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過去の記録 ～05/22｜本日 05/23 | 今後の予定 05/24～
2024年10月21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
林本 厚志 氏 (長野工業高等専門学校)
固有正則写像の連続的拡張性と正則的拡張性 (Japanese)
https://forms.gle/gTP8qNZwPyQyxjTj8
林本 厚志 氏 (長野工業高等専門学校)
固有正則写像の連続的拡張性と正則的拡張性 (Japanese)
[ 講演概要 ]
2つの有界領域があったときに, その間の固有正則写像が, ある滑らかさで定義域を拡張できるか, もし拡張できるなら, そこからどういう結論が導き出せるか, という問題を考える. 2つの領域が$m$次元球と$n$次元球で, $m$が$n$より真に小さい場合には, 連続的に拡張できない場合があることが知られている. $n \le m \le 2n-2$の場合には, もし$C^2$級に境界を越えて拡張できたら, そのような固有正則写像は自己同型写像の差を省いて分類することができ, その結果, 正則的にも拡張できることがわかる. これはgap定理からの結論であり次元の差がさらに大きい場合にも類似の結果が知られている. これが球でない場合にはどういうことが成り立つかを調べたい. 一般複素擬楕円体は, 実解析的境界を持つ擬凸領域の代表例である. ここで話す内容は次の2つである.
1. 次元の異なる一般複素擬楕円体の間の固有正則写像で, 境界を越えて連続的に定義域を拡張できない場合がある.
2. もし, 正則的に拡張できたとしたら, 自己同型写像の差を省いてそのような写像が分類できる.
[ 参考URL ]2つの有界領域があったときに, その間の固有正則写像が, ある滑らかさで定義域を拡張できるか, もし拡張できるなら, そこからどういう結論が導き出せるか, という問題を考える. 2つの領域が$m$次元球と$n$次元球で, $m$が$n$より真に小さい場合には, 連続的に拡張できない場合があることが知られている. $n \le m \le 2n-2$の場合には, もし$C^2$級に境界を越えて拡張できたら, そのような固有正則写像は自己同型写像の差を省いて分類することができ, その結果, 正則的にも拡張できることがわかる. これはgap定理からの結論であり次元の差がさらに大きい場合にも類似の結果が知られている. これが球でない場合にはどういうことが成り立つかを調べたい. 一般複素擬楕円体は, 実解析的境界を持つ擬凸領域の代表例である. ここで話す内容は次の2つである.
1. 次元の異なる一般複素擬楕円体の間の固有正則写像で, 境界を越えて連続的に定義域を拡張できない場合がある.
2. もし, 正則的に拡張できたとしたら, 自己同型写像の差を省いてそのような写像が分類できる.
https://forms.gle/gTP8qNZwPyQyxjTj8
東京確率論セミナー
16:00-17:30 数理科学研究科棟(駒場) 126号室
15:15〜 ２階のコモンルームでTea timeを行います。ぜひこちらにもご参加ください。
野田航平 氏 (九州大学 マス・フォア・インダストリ研究所)
Scaling limits of non-Hermitian Wishart random matrices and their applications (日本語)
15:15〜 ２階のコモンルームでTea timeを行います。ぜひこちらにもご参加ください。
野田航平 氏 (九州大学 マス・フォア・インダストリ研究所)
Scaling limits of non-Hermitian Wishart random matrices and their applications (日本語)
[ 講演概要 ]
This talk is based on joint work and an ongoing project with Sung-Soo Byun (Seoul National University) on the scaling limits of non-Hermitian Wishart random matrices, which were introduced in the context of quantum chromodynamics with a baryon chemical potential, and their probabilistic applications. We present a robust argument, a generalized Christoffel-Darboux type identity, to obtain the scaling limits of eigenvalue point processes (determinantal/Pfaffian point processes) for non-Hermitian Wishart ensembles. Additionally, I will discuss the fluctuation of real eigenvalues in non-Hermitian real Wishart ensembles.
This talk is based on joint work and an ongoing project with Sung-Soo Byun (Seoul National University) on the scaling limits of non-Hermitian Wishart random matrices, which were introduced in the context of quantum chromodynamics with a baryon chemical potential, and their probabilistic applications. We present a robust argument, a generalized Christoffel-Darboux type identity, to obtain the scaling limits of eigenvalue point processes (determinantal/Pfaffian point processes) for non-Hermitian Wishart ensembles. Additionally, I will discuss the fluctuation of real eigenvalues in non-Hermitian real Wishart ensembles.
2024年10月18日(金)
代数幾何学セミナー
13:30-15:00 数理科学研究科棟(駒場) 118号室
Jennifer Li 氏 (プリンストン大学)
Rational surfaces with a non-arithmetic automorphism group (英語)
Jennifer Li 氏 (プリンストン大学)
Rational surfaces with a non-arithmetic automorphism group (英語)
[ 講演概要 ]
In [Tot12], Totaro gave examples of a K3 surface such that its automorphism group is not commensurable with an arithmetic group, answering a question of Mazur. We give examples of rational surfaces with the same property. Our examples Y are log Calabi-Yau surfaces, i.e., there is a reduced normal crossing divisor D in Y such that KY+D=0. This is joint work with Sebastián Torres.
