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過去の記録 ～04/17｜本日 04/18 | 今後の予定 04/19～
博士論文発表会
13:00-14:15 数理科学研究科棟(駒場) 118号室
王 龍 氏 (東京大学大学院数理科学研究科)
Studies on the Cone Conjecture, Automorphisms, and Arithmetic Degrees
(錐予想, 自己同型と算術次数の研究)
王 龍 氏 (東京大学大学院数理科学研究科)
Studies on the Cone Conjecture, Automorphisms, and Arithmetic Degrees
(錐予想, 自己同型と算術次数の研究)
博士論文発表会
13:00-14:15 数理科学研究科棟(駒場) 122号室
キム ミンギュ 氏 (東京大学大学院数理科学研究科)
Finite path integral model and toric code based on homological algebra
(ホモロジー代数に基づく有限経路積分モデルとトーリックコード)
キム ミンギュ 氏 (東京大学大学院数理科学研究科)
Finite path integral model and toric code based on homological algebra
(ホモロジー代数に基づく有限経路積分モデルとトーリックコード)
博士論文発表会
14:45-16:00 数理科学研究科棟(駒場) 118号室
鶴崎 修功 氏 (東京大学大学院数理科学研究科)
Irreducible module decompositions of rank 2 symmetric hyperbolic Kac-Moody Lie algebras by sl2 subalgebras which are generalizations of principal sl2 subalgebras
(主sl2部分代数の一般化であるsl2部分代数によるrank2対称双曲型Kac-Moody Lie 代数の既約分解)
鶴崎 修功 氏 (東京大学大学院数理科学研究科)
Irreducible module decompositions of rank 2 symmetric hyperbolic Kac-Moody Lie algebras by sl2 subalgebras which are generalizations of principal sl2 subalgebras
(主sl2部分代数の一般化であるsl2部分代数によるrank2対称双曲型Kac-Moody Lie 代数の既約分解)
2023年01月20日(金)
談話会・数理科学講演会
15:30-16:30 ハイブリッド開催
数理科学研究科所属以外の方は、オンラインでのご参加（参考URLから参加登録）をお願いいたします。
Mikhail Bershtein 氏 (HSE大学, Skoltech)
Kyiv formula and its applications (ENGLISH)
https://u-tokyo-ac-jp.zoom.us/meeting/register/tZUrduioqjouG9wBfhl35VPxN_K92oa1wB4P
数理科学研究科所属以外の方は、オンラインでのご参加（参考URLから参加登録）をお願いいたします。
Mikhail Bershtein 氏 (HSE大学, Skoltech)
Kyiv formula and its applications (ENGLISH)
[ 講演概要 ]
The Kyiv formula gives the generic tau function of Painleve' equation (and more generally isomonodromy deformation equations) in terms of conformal blocks or Nekrasov partition function. I will explain the statement, examples and different approaches to the proof. If time permits, I will discuss some applications of this formula.
[ 参考URL ]The Kyiv formula gives the generic tau function of Painleve' equation (and more generally isomonodromy deformation equations) in terms of conformal blocks or Nekrasov partition function. I will explain the statement, examples and different approaches to the proof. If time permits, I will discuss some applications of this formula.
https://u-tokyo-ac-jp.zoom.us/meeting/register/tZUrduioqjouG9wBfhl35VPxN_K92oa1wB4P
東京名古屋代数セミナー
10:30-12:00 オンライン開催
オンライン開催の詳細は講演参考URLをご覧ください。
狩野 隼輔 氏 (東北大学)
Tropical cluster transformations and train track splittings (Japanese)
http://www.math.nagoya-u.ac.jp/~aaron.chan/TNAseminar.html
オンライン開催の詳細は講演参考URLをご覧ください。
狩野 隼輔 氏 (東北大学)
Tropical cluster transformations and train track splittings (Japanese)
[ 講演概要 ]
Fock-Goncharovは箙に対し、クラスター代数と呼ばれる組み合わせ構造を持つような概形であるクラスター多様体を定義した。
この概形は良い正値性を持つことから、半体値集合を考えることができる。
箙が点付き曲面の三角形分割から得られるとき、トロピカル半体値集合は曲面の測度付き葉層構造の空間の適切な拡張と同一視される。
クラスター多様体のトロピカル半体値集合はクラスター構造から定まるPL構造を持つが、一方で曲面の測度付き葉層構造の空間にはトレイントラックと呼ばれるグラフを用いたPL構造が定まることが知られている。
本講演では、Goncharov-Shenのクラスター多様体上のLandau-Ginzburgポテンシャル関数のトロピカル化を通してトレイントラックを翻訳し、2つのPL構造が同値であることを確認する。
またこれの応用として、一般の擬Anosov写像類が符号安定性と呼ばれる性質を持つことを説明する。
ミーティングID: 820 6834 6105
パスコード: 039914
[ 参考URL ]Fock-Goncharovは箙に対し、クラスター代数と呼ばれる組み合わせ構造を持つような概形であるクラスター多様体を定義した。
この概形は良い正値性を持つことから、半体値集合を考えることができる。
箙が点付き曲面の三角形分割から得られるとき、トロピカル半体値集合は曲面の測度付き葉層構造の空間の適切な拡張と同一視される。
クラスター多様体のトロピカル半体値集合はクラスター構造から定まるPL構造を持つが、一方で曲面の測度付き葉層構造の空間にはトレイントラックと呼ばれるグラフを用いたPL構造が定まることが知られている。
