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過去の記録
過去の記録 ～09/26｜本日 09/27 | 今後の予定 09/28～
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
2022年12月13日(火)
代数幾何学セミナー
10:30-11:30 数理科学研究科棟(駒場) ハイブリッド開催/002号室
講演者はZoomにて遠隔講演 002でも遠隔で流そうと思います。
山岸亮 氏 (NTU)
Moduli of G-constellations and crepant resolutions (日本語)
講演者はZoomにて遠隔講演 002でも遠隔で流そうと思います。
山岸亮 氏 (NTU)
Moduli of G-constellations and crepant resolutions (日本語)
[ 講演概要 ]
For a finite subgroup G of SL_n(C), a moduli space of G-constellations is a generalization of the G-Hilbert scheme and is important from the viewpoint of McKay correspondence. In this talk I will explain its basic properties and show that every projective crepant resolution of C^3/G is isomorphic to such a moduli space.
For a finite subgroup G of SL_n(C), a moduli space of G-constellations is a generalization of the G-Hilbert scheme and is important from the viewpoint of McKay correspondence. In this talk I will explain its basic properties and show that every projective crepant resolution of C^3/G is isomorphic to such a moduli space.
作用素環セミナー
16:45-18:15 数理科学研究科棟(駒場) 128号室
Feng Xu 氏 (UC Riverside)
Entropy in QFT
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
Feng Xu 氏 (UC Riverside)
Entropy in QFT
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
トポロジー火曜セミナー
17:30-18:30 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。
服部 広大 氏 (慶應義塾大学)
Spectral convergence in geometric quantization on K3 surfaces (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。
服部 広大 氏 (慶應義塾大学)
Spectral convergence in geometric quantization on K3 surfaces (JAPANESE)
[ 講演概要 ]
In this talk I will explain the geometric quantization on K3 surfaces from the viewpoint of the spectral convergence. We take a special Lagrangian fibrations on the K3 surfaces and a family of hyper-Kähler structures tending to large complex structure limit and show a spectral convergence of the d-bar-Laplacians on the prequantum line bundle to the spectral structure related to the set of Bohr-Sommerfeld fibers.
[ 参考URL ]In this talk I will explain the geometric quantization on K3 surfaces from the viewpoint of the spectral convergence. We take a special Lagrangian fibrations on the K3 surfaces and a family of hyper-Kähler structures tending to large complex structure limit and show a spectral convergence of the d-bar-Laplacians on the prequantum line bundle to the spectral structure related to the set of Bohr-Sommerfeld fibers.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
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
只野之英 氏 (東京理科大学)
Continuum limit problem of discrete Schrödinger operators on square lattices (Japanese)
https://forms.gle/CRha8hydEuXzh71S7
対面・オンラインハイブリッド開催
只野之英 氏 (東京理科大学)
Continuum limit problem of discrete Schrödinger operators on square lattices (Japanese)
[ 講演概要 ]
We consider discrete Schrödinger operators on the square lattice with its mesh size very small. The aim of this talk is to introduce the rigorous setting of continuum limit problems in the view point of operator theory and then to give its proof for the above operators, the one of which is defined on the vertices and the other of which is defined on the edges. This talk is based on joint works with Shu Nakamura (Gakushuin University) and Pavel Exner (Czech Academy of Science, Czech Technical University).
[ 参考URL ]We consider discrete Schrödinger operators on the square lattice with its mesh size very small. The aim of this talk is to introduce the rigorous setting of continuum limit problems in the view point of operator theory and then to give its proof for the above operators, the one of which is defined on the vertices and the other of which is defined on the edges. This talk is based on joint works with Shu Nakamura (Gakushuin University) and Pavel Exner (Czech Academy of Science, Czech Technical University).
https://forms.gle/CRha8hydEuXzh71S7
2022年12月12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。
稲山 貴大 氏 (東京理科大学)
$L^2$-extension index and its applications (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。
稲山 貴大 氏 (東京理科大学)
$L^2$-extension index and its applications (Japanese)
[ 講演概要 ]
In this talk, we introduce a new concept of $L^2$-extension indices. By using this notion, we propose a new way to study the positivity of curvature. We prove that there is an equivalence between how sharp the $L^2$-extension is and how positive the curvature is. As applications, we study Prekopa-type theorems and the positivity of a certain direct image sheaf.
