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過去の記録
過去の記録 ～03/31｜本日 04/01 | 今後の予定 04/02～
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。
2022年11月30日(水)
代数学コロキウム
17:00-18:00 ハイブリッド開催
Xinyao Zhang 氏 (東京大学大学院数理科学研究科)
The modularity of elliptic curves over some number fields (English)
Xinyao Zhang 氏 (東京大学大学院数理科学研究科)
The modularity of elliptic curves over some number fields (English)
[ 講演概要 ]
As a non-trivial case of the Langlands reciprocity conjecture, the modularity of elliptic curves always intrigues number theorists, and a famous result was proved for semistable elliptic curves over \mathbb{Q} by Andrew Wiles, implying Fermat's Last Theorem. In recent years, many new results have been proved using sufficiently powerful modularity lifting theorems. For instance, Thorne proved that elliptic curves over the cyclotomic \mathbb{Z}_p-extension of \mathbb{Q} are modular. In this talk, I will sketch some of these results and try to give a new one that elliptic curves over the cyclotomic \mathbb{Z}_p-extension of a real quadratic field are modular under some technical assumptions.
As a non-trivial case of the Langlands reciprocity conjecture, the modularity of elliptic curves always intrigues number theorists, and a famous result was proved for semistable elliptic curves over \mathbb{Q} by Andrew Wiles, implying Fermat's Last Theorem. In recent years, many new results have been proved using sufficiently powerful modularity lifting theorems. For instance, Thorne proved that elliptic curves over the cyclotomic \mathbb{Z}_p-extension of \mathbb{Q} are modular. In this talk, I will sketch some of these results and try to give a new one that elliptic curves over the cyclotomic \mathbb{Z}_p-extension of a real quadratic field are modular under some technical assumptions.
離散数理モデリングセミナー
15:00-16:30 数理科学研究科棟(駒場) 128号室
Mikhail Bershtein 氏 (Skoltech・HSE / IPMU)
Folding transformations for q-Painleve equations (English)
Mikhail Bershtein 氏 (Skoltech・HSE / IPMU)
Folding transformations for q-Painleve equations (English)
[ 講演概要 ]
Folding transformation of the Painleve equations is an algebraic (of degree greater than 1) transformation between solutions of different equations. In 2005 Tsuda, Okamoto and Sakai classified folding transformations of differential Painleve equations. These transformations are in correspondence with automorphisms of affine Dynkin diagrams. We give a complete classification of folding transformations of the q-difference Painleve equations, these transformations are in correspondence with certain subdiagrams of the affine Dynkin diagrams (possibly with automorphism). The method is based on Sakai's approach to Painleve equations through rational surfaces.
Based on joint work with A. Shchechkin [arXiv:2110.15320]
Folding transformation of the Painleve equations is an algebraic (of degree greater than 1) transformation between solutions of different equations. In 2005 Tsuda, Okamoto and Sakai classified folding transformations of differential Painleve equations. These transformations are in correspondence with automorphisms of affine Dynkin diagrams. We give a complete classification of folding transformations of the q-difference Painleve equations, these transformations are in correspondence with certain subdiagrams of the affine Dynkin diagrams (possibly with automorphism). The method is based on Sakai's approach to Painleve equations through rational surfaces.
Based on joint work with A. Shchechkin [arXiv:2110.15320]
2022年11月29日(火)
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
滝本和広 氏 (広島大学)
Bernstein type theorem for the parabolic 2-Hessian equation under weaker assumptions (Japanese)
https://forms.gle/93YQ9C6DGYt5Vjuf7
対面・オンラインハイブリッド開催
滝本和広 氏 (広島大学)
Bernstein type theorem for the parabolic 2-Hessian equation under weaker assumptions (Japanese)
[ 講演概要 ]
In the early twentieth century, Bernstein proved that a minimal surface which can be expressed as the graph of a function defined in $\mathbb{R}^2$ must be a plane. For Monge-Ampère equation, it is known that a convex solution to $\det D^2 u=1$ in $\mathbb{R}^n$ must be a quadratic polynomial. Such kind of theorems, which we call Bernstein type theorems in this talk, have been extensively studied for various PDEs. For the parabolic $k$-Hessian equation, Bernstein type theorem has been proved by Nakamori and Takimoto (2015, 2016) under the convexity and some growth assumptions on the solution. In this talk, we shall obtain Bernstein type theorem for the parabolic 2-Hessian equation under weaker assumptions.