本講演では、Goncharov-Shenのクラスター多様体上のLandau-Ginzburgポテンシャル関数のトロピカル化を通してトレイントラックを翻訳し、2つのPL構造が同値であることを確認する。
またこれの応用として、一般の擬Anosov写像類が符号安定性と呼ばれる性質を持つことを説明する。
ミーティングID: 820 6834 6105
パスコード: 039914
http://www.math.nagoya-u.ac.jp/~aaron.chan/TNAseminar.html
2023年01月19日(木)
情報数学セミナー
16:50-18:35 数理科学研究科棟(駒場) 123号室
成定 真太郎 氏 (KDDI総合研究所)
符号暗号とその求解アルゴリズム (Japanese)
成定 真太郎 氏 (KDDI総合研究所)
符号暗号とその求解アルゴリズム (Japanese)
[ 講演概要 ]
耐量子暗号の候補である符号暗号について紹介するとともに、符号暗号の解読アルゴリズムであるInformation Set Decoding (ISD)について解説する。また、ISDの量子アルゴリズムについて紹介する。
耐量子暗号の候補である符号暗号について紹介するとともに、符号暗号の解読アルゴリズムであるInformation Set Decoding (ISD)について解説する。また、ISDの量子アルゴリズムについて紹介する。
2023年01月18日(水)
代数学コロキウム
17:00-18:00 ハイブリッド開催
Kestutis Cesnavicius 氏 (Paris-Saclay University)
The affine Grassmannian as a presheaf quotient (English)
Kestutis Cesnavicius 氏 (Paris-Saclay University)
The affine Grassmannian as a presheaf quotient (English)
[ 講演概要 ]
The affine Grassmannian of a reductive group G is usually defined as the étale sheafification of the quotient of the loop group LG by the positive loop subgroup. I will discuss various triviality results for G-torsors which imply that this sheafification is often not necessary.
The affine Grassmannian of a reductive group G is usually defined as the étale sheafification of the quotient of the loop group LG by the positive loop subgroup. I will discuss various triviality results for G-torsors which imply that this sheafification is often not necessary.
2023年01月17日(火)
トポロジー火曜セミナー
17:00-18:00 オンライン開催
参加を希望される場合は、セミナーのホームページから参加登録を行って下さい。
Chenghan Zha 氏 (東京大学大学院数理科学研究科)
Integral structures in the local algebra of a singularity (ENGLISH)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
参加を希望される場合は、セミナーのホームページから参加登録を行って下さい。
Chenghan Zha 氏 (東京大学大学院数理科学研究科)
Integral structures in the local algebra of a singularity (ENGLISH)
[ 講演概要 ]
We compute the image of the Milnor lattice of an ADE singularity under a period map. We also prove that the Milnor lattice can be identified with an appropriate relative K-group defined through the Berglund-Huebsch dual of the corresponding singularity. Furthermore, we figure out the image of the Milnor lattice of the singularity of an invertible polynomial of chain type using the basis of middle homology constructed by Otani-Takahashi. We calculated the Seifert form of the basis as well.
[ 参考URL ]We compute the image of the Milnor lattice of an ADE singularity under a period map. We also prove that the Milnor lattice can be identified with an appropriate relative K-group defined through the Berglund-Huebsch dual of the corresponding singularity. Furthermore, we figure out the image of the Milnor lattice of the singularity of an invertible polynomial of chain type using the basis of middle homology constructed by Otani-Takahashi. We calculated the Seifert form of the basis as well.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
2023年01月16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
対面・オンラインのハイブリッド形式で行います。オンライン参加される場合は参考URLからご登録ください。
小池貴之 氏 (大阪公立大学)
Holomorphic foliation associated with a semi-positive class of numerical dimension one (Japanese)
https://forms.gle/hYT2hVhDE3q1wDSh6
対面・オンラインのハイブリッド形式で行います。オンライン参加される場合は参考URLからご登録ください。
小池貴之 氏 (大阪公立大学)
Holomorphic foliation associated with a semi-positive class of numerical dimension one (Japanese)
[ 講演概要 ]
Let $X$ be a compact Kähler manifold and $\alpha$ be a Dolbeault cohomology class of bidegree $(1,1)$ on $X$.
