2 cohomology rings of moduli stacks of vector bundles over a real algebraic curve.
代数幾何学セミナー
13:00-14:30 数理科学研究科棟(駒場) 122号室
いつもと曜日・時間・部屋が異なります。
佐野 太郎 氏 (神戸大学)
Construction of non-Kähler Calabi-Yau 3-folds by smoothing normal crossing varieties (TBA)
いつもと曜日・時間・部屋が異なります。
佐野 太郎 氏 (神戸大学)
Construction of non-Kähler Calabi-Yau 3-folds by smoothing normal crossing varieties (TBA)
[ 講演概要 ]
It is an open problem whether there are only finitely many diffeomorphism types of projective Calabi-Yau 3-folds. Kawamata--Namikawa developed log deformation theory of normal crossing Calabi-Yau varieties. As an application of their result, one can construct examples of Calabi-Yau manifolds by smoothing SNC varieties. In this talk, I will explain how to construct examples of non-Kähler Calabi-Yau 3-folds with arbitrarily large 2nd Betti numbers. If time permits, I will also explain an example of involutions on a family of K3 surfaces which do not lift biregularly to the total space. This is based on joint work with Kenji Hashimoto.
It is an open problem whether there are only finitely many diffeomorphism types of projective Calabi-Yau 3-folds. Kawamata--Namikawa developed log deformation theory of normal crossing Calabi-Yau varieties. As an application of their result, one can construct examples of Calabi-Yau manifolds by smoothing SNC varieties. In this talk, I will explain how to construct examples of non-Kähler Calabi-Yau 3-folds with arbitrarily large 2nd Betti numbers. If time permits, I will also explain an example of involutions on a family of K3 surfaces which do not lift biregularly to the total space. This is based on joint work with Kenji Hashimoto.
2019年07月08日(月)
数値解析セミナー
16:50-18:20 数理科学研究科棟(駒場) 056号室
松田孟留 氏 (東京大学大学院情報理工学系研究科)
離散化誤差を考慮した常微分方程式モデルのパラメータ推定 (Japanese)
松田孟留 氏 (東京大学大学院情報理工学系研究科)
離散化誤差を考慮した常微分方程式モデルのパラメータ推定 (Japanese)
[ 講演概要 ]
常微分方程式でモデル化される現象において、観測データをもとにモデルのパラメータを推定する問題を考える。 ルンゲクッタ法などで得られる数値解を観測データに当てはめる方法が標準的であるが、この方法では数値解に含まれる離散化誤差によって推定精度が悪化しうる。
たとえば、高次元の常微分方程式においては計算量の観点から時間刻みを十分小さくとれないため、離散化誤差を無視できないと考えられる。 そこで本研究では、データに基づいて離散化誤差の大きさを見積もることでパラメータの推定精度を改善する手法を提案する。 数値実験によって、提案手法が離散化誤差を適切に定量化して推定精度を改善することが確認された。 本研究は大阪大学の宮武勇登准教授との共同研究である。
常微分方程式でモデル化される現象において、観測データをもとにモデルのパラメータを推定する問題を考える。 ルンゲクッタ法などで得られる数値解を観測データに当てはめる方法が標準的であるが、この方法では数値解に含まれる離散化誤差によって推定精度が悪化しうる。
たとえば、高次元の常微分方程式においては計算量の観点から時間刻みを十分小さくとれないため、離散化誤差を無視できないと考えられる。 そこで本研究では、データに基づいて離散化誤差の大きさを見積もることでパラメータの推定精度を改善する手法を提案する。 数値実験によって、提案手法が離散化誤差を適切に定量化して推定精度を改善することが確認された。 本研究は大阪大学の宮武勇登准教授との共同研究である。
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
金子 宏 氏 (東京理科大学)
荷重つき無限グラフにおけるリーマン-ロッホの定理 (Japanese)
金子 宏 氏 (東京理科大学)
荷重つき無限グラフにおけるリーマン-ロッホの定理 (Japanese)
[ 講演概要 ]
A Riemann-Roch theorem on a connected finite graph was initiated by M. Baker and S. Norine, where connected graph with finite vertices was investigated and unit weight was given on each edge and vertex of the graph. Since a counterpart of the lowest exponents of the complex variable in the Laurent series was proposed as divisor for the Riemann-Roch theorem on graph, its relationships with tropical geometry were highlighted earlier than other complex analytical observations on graphs. On the other hand, M. Baker and F. Shokrieh revealed tight relationships between chip-firing games and potential theory on graphs, by characterizing reduced divisors on graphs as the solution to an energy minimization problem. The objective of this talk is to establish a Riemann-Roch theorem on an edge-weighted infinite graph. We introduce vertex weight assigned by the given weights of adjacent edges other than the units for expression of divisors and assume finiteness of total mass of graph. This is a joint work with A. Atsuji.