In [Tot12], Totaro gave examples of a K3 surface such that its automorphism group is not commensurable with an arithmetic group, answering a question of Mazur. We give examples of rational surfaces with the same property. Our examples Y are log Calabi-Yau surfaces, i.e., there is a reduced normal crossing divisor D in Y such that KY+D=0. This is joint work with Sebastián Torres.
2024年10月17日(木)
トポロジー火曜セミナー
17:00-18:30 数理科学研究科棟(駒場) ハイブリッド開催/056号室
開催日、開催場所にご注意下さい。対面参加、オンライン参加のいずれの場合もセミナーのホームページから参加登録を行って下さい。
榎園 誠 氏 (東京大学大学院数理科学研究科)
Slope inequalities for fibered complex surfaces (JAPANESE)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
開催日、開催場所にご注意下さい。対面参加、オンライン参加のいずれの場合もセミナーのホームページから参加登録を行って下さい。
榎園 誠 氏 (東京大学大学院数理科学研究科)
Slope inequalities for fibered complex surfaces (JAPANESE)
[ 講演概要 ]
Slope inequalities of fibered surfaces are important in relation to the classification of algebraic surfaces and the complex structure of Lefschetz fibrations in four-dimensional topology. It is also known that many slope inequalities for semi-stable fibered surfaces can be derived from the intersection theory on the moduli space of stable curves. In this talk, after outlining the background of these studies, I will explain how various slope inequalities can be obtained for fibered surfaces that are not necessarily semi-stable by extending the discussion of the moduli space.
[ 参考URL ]Slope inequalities of fibered surfaces are important in relation to the classification of algebraic surfaces and the complex structure of Lefschetz fibrations in four-dimensional topology. It is also known that many slope inequalities for semi-stable fibered surfaces can be derived from the intersection theory on the moduli space of stable curves. In this talk, after outlining the background of these studies, I will explain how various slope inequalities can be obtained for fibered surfaces that are not necessarily semi-stable by extending the discussion of the moduli space.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
2024年10月16日(水)
東京無限可積分系セミナー
15:30-16:30 数理科学研究科棟(駒場) 056号室
Davide Dal Martello 氏 (立教大学)
Convolutions, factorizations, and clusters from Painlevé VI (English)
Davide Dal Martello 氏 (立教大学)
Convolutions, factorizations, and clusters from Painlevé VI (English)
[ 講演概要 ]
The Painlevé VI equation governs the isomonodromic deformation problem of both 2-dimensional Fuchsian and 3-dimensional Birkhoff systems. Through duality, this feature identifies the two systems. We prove this bijection admits a more transparent middle convolution formulation, which unlocks a monodromic translation involving the Killing factorization. Moreover, exploiting a higher Teichmüller parametrization of the monodromy group, Okamoto's birational map of PVI is given a new realization as a cluster transformation. Time permitting, we conclude with a taste of the quantum version of these constructions.
The Painlevé VI equation governs the isomonodromic deformation problem of both 2-dimensional Fuchsian and 3-dimensional Birkhoff systems. Through duality, this feature identifies the two systems. We prove this bijection admits a more transparent middle convolution formulation, which unlocks a monodromic translation involving the Killing factorization. Moreover, exploiting a higher Teichmüller parametrization of the monodromy group, Okamoto's birational map of PVI is given a new realization as a cluster transformation. Time permitting, we conclude with a taste of the quantum version of these constructions.
代数学コロキウム
17:00-18:00 数理科学研究科棟(駒場) 117号室
Pierre Colmez 氏 (Sorbonne University)
On the factorisation of Beilinson-Kato system (English)
Pierre Colmez 氏 (Sorbonne University)
On the factorisation of Beilinson-Kato system (English)
[ 講演概要 ]
I will explain how one can factor Beilinson-Kato system as a product of two modular symbols, an algebraic incarnation of Rankin's method. This is joint work with Shanwen Wang.
I will explain how one can factor Beilinson-Kato system as a product of two modular symbols, an algebraic incarnation of Rankin's method. This is joint work with Shanwen Wang.