When the numerical dimension of $\alpha$ is one and $\alpha$ admits at least two smooth semi-positive representatives, we show the existence of a family of real analytic Levi-flat hypersurfaces in $X$ and a holomorphic foliation on a suitable domain of $X$ along whose leaves any semi-positive representative of $\alpha$ is zero.
As an application, we give the affirmative answer to a conjecture on the relation between the semi-positivity of the line bundle $[Y]$ and the analytic structure of a neighborhood of $Y$ for a smooth connected hypersurface $Y$ of $X$.
[ 参考URL ]Let $X$ be a compact Kähler manifold and $\alpha$ be a Dolbeault cohomology class of bidegree $(1,1)$ on $X$.
When the numerical dimension of $\alpha$ is one and $\alpha$ admits at least two smooth semi-positive representatives, we show the existence of a family of real analytic Levi-flat hypersurfaces in $X$ and a holomorphic foliation on a suitable domain of $X$ along whose leaves any semi-positive representative of $\alpha$ is zero.
As an application, we give the affirmative answer to a conjecture on the relation between the semi-positivity of the line bundle $[Y]$ and the analytic structure of a neighborhood of $Y$ for a smooth connected hypersurface $Y$ of $X$.
https://forms.gle/hYT2hVhDE3q1wDSh6
2023年01月13日(金)
離散数理モデリングセミナー
13:15-14:45 数理科学研究科棟(駒場) 126号室
Andy Hone 氏 (University of Kent)
An infinite sequence of Heron triangles with two rational medians (English)
Andy Hone 氏 (University of Kent)
An infinite sequence of Heron triangles with two rational medians (English)
[ 講演概要 ]
Triangles with integer length sides and integer area are known as Heron triangles. Taking rescaling freedom into account, one can apply the same name when all sides and the area are rational numbers. A perfect triangle is a Heron triangle with all three medians being rational, and it is a longstanding conjecture that no such triangle exists. However, despite an assertion by Schubert that even two rational medians are impossible, Buchholz and Rathbun showed that there are infinitely many Heron triangles with two rational medians, an infinite subset of which are associated with rational points on an elliptic curve E(Q) with Mordell-Weil group Z x Z/2Z, and they observed a connection with a pair of Somos-5 sequences. Here we make the latter connection more precise by providing explicit formulae for the integer side lengths, the two rational medians, and the area in this infinite family of Heron triangles. The proof uses a combined approach to Somos-5 sequences and associated Quispel-Roberts-Thompson (QRT) maps in the plane, from several different viewpoints: complex analysis, real dynamics, and reduction modulo a prime.
Triangles with integer length sides and integer area are known as Heron triangles. Taking rescaling freedom into account, one can apply the same name when all sides and the area are rational numbers. A perfect triangle is a Heron triangle with all three medians being rational, and it is a longstanding conjecture that no such triangle exists. However, despite an assertion by Schubert that even two rational medians are impossible, Buchholz and Rathbun showed that there are infinitely many Heron triangles with two rational medians, an infinite subset of which are associated with rational points on an elliptic curve E(Q) with Mordell-Weil group Z x Z/2Z, and they observed a connection with a pair of Somos-5 sequences. Here we make the latter connection more precise by providing explicit formulae for the integer side lengths, the two rational medians, and the area in this infinite family of Heron triangles. The proof uses a combined approach to Somos-5 sequences and associated Quispel-Roberts-Thompson (QRT) maps in the plane, from several different viewpoints: complex analysis, real dynamics, and reduction modulo a prime.
2023年01月12日(木)
情報数学セミナー
16:50-18:35 数理科学研究科棟(駒場) 123号室
鈴木 泰成 氏 (NTT)
誤り耐性量子計算の理論II (Japanese)
鈴木 泰成 氏 (NTT)
誤り耐性量子計算の理論II (Japanese)
[ 講演概要 ]
信頼性のある量子計算を行うには、量子誤り訂正を組み込んだ誤り耐性量子計算機の実現が重要となる。本講義では誤り耐性量子計算の基本的な考え方や、その仕組みについて解説する。
信頼性のある量子計算を行うには、量子誤り訂正を組み込んだ誤り耐性量子計算機の実現が重要となる。本講義では誤り耐性量子計算の基本的な考え方や、その仕組みについて解説する。
講演会
16:00-17:00 オンライン開催
Prof. Yi-Hsuan Lin 氏 (National Yang Ming Chiao Tung University, Taiwan)
The Calder'on problem for nonlocal parabolic operators (English)
https://u-tokyo-ac-jp.zoom.us/j/82806510515?pwd=NEk1RDlMVEFOTEg4WE1MekRySlJpdz09
Prof. Yi-Hsuan Lin 氏 (National Yang Ming Chiao Tung University, Taiwan)
The Calder'on problem for nonlocal parabolic operators (English)
[ 講演概要 ]
We investigate inverse problems in the determination of leading coefficients for nonlocal parabolic operators, by knowing the corresponding Cauchy data in the exterior space-time domain. The key contribution is that we reduce nonlocal parabolic inverse problems to the corresponding local inverse problems with the lateral boundary Cauchy data. In addition, we derive a new equation and offer a novel proof of the unique continuation property for this new equation. We also build both uniqueness and non-uniqueness results for both nonlocal isotropic and anisotropic parabolic Calder'on problems, respectively.