[ 参考URL ]In the early twentieth century, Bernstein proved that a minimal surface which can be expressed as the graph of a function defined in $\mathbb{R}^2$ must be a plane. For Monge-Ampère equation, it is known that a convex solution to $\det D^2 u=1$ in $\mathbb{R}^n$ must be a quadratic polynomial. Such kind of theorems, which we call Bernstein type theorems in this talk, have been extensively studied for various PDEs. For the parabolic $k$-Hessian equation, Bernstein type theorem has been proved by Nakamori and Takimoto (2015, 2016) under the convexity and some growth assumptions on the solution. In this talk, we shall obtain Bernstein type theorem for the parabolic 2-Hessian equation under weaker assumptions.
https://forms.gle/93YQ9C6DGYt5Vjuf7
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。
黒木 慎太郎 氏 (岡山理科大学)
GKM graph with legs and graph equivariant cohomology (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。
黒木 慎太郎 氏 (岡山理科大学)
GKM graph with legs and graph equivariant cohomology (JAPANESE)
[ 講演概要 ]
A GKM (Goresky-Kottiwicz-MacPherson) graph is a regular graph labeled on edges with some conditions. This notion has been introduced by Guillemin-Zara in 2001 to study the geometry of a nice class of manifolds with torus actions, called a GKM manifold, by a combinatorial way. In particular, we can define a ring on a GKM graph called a graph equivariant cohomology, and it is often isomorphic to the equivariant cohomology of a GKM manifold. In this talk, we introduce the GKM graph with legs (i.e., non-compact edges) related to non-compact manifolds with torus actions that may not satisfy the usual GKM conditions, and study the graph equivariant cohomology which is related to the GKM graph with legs. The talk is mainly based on the joint work with Grigory Solomadin (arXiv:2207.11380) and partially on the joint work with Vikraman Uma (arXiv:2106.11598).
[ 参考URL ]A GKM (Goresky-Kottiwicz-MacPherson) graph is a regular graph labeled on edges with some conditions. This notion has been introduced by Guillemin-Zara in 2001 to study the geometry of a nice class of manifolds with torus actions, called a GKM manifold, by a combinatorial way. In particular, we can define a ring on a GKM graph called a graph equivariant cohomology, and it is often isomorphic to the equivariant cohomology of a GKM manifold. In this talk, we introduce the GKM graph with legs (i.e., non-compact edges) related to non-compact manifolds with torus actions that may not satisfy the usual GKM conditions, and study the graph equivariant cohomology which is related to the GKM graph with legs. The talk is mainly based on the joint work with Grigory Solomadin (arXiv:2207.11380) and partially on the joint work with Vikraman Uma (arXiv:2106.11598).
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
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
荒野悠輝 氏 (京大数学)
Actions of tensor categories on $C^*$-algebras
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
荒野悠輝 氏 (京大数学)
Actions of tensor categories on $C^*$-algebras
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
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
Thomas Hall 氏 (University of Nottingham)
The behaviour of Kahler-Einstein polygons under combinatorial mutation
(English)
Thomas Hall 氏 (University of Nottingham)
The behaviour of Kahler-Einstein polygons under combinatorial mutation
(English)
[ 講演概要 ]
Combinatorial mutations play an important role in the mirror symmetry approach to the classification of Fano varieties. Another important notion for Fano varieties is that of K-polystability, which turns out to have a nice combinatorial characterisation in the toric case. In this talk, I will give an overview of how mutations work and sketch the key ideas used to explore its interaction with Kahler-Einstein polygons (i.e. the Fano polygons whose associated toric variety is K-polystable).
Combinatorial mutations play an important role in the mirror symmetry approach to the classification of Fano varieties. Another important notion for Fano varieties is that of K-polystability, which turns out to have a nice combinatorial characterisation in the toric case. In this talk, I will give an overview of how mutations work and sketch the key ideas used to explore its interaction with Kahler-Einstein polygons (i.e. the Fano polygons whose associated toric variety is K-polystable).