数値解析セミナー
16:30-18:00 数理科学研究科棟(駒場) 002号室
中井 拳吾 氏 (岡山大学学術研究院)
偏った時系列データを用いた機械学習による時間発展モデリング (Japanese)
https://sites.google.com/g.ecc.u-tokyo.ac.jp/utnas-bulletin-board/
中井 拳吾 氏 (岡山大学学術研究院)
偏った時系列データを用いた機械学習による時間発展モデリング (Japanese)
[ 講演概要 ]
リザーバーコンピューティングと呼ばれる機械学習手法が決定論的ダイナミクスのモデリングに有効であり、単に時系列予測能力が高いだけではなく力学系構造の再現性なども明らかになってきている。本講演の前半では、時系列データの学習の難しさやリザーバーコンピューティングによる学習の仕組みを説明し、周辺の問題や研究のモチベーションについて紹介する。後半では、準備できるデータが少ない場合やデータに偏りがある場合のアトラクターや不変密度分布等の再現性などの結果を紹介する。時間が許せば、現在考えている問題についても触れる。
本講演は、一橋大学の斉木吉隆氏との共同研究に基づく。
[ 参考URL ]リザーバーコンピューティングと呼ばれる機械学習手法が決定論的ダイナミクスのモデリングに有効であり、単に時系列予測能力が高いだけではなく力学系構造の再現性なども明らかになってきている。本講演の前半では、時系列データの学習の難しさやリザーバーコンピューティングによる学習の仕組みを説明し、周辺の問題や研究のモチベーションについて紹介する。後半では、準備できるデータが少ない場合やデータに偏りがある場合のアトラクターや不変密度分布等の再現性などの結果を紹介する。時間が許せば、現在考えている問題についても触れる。
本講演は、一橋大学の斉木吉隆氏との共同研究に基づく。
https://sites.google.com/g.ecc.u-tokyo.ac.jp/utnas-bulletin-board/
2024年10月10日(木)
東京確率論セミナー
10:00-11:30 数理科学研究科棟(駒場) 122号室
講演は午前中です。教室は１２２です。東京無限可積分系セミナーとの合同セミナーです。今日はTea Time はありません。
Chiara Franceschini 氏 (University of Modena and Reggio Emilia)
Harmonic models out of equilibrium: duality relations and invariant measure (英語)
講演は午前中です。教室は１２２です。東京無限可積分系セミナーとの合同セミナーです。今日はTea Time はありません。
Chiara Franceschini 氏 (University of Modena and Reggio Emilia)
Harmonic models out of equilibrium: duality relations and invariant measure (英語)
[ 講演概要 ]
Zero-range interacting systems of Harmonic type have been recently introduced by Frassek, Giardinà and Kurchan [JSP 2020] from the integrable XXX Hamiltonian with non compact spins. In this talk I will introduce this one parameter family of models on a one dimensional lattice with open boundary whose dynamics describes redistribution of energy or jump of particles between nearest neighbor sites. These models belong to the same macroscopic class of the KMP model, introduced in 1982 by Kipnis Marchioro and Presutti. First, I will show their similar algebraic structure as well as their duality relations. Second, I will present how to explicitly characterize the invariant measure out of equilibrium, a task that is, in general, quite difficult in this context and it has been achieved in very few cases, e.g. the well known exclusion process. As an application, thanks to this characterization, it is possible to compute formulas predicted by macroscopic fluctuation theory. This is from joint works with: Gioia Carinci, Rouven Frassek, Davide Gabrielli, Cirstian Giarinà, Frank Redig and Dimitrios Tsagkarogiannis.
Zero-range interacting systems of Harmonic type have been recently introduced by Frassek, Giardinà and Kurchan [JSP 2020] from the integrable XXX Hamiltonian with non compact spins. In this talk I will introduce this one parameter family of models on a one dimensional lattice with open boundary whose dynamics describes redistribution of energy or jump of particles between nearest neighbor sites. These models belong to the same macroscopic class of the KMP model, introduced in 1982 by Kipnis Marchioro and Presutti. First, I will show their similar algebraic structure as well as their duality relations. Second, I will present how to explicitly characterize the invariant measure out of equilibrium, a task that is, in general, quite difficult in this context and it has been achieved in very few cases, e.g. the well known exclusion process. As an application, thanks to this characterization, it is possible to compute formulas predicted by macroscopic fluctuation theory. This is from joint works with: Gioia Carinci, Rouven Frassek, Davide Gabrielli, Cirstian Giarinà, Frank Redig and Dimitrios Tsagkarogiannis.
東京無限可積分系セミナー
10:00-11:30 数理科学研究科棟(駒場) 122号室
Chiara Franceschini 氏 (University of Modena and Reggio Emilia)
Harmonic models out of equilibrium: duality relations and invariant measure (ENGLISH)
Chiara Franceschini 氏 (University of Modena and Reggio Emilia)
Harmonic models out of equilibrium: duality relations and invariant measure (ENGLISH)
[ 講演概要 ]
Zero-range interacting systems of Harmonic type have been recently introduced by Frassek, Giardinà and Kurchan [JSP 2020] from the integrable XXX Hamiltonian with non compact spins. In this talk I will introduce this one parameter family of models on a one dimensional lattice with open boundary whose dynamics describes redistribution of energy or jump of particles between nearest neighbor sites. These models belong to the same macroscopic class of the KMP model, introduced in 1982 by Kipnis Marchioro and Presutti. First, I will show their similar algebraic structure as well as their duality relations. Second, I will present how to explicitly characterize the invariant measure out of equilibrium, a task that is, in general, quite difficult in this context and it has been achieved in very few cases, e.g. the well known exclusion process. As an application, thanks to this characterization, it is possible to compute formulas predicted by macroscopic fluctuation theory.