This is a joint work with Ching-Lung Lin and Gunther Uhlmann.
[ 参考URL ]We investigate inverse problems in the determination of leading coefficients for nonlocal parabolic operators, by knowing the corresponding Cauchy data in the exterior space-time domain. The key contribution is that we reduce nonlocal parabolic inverse problems to the corresponding local inverse problems with the lateral boundary Cauchy data. In addition, we derive a new equation and offer a novel proof of the unique continuation property for this new equation. We also build both uniqueness and non-uniqueness results for both nonlocal isotropic and anisotropic parabolic Calder'on problems, respectively.
This is a joint work with Ching-Lung Lin and Gunther Uhlmann.
https://u-tokyo-ac-jp.zoom.us/j/82806510515?pwd=NEk1RDlMVEFOTEg4WE1MekRySlJpdz09
2023年01月11日(水)
離散数理モデリングセミナー
13:15-16:45 数理科学研究科棟(駒場) 056号室
Joe Harrow 氏 (University of Kent) 13:15-14:45
Determinantal expressions for Ohyama polynomials (English)
Discrete dynamics, continued fractions and hyperelliptic curves (English)
Joe Harrow 氏 (University of Kent) 13:15-14:45
Determinantal expressions for Ohyama polynomials (English)
[ 講演概要 ]
The Ohyama polynomials provide algebraic solutions of the D7 case of the Painleve III equation at a particular sequence of parameter values. It is known that many special function solutions of Painleve equations are expressed in terms of tau functions that can be written in the form of determinants, but until now such a representation for the Ohyama polynomials was not known. Here we present two different determinantal formulae for these polynomials: the first, in terms of Wronskian determinants related to a Darboux transformation for a Lax pair of KdV type; and the second, in terms of Hankel determinants, which is related to the Toda lattice. If time permits, then connections with orthogonal polynomials, and with the recent Riemann-Hilbert approach of Buckingham & Miller, will briefly be mentioned.
Andy Hone 氏 (University of Kent) 15:15-16:45The Ohyama polynomials provide algebraic solutions of the D7 case of the Painleve III equation at a particular sequence of parameter values. It is known that many special function solutions of Painleve equations are expressed in terms of tau functions that can be written in the form of determinants, but until now such a representation for the Ohyama polynomials was not known. Here we present two different determinantal formulae for these polynomials: the first, in terms of Wronskian determinants related to a Darboux transformation for a Lax pair of KdV type; and the second, in terms of Hankel determinants, which is related to the Toda lattice. If time permits, then connections with orthogonal polynomials, and with the recent Riemann-Hilbert approach of Buckingham & Miller, will briefly be mentioned.
Discrete dynamics, continued fractions and hyperelliptic curves (English)
[ 講演概要 ]
After reviewing some standard facts about continued fractions for quadratic irrationals, we switch from the real numbers to the field of Laurent series, and describe some classical and more recent results on continued fraction expansions for the square root of an even degree polynomial, and other functions defined on the associated hyperelliptic curve. In the latter case, we extend results of van der Poorten on continued fractions of Jacobi type (J-fractions), and explain the connection with a family of discrete integrable systems (including Quispel-Roberts-Thompson maps and Somos sequences), orthogonal polynomials, and the Toda lattice. If time permits, we will make some remarks on current work with John Roberts and Pol Vanhaecke, concerning expansions involving the square root of an odd degree polynomial, Stieltjes continued fractions, and the Volterra lattice.
After reviewing some standard facts about continued fractions for quadratic irrationals, we switch from the real numbers to the field of Laurent series, and describe some classical and more recent results on continued fraction expansions for the square root of an even degree polynomial, and other functions defined on the associated hyperelliptic curve. In the latter case, we extend results of van der Poorten on continued fractions of Jacobi type (J-fractions), and explain the connection with a family of discrete integrable systems (including Quispel-Roberts-Thompson maps and Somos sequences), orthogonal polynomials, and the Toda lattice. If time permits, we will make some remarks on current work with John Roberts and Pol Vanhaecke, concerning expansions involving the square root of an odd degree polynomial, Stieltjes continued fractions, and the Volterra lattice.