2022年11月25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。
Shane Kelly 氏 (東京大学大学院数理科学研究科)
Motivic cohomology: theory and applications
(ENGLISH)
https://u-tokyo-ac-jp.zoom.us/meeting/register/tZErcumupjouGdXpOac2j3rcFFN545yAuoSb
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。
Shane Kelly 氏 (東京大学大学院数理科学研究科)
Motivic cohomology: theory and applications
(ENGLISH)
[ 講演概要 ]
The motive of a smooth projective algebraic variety was originally envisaged by Grothendieck in the 60's as a generalisation of the Jacobian of a curve, and formed part of a strategy to prove the Weil conjectures. In the 90s, following conjectures of Beilinson on special values of L-functions, Voevodsky, together with Friedlander, Morel, Suslin, and others, generalised this to the A^1-homotopy type of a general algebraic variety. This A^1-homotopy theory lead to a proof of the Block-Kato conjecture (and a Fields Medal for Voevodsky).
One consequence of making things A^1-invariant is that unipotent groups (as well as wild ramification, irregular singularities, nilpotents including higher nilpotents in the sense of derived algebraic geometry, certain parts of K-theory, etc) become invisible and the last decade has seen a number of candidates for a non-A^1-invariant theory.
In this talk I will give an introduction to the classical theory and discuss some current and future research directions.
[ 参考URL ]The motive of a smooth projective algebraic variety was originally envisaged by Grothendieck in the 60's as a generalisation of the Jacobian of a curve, and formed part of a strategy to prove the Weil conjectures. In the 90s, following conjectures of Beilinson on special values of L-functions, Voevodsky, together with Friedlander, Morel, Suslin, and others, generalised this to the A^1-homotopy type of a general algebraic variety. This A^1-homotopy theory lead to a proof of the Block-Kato conjecture (and a Fields Medal for Voevodsky).
One consequence of making things A^1-invariant is that unipotent groups (as well as wild ramification, irregular singularities, nilpotents including higher nilpotents in the sense of derived algebraic geometry, certain parts of K-theory, etc) become invisible and the last decade has seen a number of candidates for a non-A^1-invariant theory.
In this talk I will give an introduction to the classical theory and discuss some current and future research directions.
https://u-tokyo-ac-jp.zoom.us/meeting/register/tZErcumupjouGdXpOac2j3rcFFN545yAuoSb
2022年11月24日(木)
応用解析セミナー
16:00-17:30 数理科学研究科棟(駒場) 370号室
対面・オンラインハイブリッド開催
板倉 恭平 氏 (東京大学 大学院数理科学研究科)
シュタルク・シュレディンガー作用素に対する放射条件評価と定常散乱理論 (Japanese)
https://forms.gle/admRaVnmPjFyp5op9
対面・オンラインハイブリッド開催
板倉 恭平 氏 (東京大学 大学院数理科学研究科)
シュタルク・シュレディンガー作用素に対する放射条件評価と定常散乱理論 (Japanese)
[ 講演概要 ]
本講演では1体粒子系のシュタルク・シュレディンガー作用素に対し，古典力学から類推される最良な重み付き放射条件評価の導出を行い，これを土台として定常波動作用素の存在性と完全性を調べる．さらに関連する話題として，定常散乱行列のユニタリ性，一般化フーリエ変換の構成，および最小増大度をもつ一般化固有関数に対する定常散乱行列と近似外向・内向波を用いた空間遠方での漸近挙動の特徴づけについても考察する．本研究では，対応する古典力学を適切に反映させたエスケープ関数と，それに付随するアグモン-ヘルマンダー空間の使用が肝要となる．本講演の内容は足立匡義氏(京都大学)，伊藤健一氏(東京大学)，Skibsted Erik氏(オーフス大学)との共同研究に基づく．
[ 参考URL ]本講演では1体粒子系のシュタルク・シュレディンガー作用素に対し，古典力学から類推される最良な重み付き放射条件評価の導出を行い，これを土台として定常波動作用素の存在性と完全性を調べる．さらに関連する話題として，定常散乱行列のユニタリ性，一般化フーリエ変換の構成，および最小増大度をもつ一般化固有関数に対する定常散乱行列と近似外向・内向波を用いた空間遠方での漸近挙動の特徴づけについても考察する．本研究では，対応する古典力学を適切に反映させたエスケープ関数と，それに付随するアグモン-ヘルマンダー空間の使用が肝要となる．本講演の内容は足立匡義氏(京都大学)，伊藤健一氏(東京大学)，Skibsted Erik氏(オーフス大学)との共同研究に基づく．