This is from joint works with: Gioia Carinci, Rouven Frassek, Davide Gabrielli, Cirstian Giarinà, Frank Redig and Dimitrios Tsagkarogiannis.
Zero-range interacting systems of Harmonic type have been recently introduced by Frassek, Giardinà and Kurchan [JSP 2020] from the integrable XXX Hamiltonian with non compact spins. In this talk I will introduce this one parameter family of models on a one dimensional lattice with open boundary whose dynamics describes redistribution of energy or jump of particles between nearest neighbor sites. These models belong to the same macroscopic class of the KMP model, introduced in 1982 by Kipnis Marchioro and Presutti. First, I will show their similar algebraic structure as well as their duality relations. Second, I will present how to explicitly characterize the invariant measure out of equilibrium, a task that is, in general, quite difficult in this context and it has been achieved in very few cases, e.g. the well known exclusion process. As an application, thanks to this characterization, it is possible to compute formulas predicted by macroscopic fluctuation theory.
This is from joint works with: Gioia Carinci, Rouven Frassek, Davide Gabrielli, Cirstian Giarinà, Frank Redig and Dimitrios Tsagkarogiannis.
2024年10月08日(火)
作用素環セミナー
16:45-18:15 数理科学研究科棟(駒場) 122号室
紅村冬大 氏 (理研)
Weyl groups of groupoid $C^*$-algebras
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
紅村冬大 氏 (理研)
Weyl groups of groupoid $C^*$-algebras
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
解析学火曜セミナー
16:00-17:30 数理科学研究科棟(駒場) 128号室
対面・オンラインハイブリッド開催，場所にご注意ください
Erik Skibsted 氏 (Aarhus University)
Scattering subspace for time-periodic $N$-body Schrödinger operators (English)
https://forms.gle/it1Kc4voAXK5vpcB9
対面・オンラインハイブリッド開催，場所にご注意ください
Erik Skibsted 氏 (Aarhus University)
Scattering subspace for time-periodic $N$-body Schrödinger operators (English)
[ 講演概要 ]
We propose a definition of a scattering subspace for many-body Schrödinger operators with time-periodic short-range pair-potentials. This in given in geometric terms. We then show that all channel wave operators exist, and that their ranges span the scattering subspace. This may possibly serve as an intermediate step for proving the longstanding open problem of asymptotic completeness, which may be reformulated as the assertion that the scattering subspace is the orthogonal subspace of the pure point subspace of the monodromy operator.
[ 参考URL ]We propose a definition of a scattering subspace for many-body Schrödinger operators with time-periodic short-range pair-potentials. This in given in geometric terms. We then show that all channel wave operators exist, and that their ranges span the scattering subspace. This may possibly serve as an intermediate step for proving the longstanding open problem of asymptotic completeness, which may be reformulated as the assertion that the scattering subspace is the orthogonal subspace of the pure point subspace of the monodromy operator.
https://forms.gle/it1Kc4voAXK5vpcB9
トポロジー火曜セミナー
17:00-18:30 数理科学研究科棟(駒場) ハイブリッド開催/123号室
開催場所にご注意下さい。対面参加、オンライン参加のいずれの場合もセミナーのホームページから参加登録を行って下さい。
今野 北斗 氏 (東京大学大学院数理科学研究科)
Dehn twists on 4-manifolds (JAPANESE)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
開催場所にご注意下さい。対面参加、オンライン参加のいずれの場合もセミナーのホームページから参加登録を行って下さい。
今野 北斗 氏 (東京大学大学院数理科学研究科)
Dehn twists on 4-manifolds (JAPANESE)
[ 講演概要 ]
Dehn twists on surfaces form a basic class of diffeomorphisms. On 4-manifolds, an analogue of Dehn twist can be defined by considering twists along Seifert fibered 3-manifolds. In this talk, I will explain how this type of diffeomorphism exhibits interesting properties from the perspective of differential topology, and occasionally from the viewpoint of symplectic geometry as well. The proof involves gauge theory for families. This talk includes joint work with Abhishek Mallick and Masaki Taniguchi, as well as joint work with Jianfeng Lin, Anubhav Mukherjee, and Juan Muñoz-Echániz.