2023年01月10日(火)
代数幾何学セミナー
10:30-12:00 数理科学研究科棟(駒場) ハイブリッド開催/002号室
講演は対面で行い、Zoomで中継します。
東谷 章弘 氏 (大阪大情報)
Toric Fano varieties arising from posets and their combinatorial mutation equivalence (日本語)
講演は対面で行い、Zoomで中継します。
東谷 章弘 氏 (大阪大情報)
Toric Fano varieties arising from posets and their combinatorial mutation equivalence (日本語)
[ 講演概要 ]
In 1986, Stanley introduced two polytopes arising from posets, called order polytopes and chain polytopes. Since then, those polytopes have been studied from viewpoints of combinatorics. Projective toric varieties arising from order polytopes are called Hibi toric varieties in these days. On the other hand, combinatorial mutations were introduced by Akhtar-Coates-Galkin-Kasprzyk in 2012 in the context of the classification problem of Fano varieties using mirror symmetry.
In this talk, after surveying two poset polytopes and combinatorial mutations, we discuss the combinatorial mutation equivalence of two poset polytopes. Those equivalence implies qG-deformation equivalence of projective toric varieties arising from two poset polytopes.
Moreover, it turns out that order polytopes, chain polytopes and their intermediate polytopes correspond to some toric Fano varieties.
In 1986, Stanley introduced two polytopes arising from posets, called order polytopes and chain polytopes. Since then, those polytopes have been studied from viewpoints of combinatorics. Projective toric varieties arising from order polytopes are called Hibi toric varieties in these days. On the other hand, combinatorial mutations were introduced by Akhtar-Coates-Galkin-Kasprzyk in 2012 in the context of the classification problem of Fano varieties using mirror symmetry.
In this talk, after surveying two poset polytopes and combinatorial mutations, we discuss the combinatorial mutation equivalence of two poset polytopes. Those equivalence implies qG-deformation equivalence of projective toric varieties arising from two poset polytopes.
Moreover, it turns out that order polytopes, chain polytopes and their intermediate polytopes correspond to some toric Fano varieties.
講演会
16:00-17:00 オンライン開催
Professor Salah-Eddine CHORFI 氏 (Cadi Ayyad University, Faculty of Sciences, モロッコ)
Logarithmic convexity of semigroups and inverse problems for parabolic equations (English)
[ 参考URL ]
https://u-tokyo-ac-jp.zoom.us/j/83149935801?pwd=OE5aanNBVGxvajNycXgyb2RKcW1kZz09
Professor Salah-Eddine CHORFI 氏 (Cadi Ayyad University, Faculty of Sciences, モロッコ)
Logarithmic convexity of semigroups and inverse problems for parabolic equations (English)
[ 参考URL ]
https://u-tokyo-ac-jp.zoom.us/j/83149935801?pwd=OE5aanNBVGxvajNycXgyb2RKcW1kZz09
トポロジー火曜セミナー
17:00-18:00 オンライン開催
参加を希望される場合は、セミナーのホームページから参加登録を行って下さい。
浅香 猛 氏 (東京大学大学院数理科学研究科)
Some calculations of an earthquake map in the cross ratio coordinates and the earthquake theorem of cluster algebras of finite type (JAPANESE)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
参加を希望される場合は、セミナーのホームページから参加登録を行って下さい。
浅香 猛 氏 (東京大学大学院数理科学研究科)
Some calculations of an earthquake map in the cross ratio coordinates and the earthquake theorem of cluster algebras of finite type (JAPANESE)
[ 講演概要 ]
Thurston defined an earthquake, which cuts the Poincaré half-plane model and shifts it. Though it is a discontinuous bijective map, it can be extended to a homeomorphism of a circumference. Also, if an earthquake is equivalent relative to a Fuchsian group, the homeomorphism is equivalent, too. Moreover, Thurston proved the earthquake theorem saying that there uniquely exists an earthquake for any orient-preserving homeomorphism of a circumference, and Bonsante-Krasnov-Schlenker extended it to the case of marked surfaces. We calculate some earthquake maps by the cross ratio coordinates. The cross ratio coordinates are deeply related by the cluster algebra (Fock-Goncharov). We prove the earthquake theorem of cluster algebras of finite type. It is a joint work with Tsukasa Ishibashi and Shunsuke Kano.