A Riemann-Roch theorem on a connected finite graph was initiated by M. Baker and S. Norine, where connected graph with finite vertices was investigated and unit weight was given on each edge and vertex of the graph. Since a counterpart of the lowest exponents of the complex variable in the Laurent series was proposed as divisor for the Riemann-Roch theorem on graph, its relationships with tropical geometry were highlighted earlier than other complex analytical observations on graphs. On the other hand, M. Baker and F. Shokrieh revealed tight relationships between chip-firing games and potential theory on graphs, by characterizing reduced divisors on graphs as the solution to an energy minimization problem. The objective of this talk is to establish a Riemann-Roch theorem on an edge-weighted infinite graph. We introduce vertex weight assigned by the given weights of adjacent edges other than the units for expression of divisors and assume finiteness of total mass of graph. This is a joint work with A. Atsuji.
2019年07月05日(金)
代数幾何学セミナー
10:30-12:00 数理科学研究科棟(駒場) 123号室
いつもと曜日・時間・部屋が異なります。
榎園 誠 氏 (東京理科大学)
Durfee-type inequality for complete intersection surface singularities
いつもと曜日・時間・部屋が異なります。
榎園 誠 氏 (東京理科大学)
Durfee-type inequality for complete intersection surface singularities
[ 講演概要 ]
Durfee's negativity conjecture says that the signature of the Milnor fiber of a 2-dimensional isolated complete intersection singularity is always negative. In this talk, I will explain that this conjecture is true (more precisely, the signature is bounded above by the negative number determined by the geometric genus, the embedding dimension and the number of irreducible components of the exceptional set of the minimal resolution) by using the theory of invariants of fibered surfaces. If time permits, I will explain the higher dimensional analogue of Durfee's conjecture for isolated complete intersection singularities.
Durfee's negativity conjecture says that the signature of the Milnor fiber of a 2-dimensional isolated complete intersection singularity is always negative. In this talk, I will explain that this conjecture is true (more precisely, the signature is bounded above by the negative number determined by the geometric genus, the embedding dimension and the number of irreducible components of the exceptional set of the minimal resolution) by using the theory of invariants of fibered surfaces. If time permits, I will explain the higher dimensional analogue of Durfee's conjecture for isolated complete intersection singularities.
2019年07月04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)
同種写像暗号 (Japanese)
高島 克幸 氏 (三菱電機/九州大学)
同種写像暗号 (Japanese)
[ 講演概要 ]
本セミナーでは，既に「ポスト量子」暗号への取り組みとして格子暗号を紹介したが，今回は，別の取り組みである楕円曲線を用いた同種写像暗号を紹介する．暗号演算には，同種写像からなるグラフ上のランダムウォークが使われるので，例えば，超特異曲線同種写像から得られるラマヌジャングラフの数理的な性質が，暗号の性能・安全性を理解する上で重要になる．それら数理的側面と共に，同種写像を使った鍵共有や署名方式について紹介する．
本セミナーでは，既に「ポスト量子」暗号への取り組みとして格子暗号を紹介したが，今回は，別の取り組みである楕円曲線を用いた同種写像暗号を紹介する．暗号演算には，同種写像からなるグラフ上のランダムウォークが使われるので，例えば，超特異曲線同種写像から得られるラマヌジャングラフの数理的な性質が，暗号の性能・安全性を理解する上で重要になる．それら数理的側面と共に，同種写像を使った鍵共有や署名方式について紹介する．
2019年07月03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
Amine Marrakchi 氏 (京大数理研)
Tensor product decompositions and rigidity of full factors
Amine Marrakchi 氏 (京大数理研)
Tensor product decompositions and rigidity of full factors
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
佐藤謙 氏 (東京大学数理科学研究科)
Explicit calculation of values of the regulator maps on a certain type of Kummer surfaces (Japanese)
佐藤謙 氏 (東京大学数理科学研究科)
Explicit calculation of values of the regulator maps on a certain type of Kummer surfaces (Japanese)
[ 講演概要 ]