[ 参考URL ]In this talk, we introduce a new concept of $L^2$-extension indices. By using this notion, we propose a new way to study the positivity of curvature. We prove that there is an equivalence between how sharp the $L^2$-extension is and how positive the curvature is. As applications, we study Prekopa-type theorems and the positivity of a certain direct image sheaf.
https://forms.gle/hYT2hVhDE3q1wDSh6
2022年12月08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
遠藤 傑 氏 (NTT)
Near-term 量子アルゴリズムと量子エラー抑制 (Japanese)
遠藤 傑 氏 (NTT)
Near-term 量子アルゴリズムと量子エラー抑制 (Japanese)
[ 講演概要 ]
現在、量子コンピュータ研究が加速しているが、現在および近未来の量子コンピュータは小中規模で計算エラーもまだまだ大きい。この講演ではそのような量子コンピュータに適していると考えられているNear-term の量子アルゴリズムと、計算エラーを取り除くための量子エラー抑制について解説する。
現在、量子コンピュータ研究が加速しているが、現在および近未来の量子コンピュータは小中規模で計算エラーもまだまだ大きい。この講演ではそのような量子コンピュータに適していると考えられているNear-term の量子アルゴリズムと、計算エラーを取り除くための量子エラー抑制について解説する。
2022年12月06日(火)
作用素環セミナー
16:45-18:15 数理科学研究科棟(駒場) 128号室
星野真生 氏 (東大数理)
Equivariant covering spaces of quantum homogeneous spaces
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
星野真生 氏 (東大数理)
Equivariant covering spaces of quantum homogeneous spaces
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
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。
Quentin Faes 氏 (東京大学大学院数理科学研究科)
Torsion in the abelianization of the Johnson kernel (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。
Quentin Faes 氏 (東京大学大学院数理科学研究科)
Torsion in the abelianization of the Johnson kernel (ENGLISH)
[ 講演概要 ]
The Johnson kernel is the subgroup of the mapping class group of a closed oriented surface that is generated by Dehn twists along separating simple closed curves, and is also the second term of the so-called Johnson filtration of the mapping class group. The rational abelianization of this group is known, but it was recently proved by Nozaki, Sato and Suzuki, that the abelianization has torsion. They used the LMO homomorphism. In this talk, I will explain a purely two-dimensional proof of this result, which provides a lower bound for the cardinality of the torsion part of the abelianization. These results are also valid for the case of an open surface. This is joint work with Gwénaël Massuyeau.
[ 参考URL ]The Johnson kernel is the subgroup of the mapping class group of a closed oriented surface that is generated by Dehn twists along separating simple closed curves, and is also the second term of the so-called Johnson filtration of the mapping class group. The rational abelianization of this group is known, but it was recently proved by Nozaki, Sato and Suzuki, that the abelianization has torsion. They used the LMO homomorphism. In this talk, I will explain a purely two-dimensional proof of this result, which provides a lower bound for the cardinality of the torsion part of the abelianization. These results are also valid for the case of an open surface. This is joint work with Gwénaël Massuyeau.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
2022年12月05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。
菊池 翔太 氏 (鈴鹿工業高等専門学校)
On sharper estimates of Ohsawa--Takegoshi $L^2$-extension theorem in higher dimensional case (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。
菊池 翔太 氏 (鈴鹿工業高等専門学校)
On sharper estimates of Ohsawa--Takegoshi $L^2$-extension theorem in higher dimensional case (Japanese)
[ 講演概要 ]
Hosono proposed an idea of getting an $L^2$-estimate sharper than the one of Berndtsson--Lempert type $L^2$-extension theorem by allowing constants depending on weight functions in $\mathbb{C}$.
In this talk, I explain the details of "sharper estimates" and the higher dimensional case of it. Also, I explain my recent studies related to it.
[ 参考URL ]Hosono proposed an idea of getting an $L^2$-estimate sharper than the one of Berndtsson--Lempert type $L^2$-extension theorem by allowing constants depending on weight functions in $\mathbb{C}$.