[ 参考URL ]Thurston defined an earthquake, which cuts the Poincaré half-plane model and shifts it. Though it is a discontinuous bijective map, it can be extended to a homeomorphism of a circumference. Also, if an earthquake is equivalent relative to a Fuchsian group, the homeomorphism is equivalent, too. Moreover, Thurston proved the earthquake theorem saying that there uniquely exists an earthquake for any orient-preserving homeomorphism of a circumference, and Bonsante-Krasnov-Schlenker extended it to the case of marked surfaces. We calculate some earthquake maps by the cross ratio coordinates. The cross ratio coordinates are deeply related by the cluster algebra (Fock-Goncharov). We prove the earthquake theorem of cluster algebras of finite type. It is a joint work with Tsukasa Ishibashi and Shunsuke Kano.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
統計数学セミナー
10:50-11:30 数理科学研究科棟(駒場) 号室
現地参加（駒場Iキャンパス16号館827号室）とZoomによるハイブリッド配信
井口優雅 氏 (University College London)
Parameter Estimation with Increased Precision for Elliptic and Hypo-elliptic Diffusions
(現地参加) https://forms.gle/qwssLccVgsAWcfps7 (Zoom参加) (1/8迄) https://docs.google.com/forms/d/e/1FAIpQLSe7OYeMDfaZ7pTLO42k43Tn5dWKpsyw
現地参加（駒場Iキャンパス16号館827号室）とZoomによるハイブリッド配信
井口優雅 氏 (University College London)
Parameter Estimation with Increased Precision for Elliptic and Hypo-elliptic Diffusions
[ 講演概要 ]
Parametric inference for multi-dimensional diffusion processes has been studied over the past decades. Established approaches for likelihood-based estimation invoke a numerical time-discretisation scheme for the approximation of the (typically intractable) transition dynamics of the Stochastic Differential Equation (SDE) over finite time periods. Especially in the setting of some class of hypo-elliptic models, recent research (Ditlevsen and Samson 2019, Gloter and Yoshida 2021) has highlighted the critical effect of the choice of numerical scheme on the behaviour of derived parameter estimates. In our work, first, we develop two weak second order ‘sampling schemes' (to cover both the hypo-elliptic and elliptic classes) and generate accompanying ‘transition density schemes' of the SDE (i.e., approximations of the SDE transition density). Then, we produce a collection of analytic results, providing a complete theoretical framework that solidifies the proposed schemes and showcases advantages from their incorporation within SDE calibration methods, in both high and low frequency observations regime. We also present numerical results from carrying out classical or Bayesian inference. This is a joint work with Alexandros Beskos and Matthew Graham, and the preprint is available at https://arxiv.org/abs/2211.16384.
[ 参考URL ]Parametric inference for multi-dimensional diffusion processes has been studied over the past decades. Established approaches for likelihood-based estimation invoke a numerical time-discretisation scheme for the approximation of the (typically intractable) transition dynamics of the Stochastic Differential Equation (SDE) over finite time periods. Especially in the setting of some class of hypo-elliptic models, recent research (Ditlevsen and Samson 2019, Gloter and Yoshida 2021) has highlighted the critical effect of the choice of numerical scheme on the behaviour of derived parameter estimates. In our work, first, we develop two weak second order ‘sampling schemes' (to cover both the hypo-elliptic and elliptic classes) and generate accompanying ‘transition density schemes' of the SDE (i.e., approximations of the SDE transition density). Then, we produce a collection of analytic results, providing a complete theoretical framework that solidifies the proposed schemes and showcases advantages from their incorporation within SDE calibration methods, in both high and low frequency observations regime. We also present numerical results from carrying out classical or Bayesian inference. This is a joint work with Alexandros Beskos and Matthew Graham, and the preprint is available at https://arxiv.org/abs/2211.16384.
(現地参加) https://forms.gle/qwssLccVgsAWcfps7 (Zoom参加) (1/8迄) https://docs.google.com/forms/d/e/1FAIpQLSe7OYeMDfaZ7pTLO42k43Tn5dWKpsyw
2023年01月04日(水)
代数学コロキウム
17:00-18:00 ハイブリッド開催
伊藤和広 氏 (東京大学カブリ数物連携宇宙研究機構)
G-displays over prisms and deformation theory (Japanese)
伊藤和広 氏 (東京大学カブリ数物連携宇宙研究機構)
G-displays over prisms and deformation theory (Japanese)
[ 講演概要 ]
The notion of display, which was introduced by Zink, has been successfully applied to the deformation theory of p-divisible groups. Recently, for a reductive group G over the ring of p-adic integers, Lau introduced the notion of G-display. In this talk, following the approach of Lau, we study displays and G-displays over the prismatic site of Bhatt-Scholze, and explain the deformation theory for them. As an application, we give an alternative proof of the classification of p-divisible groups over a complete discrete valuation ring of mixed characteristic (0, p) with perfect residue field, using our deformation theory.
The notion of display, which was introduced by Zink, has been successfully applied to the deformation theory of p-divisible groups. Recently, for a reductive group G over the ring of p-adic integers, Lau introduced the notion of G-display. In this talk, following the approach of Lau, we study displays and G-displays over the prismatic site of Bhatt-Scholze, and explain the deformation theory for them. As an application, we give an alternative proof of the classification of p-divisible groups over a complete discrete valuation ring of mixed characteristic (0, p) with perfect residue field, using our deformation theory.