[ 参考URL ]Dehn twists on surfaces form a basic class of diffeomorphisms. On 4-manifolds, an analogue of Dehn twist can be defined by considering twists along Seifert fibered 3-manifolds. In this talk, I will explain how this type of diffeomorphism exhibits interesting properties from the perspective of differential topology, and occasionally from the viewpoint of symplectic geometry as well. The proof involves gauge theory for families. This talk includes joint work with Abhishek Mallick and Masaki Taniguchi, as well as joint work with Jianfeng Lin, Anubhav Mukherjee, and Juan Muñoz-Echániz.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
2024年10月07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
田島 慎一 氏 (新潟大学)
非孤立特異点を持つ超曲面の代数解析と計算複素解析 (Japanese)
https://forms.gle/gTP8qNZwPyQyxjTj8
田島 慎一 氏 (新潟大学)
非孤立特異点を持つ超曲面の代数解析と計算複素解析 (Japanese)
[ 講演概要 ]
Bernstein-Sato多項式(b-関数)は、超曲面のvanishing cycleやmultiplier idealとも関係する重要な不変量として知られている。b-関数の根に付随して定められるホロノミーD-加群は、豊かな複素解析幾何的構造を持つ。例えば、ホロノミーD-加群の特性多様体は特異点集合のWhitney stratificationと直接係わる。またその解層のなすperverse sheafは、monodromy (D. Siersmaのvertical monodromyに対応)という複素解析的構造を有する。
本講演では、これらホロノミーD-加群の構造を解析するための数学的枠組みを紹介する。準素イデアルに付随したlocal chomologyに対しネター作用素の概念を導入し、可換代数の世界と複素解析の世界を結ぶ懸け橋として用いる。これらを用いることで、(Whitney stratification）の各stratum上でホロノミーD-加群を解析することが可能となる事を示す。
応用として, monodromy構造やmicrolocal b-関数を求めるこ都が出来ることを紹介する。また、Newton 非退化な孤立特異点をもつ超曲面のb-関数の計算、map germの複素解析への応用などについても紹介したい。
[ 参考URL ]Bernstein-Sato多項式(b-関数)は、超曲面のvanishing cycleやmultiplier idealとも関係する重要な不変量として知られている。b-関数の根に付随して定められるホロノミーD-加群は、豊かな複素解析幾何的構造を持つ。例えば、ホロノミーD-加群の特性多様体は特異点集合のWhitney stratificationと直接係わる。またその解層のなすperverse sheafは、monodromy (D. Siersmaのvertical monodromyに対応)という複素解析的構造を有する。
本講演では、これらホロノミーD-加群の構造を解析するための数学的枠組みを紹介する。準素イデアルに付随したlocal chomologyに対しネター作用素の概念を導入し、可換代数の世界と複素解析の世界を結ぶ懸け橋として用いる。これらを用いることで、(Whitney stratification）の各stratum上でホロノミーD-加群を解析することが可能となる事を示す。
応用として, monodromy構造やmicrolocal b-関数を求めるこ都が出来ることを紹介する。また、Newton 非退化な孤立特異点をもつ超曲面のb-関数の計算、map germの複素解析への応用などについても紹介したい。
https://forms.gle/gTP8qNZwPyQyxjTj8
2024年10月04日(金)
代数幾何学セミナー
13:30-15:00 数理科学研究科棟(駒場) 118号室
高松哲平 氏 (京都大学)
Arithmetic finiteness of Mukai varieties of genus 7 (日本語)
高松哲平 氏 (京都大学)
Arithmetic finiteness of Mukai varieties of genus 7 (日本語)
[ 講演概要 ]
Fano threefolds over C with Picard number and index equal to 1 are known to be classified by their genus g (where 2≤g≤12 and g≠11). In particular, Mukai has shown that those with genus 7 can be described as hyperplane sections of a connected component of the 10-dimensional orthogonal Grassmannian.
In this talk, we discuss the arithmetic properties of these genus 7 threefolds and their higher-dimensional generalizations (called Mukai varieties of genus 7). More precisely, we consider the finiteness problem of varieties over a ring of S-integers (so called the Shafarevich conjecture), and the existence problem of varieties over the rational integer ring Z.
This talk is based on a joint work with Tetsushi Ito, Akihiro Kanemitsu, and Yuuji Tanaka.
Fano threefolds over C with Picard number and index equal to 1 are known to be classified by their genus g (where 2≤g≤12 and g≠11). In particular, Mukai has shown that those with genus 7 can be described as hyperplane sections of a connected component of the 10-dimensional orthogonal Grassmannian.
In this talk, we discuss the arithmetic properties of these genus 7 threefolds and their higher-dimensional generalizations (called Mukai varieties of genus 7). More precisely, we consider the finiteness problem of varieties over a ring of S-integers (so called the Shafarevich conjecture), and the existence problem of varieties over the rational integer ring Z.
This talk is based on a joint work with Tetsushi Ito, Akihiro Kanemitsu, and Yuuji Tanaka.
2024年10月03日(木)
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) 270号室
Anton Dzhamay 氏 (BIMSA, Beijing)
Some Examples of Geometric Deautonomization
Anton Dzhamay 氏 (BIMSA, Beijing)
Some Examples of Geometric Deautonomization
[ 講演概要 ]
It is well-known that many interesting examples of discrete Painlevé equations can be obtained from QRT mappings via a deautonomization process. There is an algebraic approach by B. Grammaticos, A. Ramani, and their collaborators, that uses the notion of singularity confinement to perform this process.
Recently, together with A. S. Carstea and T. Takenawa, we introduced the notion of geometric deautonomization of QRT maps based on a choice of a fiber in the QRT fibration. In this talk we present some examples of geometric deautonomization using a particular QRT map that appears in the discretization of the Nahm equations.