In this talk, I explain the details of "sharper estimates" and the higher dimensional case of it. Also, I explain my recent studies related to it.
https://forms.gle/hYT2hVhDE3q1wDSh6
統計数学セミナー
14:40-15:50 数理科学研究科棟(駒場) 号室
現地参加（統計数理研究所）とZoomによるハイブリッド配信 （※状況によりオンライン配信のみとなる可能性もございます）
Michael Choi 氏 (National University of Singapore and Yale-NUS College)
A binary branching model with Moran-type interactions (English)
(Zoom参加) 12/1締切https://docs.google.com/forms/d/e/1FAIpQLSdyluSozvNOGmDcXzGv496v2AQNiPePqIerLaBN9pD4wxEmnw/viewform (現地参加) 先着20名https://forms.gle/rS9rjhL2jXo6eGgt5
現地参加（統計数理研究所）とZoomによるハイブリッド配信 （※状況によりオンライン配信のみとなる可能性もございます）
Michael Choi 氏 (National University of Singapore and Yale-NUS College)
A binary branching model with Moran-type interactions (English)
[ 講演概要 ]
Branching processes naturally arise as pertinent models in a variety of applications such as population size dynamics, neutron transport and cell proliferation kinetics. A key result for understanding the behaviour of such systems is the Perron Frobenius decomposition, which allows one to characterise the large time average behaviour of the branching process via its leading eigenvalue and corresponding left and right eigenfunctions. However, obtaining estimates of these quantities can be challenging, for example when the branching process is spatially dependent with inhomogeneous rates. In this talk, I will introduce a new interacting particle model that combines the natural branching behaviour of the underlying process with a selection and resampling mechanism, which allows one to maintain some control over the system and more efficiently estimate the eigenelements. I will then present the main result, which provides an explicit relation between the particle system and the branching process via a many-to-one formula and also quantifies the L^2 distance between the occupation measures of the two systems. Finally, I will discuss some examples in order to illustrate the scope and possible extensions of the model, and to provide some comparisons with the Fleming Viot interacting particle system. This is based on work with Alex Cox (University of Bath) and Denis Villemonais (Université de Lorraine).
[ 参考URL ]Branching processes naturally arise as pertinent models in a variety of applications such as population size dynamics, neutron transport and cell proliferation kinetics. A key result for understanding the behaviour of such systems is the Perron Frobenius decomposition, which allows one to characterise the large time average behaviour of the branching process via its leading eigenvalue and corresponding left and right eigenfunctions. However, obtaining estimates of these quantities can be challenging, for example when the branching process is spatially dependent with inhomogeneous rates. In this talk, I will introduce a new interacting particle model that combines the natural branching behaviour of the underlying process with a selection and resampling mechanism, which allows one to maintain some control over the system and more efficiently estimate the eigenelements. I will then present the main result, which provides an explicit relation between the particle system and the branching process via a many-to-one formula and also quantifies the L^2 distance between the occupation measures of the two systems. Finally, I will discuss some examples in order to illustrate the scope and possible extensions of the model, and to provide some comparisons with the Fleming Viot interacting particle system. This is based on work with Alex Cox (University of Bath) and Denis Villemonais (Université de Lorraine).
(Zoom参加) 12/1締切https://docs.google.com/forms/d/e/1FAIpQLSdyluSozvNOGmDcXzGv496v2AQNiPePqIerLaBN9pD4wxEmnw/viewform (現地参加) 先着20名https://forms.gle/rS9rjhL2jXo6eGgt5
2022年12月01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
山川 高志 氏 (NTT)
量子計算と暗号理論 (Japanese)
山川 高志 氏 (NTT)
量子計算と暗号理論 (Japanese)
[ 講演概要 ]
量子計算と暗号理論の関わりについていくつかのトピック、具体的にはショアの素因数分解・離散対数アルゴリズム、量子マネー、暗号を用いた量子計算機の検証等について解説する。
量子計算と暗号理論の関わりについていくつかのトピック、具体的にはショアの素因数分解・離散対数アルゴリズム、量子マネー、暗号を用いた量子計算機の検証等について解説する。
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