https://forms.gle/admRaVnmPjFyp5op9
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
安田 雅哉 氏 (立教大学)
格子暗号の安全性を支える格子問題の解読法 (Japanese)
安田 雅哉 氏 (立教大学)
格子暗号の安全性を支える格子問題の解読法 (Japanese)
[ 講演概要 ]
格子暗号は耐量子計算機暗号の一つであり、完全準同型暗号などの高機能暗号の構成にも有用である。本講演では、格子暗号の安全性を支える数学問題である格子問題を解読する方法を紹介する。具体的には、格子問題を解くための必須の技術であるLLLやBKZなどの格子基底簡約アルゴリズムを紹介すると共に、LWEやNTRUの格子問題への適用方法を説明する。
格子暗号は耐量子計算機暗号の一つであり、完全準同型暗号などの高機能暗号の構成にも有用である。本講演では、格子暗号の安全性を支える数学問題である格子問題を解読する方法を紹介する。具体的には、格子問題を解くための必須の技術であるLLLやBKZなどの格子基底簡約アルゴリズムを紹介すると共に、LWEやNTRUの格子問題への適用方法を説明する。
2022年11月22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) 002号室
90分ハイブリッド開催です。
谷本祥 氏 (名古屋多元)
Non-free sections of Fano fibrations (日本語)
90分ハイブリッド開催です。
谷本祥 氏 (名古屋多元)
Non-free sections of Fano fibrations (日本語)
[ 講演概要 ]
Manin’s Conjecture predicts the asymptotic formula for the counting function of rational points over number fields or global function fields. In the late 80’s, Batyrev developed a heuristic argument for Manin’s Conjecture over global function fields, and the assumptions underlying Batyrev’s heuristics are refined and formulated as Geometric Manin’s Conjecture. Geometric Manin’s Conjecture is a set of conjectures regarding properties of the space of sections of Fano fibrations, and it consists of three conjectures: (i) Pathological components are controlled by Fujita invariants; (ii) For each nef algebraic class, a non-pathological component which should be counted in Manin’s Conjecture is unique (This component is called as Manin components); (iii) Manin components exhibit homological or motivic stability. In this talk we discuss our proofs of GMC (i) over complex numbers using theory of foliations and the minimal model program. Using this result, we prove that these pathological components are coming from a bounded family of accumulating maps. This is joint work in progress with Brian Lehmann and Eric Riedl.
Manin’s Conjecture predicts the asymptotic formula for the counting function of rational points over number fields or global function fields. In the late 80’s, Batyrev developed a heuristic argument for Manin’s Conjecture over global function fields, and the assumptions underlying Batyrev’s heuristics are refined and formulated as Geometric Manin’s Conjecture. Geometric Manin’s Conjecture is a set of conjectures regarding properties of the space of sections of Fano fibrations, and it consists of three conjectures: (i) Pathological components are controlled by Fujita invariants; (ii) For each nef algebraic class, a non-pathological component which should be counted in Manin’s Conjecture is unique (This component is called as Manin components); (iii) Manin components exhibit homological or motivic stability. In this talk we discuss our proofs of GMC (i) over complex numbers using theory of foliations and the minimal model program. Using this result, we prove that these pathological components are coming from a bounded family of accumulating maps. This is joint work in progress with Brian Lehmann and Eric Riedl.
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
佐藤僚亮 氏 (中央大物理)
Multiplicative characters and Gaussian fluctuation limits
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
佐藤僚亮 氏 (中央大物理)
Multiplicative characters and Gaussian fluctuation limits
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
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