講演会
17:00-18:00 オンライン開催
Professor Debora Presti 氏 (Messina University)
On the source of the catastrophic 1908 Messina tsunami, southern Italy (English)
[ 参考URL ]
https://u-tokyo-ac-jp.zoom.us/j/81296515694?pwd=dlNZY2dZWDRENmdscjRWcFM1MjRCQT09
Professor Debora Presti 氏 (Messina University)
On the source of the catastrophic 1908 Messina tsunami, southern Italy (English)
[ 参考URL ]
https://u-tokyo-ac-jp.zoom.us/j/81296515694?pwd=dlNZY2dZWDRENmdscjRWcFM1MjRCQT09
2022年12月27日(火)
講演会
16:00-17:00 オンライン開催
Professor Salah-Eddine CHORFI 氏 (Cadi Ayyad University, Faculty of Sciences, モロッコ)
Controllability and inverse problems for parabolic equations with dynamic boundary conditions. (English)
[ 参考URL ]
https://u-tokyo-ac-jp.zoom.us/j/83149935801?pwd=OE5aanNBVGxvajNycXgyb2RKcW1kZz09
Professor Salah-Eddine CHORFI 氏 (Cadi Ayyad University, Faculty of Sciences, モロッコ)
Controllability and inverse problems for parabolic equations with dynamic boundary conditions. (English)
[ 参考URL ]
https://u-tokyo-ac-jp.zoom.us/j/83149935801?pwd=OE5aanNBVGxvajNycXgyb2RKcW1kZz09
2022年12月22日(木)
情報数学セミナー
16:50-18:35 数理科学研究科棟(駒場) 123号室
12月15日（木）は講演なし
鈴木 泰成 氏 (NTT)
誤り耐性量子計算の理論I (Japanese)
12月15日（木）は講演なし
鈴木 泰成 氏 (NTT)
誤り耐性量子計算の理論I (Japanese)
[ 講演概要 ]
信頼性のある量子計算を行うには、量子誤り訂正を組み込んだ誤り耐性量子計算機の実現が重要となる。本講義では誤り耐性量子計算の基本的な考え方や、その仕組みについて解説する。
信頼性のある量子計算を行うには、量子誤り訂正を組み込んだ誤り耐性量子計算機の実現が重要となる。本講義では誤り耐性量子計算の基本的な考え方や、その仕組みについて解説する。
2022年12月21日(水)
代数幾何学セミナー
13:00-14:00 or 14:30 数理科学研究科棟(駒場) ハイブリッド開催/056号室
いつもと部屋が異なります. 京大代数幾何セミナーと共催です.
Hsueh-Yung Lin 氏 (NTU)
Towards a geometric origin of the dynamical filtrations (English)
いつもと部屋が異なります. 京大代数幾何セミナーと共催です.
Hsueh-Yung Lin 氏 (NTU)
Towards a geometric origin of the dynamical filtrations (English)
[ 講演概要 ]
Let X be a smooth projective variety with an automorphism f. When X is a threefold, Serge Cantat asked whether X has a non-trivial equivariant rational fibration, if the action of f on the Néron-Severi space is non-trivial and unipotent. We will propose a precise conjecture related to Cantat's question for minimal varieties in arbitrary dimension, in light of the "dynamical filtrations" arising in the study of zero entropy group actions. This conjecture also suggests a geometric origin of dynamical filtrations, whose definition is purely cohomological. We will provide some heuristic evidence from the relative abundance conjecture.
If time permits, we will also explain how the study of dynamical filtrations leads to new results about solvable group actions, which are not necessarily of zero entropy.
Let X be a smooth projective variety with an automorphism f. When X is a threefold, Serge Cantat asked whether X has a non-trivial equivariant rational fibration, if the action of f on the Néron-Severi space is non-trivial and unipotent. We will propose a precise conjecture related to Cantat's question for minimal varieties in arbitrary dimension, in light of the "dynamical filtrations" arising in the study of zero entropy group actions. This conjecture also suggests a geometric origin of dynamical filtrations, whose definition is purely cohomological. We will provide some heuristic evidence from the relative abundance conjecture.
If time permits, we will also explain how the study of dynamical filtrations leads to new results about solvable group actions, which are not necessarily of zero entropy.
2022年12月20日(火)
代数幾何学セミナー
9:30-10:30 数理科学研究科棟(駒場) オンラインZoom号室
Takumi Murayama 氏 (パーデュー大学)
The relative minimal model program for excellent algebraic spaces and analytic spaces in equal characteristic zero (English)
Takumi Murayama 氏 (パーデュー大学)
The relative minimal model program for excellent algebraic spaces and analytic spaces in equal characteristic zero (English)
[ 講演概要 ]
In 2010, Birkar, Cascini, Hacon, and McKernan proved a relative version of the minimal model program for projective morphisms of complex quasi-projective varieties, called the relative minimal model program with scaling. Their result is now fundamental to our understanding of the birational classification of quasi-projective varieties and has numerous applications.