複素数に埋め込まれた体K上定義された射影代数多様体Xに対して、レギュレーター写像というモチヴィックコホモロジーからDeligneコホモロジーへの写像がBeilinsonにより定義された。特にKが有理数体の時、Beilinsonによりレギュレーター写像の値はモチーフのL関数の特殊値の無理数部分と結びつくと予想されているが、予想が成り立つことが知られている例は少ない。しかしながら、レギュレーター写像の値を超幾何関数のような特殊関数を用いて表す研究は朝倉政典氏や大坪紀之氏の研究に見られるように近年盛んである。本講演では、楕円曲線の直積に付随するようなKummer曲面に対し、高次Chow群との同型を用いてモチヴィックコホモロジーの中に具体的に元を構成し、その元のレギュレーター写像による値を考察する。またその応用として、上記の曲面のモチヴィックコホモロジーのindecomposal partが複素数体上十分一般の場合に消えていないことを示す。
複素数に埋め込まれた体K上定義された射影代数多様体Xに対して、レギュレーター写像というモチヴィックコホモロジーからDeligneコホモロジーへの写像がBeilinsonにより定義された。特にKが有理数体の時、Beilinsonによりレギュレーター写像の値はモチーフのL関数の特殊値の無理数部分と結びつくと予想されているが、予想が成り立つことが知られている例は少ない。しかしながら、レギュレーター写像の値を超幾何関数のような特殊関数を用いて表す研究は朝倉政典氏や大坪紀之氏の研究に見られるように近年盛んである。本講演では、楕円曲線の直積に付随するようなKummer曲面に対し、高次Chow群との同型を用いてモチヴィックコホモロジーの中に具体的に元を構成し、その元のレギュレーター写像による値を考察する。またその応用として、上記の曲面のモチヴィックコホモロジーのindecomposal partが複素数体上十分一般の場合に消えていないことを示す。
2019年07月02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
若月 駿 氏 (東京大学大学院数理科学研究科)
Brane coproducts and their applications (JAPANESE)
Tea: Common Room 16:30-17:00
若月 駿 氏 (東京大学大学院数理科学研究科)
Brane coproducts and their applications (JAPANESE)
[ 講演概要 ]
The loop coproduct is a coproduct on the homology of the free loop space of a Poincaré duality space (or more generally a Gorenstein space). In this talk, I will introduce two kinds of brane coproducts which are generalizations of the loop coproduct to the homology of a sphere space (i.e. the mapping space from a sphere). Their constructions are based on the finiteness of the dimensions of mapping spaces in some sense. As an application, I will show the vanishing of some cup products on sphere spaces by comparing these two brane coproducts. This gives a generalization of a result of Menichi for the case of free loop spaces.
The loop coproduct is a coproduct on the homology of the free loop space of a Poincaré duality space (or more generally a Gorenstein space). In this talk, I will introduce two kinds of brane coproducts which are generalizations of the loop coproduct to the homology of a sphere space (i.e. the mapping space from a sphere). Their constructions are based on the finiteness of the dimensions of mapping spaces in some sense. As an application, I will show the vanishing of some cup products on sphere spaces by comparing these two brane coproducts. This gives a generalization of a result of Menichi for the case of free loop spaces.
2019年07月01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
Yeping Zhang 氏 (京都大学)
BCOV invariant and birational equivalence (English)
Yeping Zhang 氏 (京都大学)
BCOV invariant and birational equivalence (English)
[ 講演概要 ]
Bershadsky, Cecotti, Ooguri and Vafa constructed a real valued invariant for Calabi-Yau manifolds, which is now called BCOV invariant. Now we consider a pair (X,Y), where X is a Kaehler manifold and $Y ¥subseteq X$ is a canonical divisor. In this talk, we extend the BCOV invariant to such pairs. The extended BCOV invariant is well-behaved under birational equivalence. We expect that these considerations may eventually lead to a positive answer to Yoshikawa's conjecture that the BCOV invariant for Calabi-Yau threefold is a birational invariant.
Bershadsky, Cecotti, Ooguri and Vafa constructed a real valued invariant for Calabi-Yau manifolds, which is now called BCOV invariant. Now we consider a pair (X,Y), where X is a Kaehler manifold and $Y ¥subseteq X$ is a canonical divisor. In this talk, we extend the BCOV invariant to such pairs. The extended BCOV invariant is well-behaved under birational equivalence. We expect that these considerations may eventually lead to a positive answer to Yoshikawa's conjecture that the BCOV invariant for Calabi-Yau threefold is a birational invariant.