It is well-known that many interesting examples of discrete Painlevé equations can be obtained from QRT mappings via a deautonomization process. There is an algebraic approach by B. Grammaticos, A. Ramani, and their collaborators, that uses the notion of singularity confinement to perform this process.
Recently, together with A. S. Carstea and T. Takenawa, we introduced the notion of geometric deautonomization of QRT maps based on a choice of a fiber in the QRT fibration. In this talk we present some examples of geometric deautonomization using a particular QRT map that appears in the discretization of the Nahm equations.
2024年10月02日(水)
日仏数学拠点FJ-LMIセミナー
13:30-14:30 数理科学研究科棟(駒場) 122号室
Daniel CARO 氏 (Université de Caen Normandie)
Introduction to arithmetic D-modules (英語)
https://fj-lmi.cnrs.fr/seminars/
Daniel CARO 氏 (Université de Caen Normandie)
Introduction to arithmetic D-modules (英語)
[ 講演概要 ]
In this talk, I will give a brief overview of the theory of D-arithmetic modules, initiated by P. Berthelot in the 90's. By replacing the analytic or complex algebraic varieties by algebraic varieties defined over a field of characteristic p>0, this corresponds to an arithmetic analogue of the usual theory of D-modules. This makes it possible to obtain categories of p-adic objects associated with varieties of characteristic p; these p-adic coefficients satisfying a six functors formalism as expected. Via the de Rham cohomology associated with the constant arithmetic D-module, we obtain a p-adic interpretation and the rationality of the Weil zeta function, an arithmetic avatar of the Riemann zeta function, as well as a p-adic analogue of the Riemann hypothesis.
[ 参考URL ]In this talk, I will give a brief overview of the theory of D-arithmetic modules, initiated by P. Berthelot in the 90's. By replacing the analytic or complex algebraic varieties by algebraic varieties defined over a field of characteristic p>0, this corresponds to an arithmetic analogue of the usual theory of D-modules. This makes it possible to obtain categories of p-adic objects associated with varieties of characteristic p; these p-adic coefficients satisfying a six functors formalism as expected. Via the de Rham cohomology associated with the constant arithmetic D-module, we obtain a p-adic interpretation and the rationality of the Weil zeta function, an arithmetic avatar of the Riemann zeta function, as well as a p-adic analogue of the Riemann hypothesis.
https://fj-lmi.cnrs.fr/seminars/
代数学コロキウム
17:00-18:00 数理科学研究科棟(駒場) 117号室
Hui Gao 氏 (Southern University of Science and Technology)
Filtered integral Sen theory (English)
Hui Gao 氏 (Southern University of Science and Technology)
Filtered integral Sen theory (English)
[ 講演概要 ]
Using the Breuil--Kisin module attached to an integral crystalline representation, one can define an integral Hodge filtration whose behavior is closely related to arithmetic and geometry of the representation. In this talk, we discuss vanishing and torsion bound on graded pieces of this filtration, using a filtered integral Sen theory as key tool. This is joint work with Tong Liu.
Using the Breuil--Kisin module attached to an integral crystalline representation, one can define an integral Hodge filtration whose behavior is closely related to arithmetic and geometry of the representation. In this talk, we discuss vanishing and torsion bound on graded pieces of this filtration, using a filtered integral Sen theory as key tool. This is joint work with Tong Liu.
2024年10月01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) 128号室
東京確率論セミナーと合同開催，対面のみでオンライン配信は行いません，場所にご注意ください
Patrícia Gonçalves 氏 (IST Lisbon)
Hydrodynamics, fluctuations, and universality of exclusion processes (English)
東京確率論セミナーと合同開催，対面のみでオンライン配信は行いません，場所にご注意ください
Patrícia Gonçalves 氏 (IST Lisbon)
Hydrodynamics, fluctuations, and universality of exclusion processes (English)
[ 講演概要 ]
In the seventies, Frank Spitzer introduced interacting particle systems to the mathematics community. These systems consist of particles evolving randomly according to Markovian dynamics that conserve certain quantities. Interacting particle systems were already known in the physics and biophysics communities and served as toy models for a variety of interesting phenomena. One of the most classical interacting particle systems is the exclusion process, where particles evolve in a discrete space according to a transition probability, but at each site, only one particle is allowed. One of the goals of studying these models is to derive their hydrodynamic limit, i.e., to deduce the macroscopic equations governing the space-time evolution of the conserved quantities of the system from the underlying random motion of the microscopic particles.
In this talk, I will review the derivation of these limits for the exclusion process. I will also discuss their equilibrium fluctuations, i.e., the fluctuations around the typical profile when the system starts from the invariant measure. Our focus will then shift to the two-species exclusion process, a system with two conservation laws, namely particles of type A and B. We will see that for proper linear combinations of the conserved quantities, their evolution is autonomous. This advances our understanding of the universal behavior of these systems. This presentation is based on joint work with G. Cannizzaro, R. Misturini, and A. Occelli.