In this talk, I will discuss recent joint work with Shiji Lyu that establishes the relative minimal model program with scaling for excellent schemes, excellent algebraic spaces, and analytic spaces simultaneously in equal characteristic zero. This not only recovers previous results for complex varieties, complex algebraic spaces, and complex analytic spaces, but also greatly extends the scope of the relative minimal model program with scaling to a broader class of geometric spaces, including formal schemes, rigid analytic spaces, and Berkovich spaces, all in equal characteristic zero. Our results for (non-algebraic) schemes and rigid analytic spaces were previously only known in dimensions ≤3 and ≤2, respectively, and our results for formal schemes and Berkovich spaces are completely new.
In 2010, Birkar, Cascini, Hacon, and McKernan proved a relative version of the minimal model program for projective morphisms of complex quasi-projective varieties, called the relative minimal model program with scaling. Their result is now fundamental to our understanding of the birational classification of quasi-projective varieties and has numerous applications.
In this talk, I will discuss recent joint work with Shiji Lyu that establishes the relative minimal model program with scaling for excellent schemes, excellent algebraic spaces, and analytic spaces simultaneously in equal characteristic zero. This not only recovers previous results for complex varieties, complex algebraic spaces, and complex analytic spaces, but also greatly extends the scope of the relative minimal model program with scaling to a broader class of geometric spaces, including formal schemes, rigid analytic spaces, and Berkovich spaces, all in equal characteristic zero. Our results for (non-algebraic) schemes and rigid analytic spaces were previously only known in dimensions ≤3 and ≤2, respectively, and our results for formal schemes and Berkovich spaces are completely new.
解析学火曜セミナー
16:00-17:30 数理科学研究科棟(駒場) 126号室
対面・オンラインハイブリッド開催
片岡清臣 氏 (東京大学)
J.Boman氏の最近の２つの関連する結果，distributionの台と解析性，Radon変換と楕円体領域の特殊な関係性についての解説 (Japanese)
https://forms.gle/BpciRTzKh9FPUV8D7
対面・オンラインハイブリッド開催
片岡清臣 氏 (東京大学)
J.Boman氏の最近の２つの関連する結果，distributionの台と解析性，Radon変換と楕円体領域の特殊な関係性についての解説 (Japanese)
[ 講演概要 ]
Jan Boman's (Stockholm Univ.) recent two papers:
[1], Regularity of a distribution and of the boundary of its support, The Journal of Geometric Analysis vol.32, Article number: 300 (2022).
[2], A hypersurface containing the support of a Radon transform must be an ellipsoid. II: The general case; J. Inverse Ill-Posed Probl. 2021; 29(3): 351–367.
In [1] he proved "Let $f(x_1,…,x_n,y)$ be a non-zero distribution with support in a $C^1$ surface $N=\{y=F(x)\}$. If $f(x,y)$ is depending real analytically on x-variables, then $F(x)$ is analytic". As an application, he reinforced the main result of [2]. These results are obtained essentially by means of matrix algebra and a number theoretic method.
[ 参考URL ]Jan Boman's (Stockholm Univ.) recent two papers:
[1], Regularity of a distribution and of the boundary of its support, The Journal of Geometric Analysis vol.32, Article number: 300 (2022).
[2], A hypersurface containing the support of a Radon transform must be an ellipsoid. II: The general case; J. Inverse Ill-Posed Probl. 2021; 29(3): 351–367.
In [1] he proved "Let $f(x_1,…,x_n,y)$ be a non-zero distribution with support in a $C^1$ surface $N=\{y=F(x)\}$. If $f(x,y)$ is depending real analytically on x-variables, then $F(x)$ is analytic". As an application, he reinforced the main result of [2]. These results are obtained essentially by means of matrix algebra and a number theoretic method.
https://forms.gle/BpciRTzKh9FPUV8D7
作用素環セミナー
16:45-18:15 オンライン開催
窪田陽介 氏 (信州大学)
Band width and the Rosenberg index
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
窪田陽介 氏 (信州大学)
Band width and the Rosenberg index
[ 講演概要 ]
Band width is a concept recently proposed by Gromov. It is based on the idea that when a certain band (i.e., manifold with two boundaries) is openly immersed to a target manifold M with positive scalar curvature metric, then its width is bounded by a uniform constant called the band width of M. A qualitative consequence is that infiniteness of the band width of M obstructs to positive scalar curvature.
In this talk, infiniteness of a version of the band width, Zeidler's KO-band width, is dominated as a PSC obstruction by an existing obstruction, the Rosenberg index. This answers to a conjecture by Zeidler.
[ 参考URL ]Band width is a concept recently proposed by Gromov. It is based on the idea that when a certain band (i.e., manifold with two boundaries) is openly immersed to a target manifold M with positive scalar curvature metric, then its width is bounded by a uniform constant called the band width of M. A qualitative consequence is that infiniteness of the band width of M obstructs to positive scalar curvature.
In this talk, infiniteness of a version of the band width, Zeidler's KO-band width, is dominated as a PSC obstruction by an existing obstruction, the Rosenberg index. This answers to a conjecture by Zeidler.
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
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