社会数理コロキウム
17:00-18:30 数理科学研究科棟(駒場) 056号室
18:30から 2階コモンルームで講演者を囲んで情報交換会を予定しております。
藤原 洋 氏 (株式会社ブロードバンドタワー 代表取締役会長兼社長CEO)
全産業デジタル化と数学力による日本創生戦略 (JAPANESE)
http://fmsp.ms.u-tokyo.ac.jp/FMSP_colloquium20190701.pdf
18:30から 2階コモンルームで講演者を囲んで情報交換会を予定しております。
藤原 洋 氏 (株式会社ブロードバンドタワー 代表取締役会長兼社長CEO)
全産業デジタル化と数学力による日本創生戦略 (JAPANESE)
[ 講演概要 ]
AI や5G、IoT（モノのインターネット）は、近い将来、日本経済に多大な恩恵をもたらしうる。実際、AI やIoT を「武器」に、成長し続ける日本企業は少なくない。そこで本講演では、デジタル産業の創生に関わり続けてきた経験をもとに、「デジタルトランスフォーメーションという大きなうねり」によって、情報通信、流通、農業、金融・保険、医療・福祉がどう変わるかついて述べる。そして、急速に進化するデジタル社会を生き抜くには何が必要か？ 変化の本質を見極め牽引するために不可欠な数学・数理科学の重要性を説く。
[ 参考URL ]AI や5G、IoT（モノのインターネット）は、近い将来、日本経済に多大な恩恵をもたらしうる。実際、AI やIoT を「武器」に、成長し続ける日本企業は少なくない。そこで本講演では、デジタル産業の創生に関わり続けてきた経験をもとに、「デジタルトランスフォーメーションという大きなうねり」によって、情報通信、流通、農業、金融・保険、医療・福祉がどう変わるかついて述べる。そして、急速に進化するデジタル社会を生き抜くには何が必要か？ 変化の本質を見極め牽引するために不可欠な数学・数理科学の重要性を説く。
http://fmsp.ms.u-tokyo.ac.jp/FMSP_colloquium20190701.pdf
数値解析セミナー
16:50-18:20 数理科学研究科棟(駒場) 117号室
河原田秀夫 氏 (AMSOK, 千葉大学名誉教授)
セラミックス球によるスケール形成防止効果と人体に及ぼす効用 (Japanese)
河原田秀夫 氏 (AMSOK, 千葉大学名誉教授)
セラミックス球によるスケール形成防止効果と人体に及ぼす効用 (Japanese)
[ 講演概要 ]
セラミックス球を電解質溶液に浸したその界面に超強電場が発生することが知られている 。その電場に接触した炭酸カルシウム結晶に電気分極を生じ、それに基づく電気的エネル ギー（分極エネルギー）が化学ポテンシャルの一部として分配される。この分極エネルギ ーは核の生成を極端に妨害すると同時に生成した核の表面自由エネルギーを減少させる。 この現象がスケール形成防止効果を表現している。そのメカニズムが数理的手法を用いて 解明される。 更に、上記超強電場が水の分子集団に上記と同様な変化を生成することが 示される。この事実をもとにセラミックス球を人体に接触させたとき、如何なる現象が生 じるかについて議論する。
セラミックス球を電解質溶液に浸したその界面に超強電場が発生することが知られている 。その電場に接触した炭酸カルシウム結晶に電気分極を生じ、それに基づく電気的エネル ギー（分極エネルギー）が化学ポテンシャルの一部として分配される。この分極エネルギ ーは核の生成を極端に妨害すると同時に生成した核の表面自由エネルギーを減少させる。 この現象がスケール形成防止効果を表現している。そのメカニズムが数理的手法を用いて 解明される。 更に、上記超強電場が水の分子集団に上記と同様な変化を生成することが 示される。この事実をもとにセラミックス球を人体に接触させたとき、如何なる現象が生 じるかについて議論する。
数理人口学・数理生物学セミナー
11:00-12:00 数理科学研究科棟(駒場) 123号室
Joel E. Cohen 氏 (The Rockefeller University and Columbia University)
Taylor's Law of Fluctuation Scaling
https://www.rockefeller.edu/our-scientists/heads-of-laboratories/940-joel-e-cohen/
Joel E. Cohen 氏 (The Rockefeller University and Columbia University)
Taylor's Law of Fluctuation Scaling
[ 講演概要 ]
A family of nonnegative random variables is said to obey Taylor's law when the variance is proportional to some power b of the mean. For example, in the family of exponential distributions, if the mean is m, then the variance is m^2, so the family of exponential distributions obeys Taylor's law exactly with b=2. Many stochastic processes and the prime numbers obey Taylor's law (exactly or asymptotically). Thousands of empirical illustrations of Taylor's law have been published in many different fields including ecology, demography, finance (stock and currency trading), cancer biology, genetics, fisheries, forestry, meteorology, agriculture, physics, cell biology, computer network engineering, and number theory. This survey talk will review some empirical and theoretical results and open problems about Taylor's law, including recently proved versions of Taylor's law for nonnegative stable laws with infinite mean.
[ 参考URL ]A family of nonnegative random variables is said to obey Taylor's law when the variance is proportional to some power b of the mean. For example, in the family of exponential distributions, if the mean is m, then the variance is m^2, so the family of exponential distributions obeys Taylor's law exactly with b=2. Many stochastic processes and the prime numbers obey Taylor's law (exactly or asymptotically). Thousands of empirical illustrations of Taylor's law have been published in many different fields including ecology, demography, finance (stock and currency trading), cancer biology, genetics, fisheries, forestry, meteorology, agriculture, physics, cell biology, computer network engineering, and number theory. This survey talk will review some empirical and theoretical results and open problems about Taylor's law, including recently proved versions of Taylor's law for nonnegative stable laws with infinite mean.
https://www.rockefeller.edu/our-scientists/heads-of-laboratories/940-joel-e-cohen/
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