In the seventies, Frank Spitzer introduced interacting particle systems to the mathematics community. These systems consist of particles evolving randomly according to Markovian dynamics that conserve certain quantities. Interacting particle systems were already known in the physics and biophysics communities and served as toy models for a variety of interesting phenomena. One of the most classical interacting particle systems is the exclusion process, where particles evolve in a discrete space according to a transition probability, but at each site, only one particle is allowed. One of the goals of studying these models is to derive their hydrodynamic limit, i.e., to deduce the macroscopic equations governing the space-time evolution of the conserved quantities of the system from the underlying random motion of the microscopic particles.
In this talk, I will review the derivation of these limits for the exclusion process. I will also discuss their equilibrium fluctuations, i.e., the fluctuations around the typical profile when the system starts from the invariant measure. Our focus will then shift to the two-species exclusion process, a system with two conservation laws, namely particles of type A and B. We will see that for proper linear combinations of the conserved quantities, their evolution is autonomous. This advances our understanding of the universal behavior of these systems. This presentation is based on joint work with G. Cannizzaro, R. Misturini, and A. Occelli.
東京確率論セミナー
16:00-17:30 数理科学研究科棟(駒場) 128号室
教室は１２８です。解析学火曜セミナーとの合同セミナーです。今日はTea Time はありません。
Patricia Goncalves 氏 (Instituto Superior Técnico)
Hydrodynamics, fluctuations, and universality of exclusion processes (英語)
教室は１２８です。解析学火曜セミナーとの合同セミナーです。今日はTea Time はありません。
Patricia Goncalves 氏 (Instituto Superior Técnico)
Hydrodynamics, fluctuations, and universality of exclusion processes (英語)
[ 講演概要 ]
In the seventies, Frank Spitzer introduced interacting particle systems to the mathematics community. These systems consist of particles evolving randomly according to Markovian dynamics that conserve certain quantities. Interacting particle systems were already known in the physics and biophysics communities and served as toy models for a variety of interesting phenomena. One of the most classical interacting particle systems is the exclusion process, where particles evolve in a discrete space according to a transition probability, but at each site, only one particle is allowed. One of the goals of studying these models is to derive their hydrodynamic limit, i.e., to deduce the macroscopic equations governing the space-time evolution of the conserved quantities of the system from the underlying random motion of the microscopic particles.
In this talk, I will review the derivation of these limits for the exclusion process. I will also discuss their equilibrium fluctuations, i.e., the fluctuations around the typical profile when the system starts from the invariant measure. Our focus will then shift to the two-species exclusion process, a system with two conservation laws, namely particles of type A and B. We will see that for proper linear combinations of the conserved quantities, their evolution is autonomous. This advances our understanding of the universal behavior of these systems. This presentation is based on joint work with G. Cannizzaro, R. Misturini, and A. Occelli.
In the seventies, Frank Spitzer introduced interacting particle systems to the mathematics community. These systems consist of particles evolving randomly according to Markovian dynamics that conserve certain quantities. Interacting particle systems were already known in the physics and biophysics communities and served as toy models for a variety of interesting phenomena. One of the most classical interacting particle systems is the exclusion process, where particles evolve in a discrete space according to a transition probability, but at each site, only one particle is allowed. One of the goals of studying these models is to derive their hydrodynamic limit, i.e., to deduce the macroscopic equations governing the space-time evolution of the conserved quantities of the system from the underlying random motion of the microscopic particles.
In this talk, I will review the derivation of these limits for the exclusion process. I will also discuss their equilibrium fluctuations, i.e., the fluctuations around the typical profile when the system starts from the invariant measure. Our focus will then shift to the two-species exclusion process, a system with two conservation laws, namely particles of type A and B. We will see that for proper linear combinations of the conserved quantities, their evolution is autonomous. This advances our understanding of the universal behavior of these systems. This presentation is based on joint work with G. Cannizzaro, R. Misturini, and A. Occelli.
2024年09月30日(月)
東京確率論セミナー
16:00-17:30 数理科学研究科棟(駒場) 126号室
15:15〜 ２階のコモンルームでTea timeを行います。ぜひこちらにもご参加ください。
梶野直孝 氏 (京都大学)
Heat kernel estimates for boundary traces of reflected diffusions on uniform domains
15:15〜 ２階のコモンルームでTea timeを行います。ぜひこちらにもご参加ください。
梶野直孝 氏 (京都大学)
Heat kernel estimates for boundary traces of reflected diffusions on uniform domains
[ 講演概要 ]
This talk is aimed at presenting the results of the speaker's recent joint work (arXiv:2312.08546) with Mathav Murugan (University of British Columbia) on the boundary trace processes of reflected diffusions on uniform domains. We obtain stable-like heat kernel estimates for such a boundary trace process when the diffusion on the underlying ambient space satisfies sub-Gaussian heat kernel estimates. Our arguments rely on new results of independent interest such as sharp two-sided estimates and the volume doubling property of the harmonic measure, the existence of a continuous extension of the Na\"im kernel to the topological boundary, and the Doob--Na\"im formula identifying the Dirichlet form of the boundary trace process as the pure-jump Dirichlet form whose jump kernel with respect to the harmonic measure is exactly (the continuous extension of) the Na\"im kernel.
This talk is aimed at presenting the results of the speaker's recent joint work (arXiv:2312.08546) with Mathav Murugan (University of British Columbia) on the boundary trace processes of reflected diffusions on uniform domains. We obtain stable-like heat kernel estimates for such a boundary trace process when the diffusion on the underlying ambient space satisfies sub-Gaussian heat kernel estimates. Our arguments rely on new results of independent interest such as sharp two-sided estimates and the volume doubling property of the harmonic measure, the existence of a continuous extension of the Na\"im kernel to the topological boundary, and the Doob--Na\"im formula identifying the Dirichlet form of the boundary trace process as the pure-jump Dirichlet form whose jump kernel with respect to the harmonic measure is exactly (the continuous extension of) the Na\"im kernel.
2024年09月18日(水)
代数学コロキウム
17:00-18:00 数理科学研究科棟(駒場) 117号室
Ishan Levy 氏 (University of Copenhagen)
Telescopic stable homotopy theory (English)
Ishan Levy 氏 (University of Copenhagen)
Telescopic stable homotopy theory (English)
[ 講演概要 ]
Chromatic homotopy theory attempts to study the stable homotopy category by breaking it into v_n-periodic layers corresponding to height n formal groups. There are two natural ways to do this, via either the K(n)-localizations which are computationally accessible, or via the T(n)-localizations, which detect the v_n-periodic parts of the stable homotopy groups of spheres. Ravenel's telescope conjecture asks that these two localizations agree. For n at least 2 and all primes, I will discuss counterexamples to Ravenel’s telescope conjecture. Our counterexamples come from using trace methods to compute the T(n) and K(n)-localizations of the algebraic K-theory of a family of ring spectra, which in the case n=2 are certain finite Galois extensions of the K(1)-local sphere. I will then explain that this can be used to obtain an infinite family of elements in the v_n-periodic stable homotopy groups of spheres, giving the best known lower bound on the asymptotic average ranks of the stable stems. Finally, I will explain that the Galois group of the T(n)-local category agrees with that of the K(n)-local category, and how the failure of the telescope conjecture comes entirely from the failure of Galois hyperdescent. This talk comes from projects that are joint with Burklund, Carmeli, Clausen, Hahn, Schlank, and Yanovski.
Chromatic homotopy theory attempts to study the stable homotopy category by breaking it into v_n-periodic layers corresponding to height n formal groups. There are two natural ways to do this, via either the K(n)-localizations which are computationally accessible, or via the T(n)-localizations, which detect the v_n-periodic parts of the stable homotopy groups of spheres. Ravenel's telescope conjecture asks that these two localizations agree. For n at least 2 and all primes, I will discuss counterexamples to Ravenel’s telescope conjecture. Our counterexamples come from using trace methods to compute the T(n) and K(n)-localizations of the algebraic K-theory of a family of ring spectra, which in the case n=2 are certain finite Galois extensions of the K(1)-local sphere. I will then explain that this can be used to obtain an infinite family of elements in the v_n-periodic stable homotopy groups of spheres, giving the best known lower bound on the asymptotic average ranks of the stable stems. Finally, I will explain that the Galois group of the T(n)-local category agrees with that of the K(n)-local category, and how the failure of the telescope conjecture comes entirely from the failure of Galois hyperdescent. This talk comes from projects that are joint with Burklund, Carmeli, Clausen, Hahn, Schlank, and Yanovski.
2024年09月11日(水)
日仏数学拠点FJ-LMIセミナー
13:30-14:30 数理科学研究科棟(駒場) 122号室
Çağrı SERT 氏 (Univeristy of Warwick)
Counting limit theorems for representations of Gromov-hyperbolic groups (英語)
https://fj-lmi.cnrs.fr/seminars/
Çağrı SERT 氏 (Univeristy of Warwick)
Counting limit theorems for representations of Gromov-hyperbolic groups (英語)
[ 講演概要 ]
Let Г be a Gromov-hyperbolic group and S a finite symmetric generating set. The choice of S determines a metric on Г (namely the graph metric on the associated Cayley graph).
Given a representation ρ: Г→GL_d(R), we are interested in obtaining probabilistic limit theorems for the deterministic sequence of spherical averages (with respect to S-metric) for various numerical quantities (such as the operator norm) associated to elements of Г via the representation. We will discuss a general law of large numbers and more refined limit theorems such as central limit theorem and large deviations. Time permitting, connections with the results of Lubotzky–Mozes–Raghunathan and Kaimanovich–Kapovich–Schupp will also be mentioned. Joint work with Stephen Cantrell.
[ 参考URL ]Let Г be a Gromov-hyperbolic group and S a finite symmetric generating set. The choice of S determines a metric on Г (namely the graph metric on the associated Cayley graph).
Given a representation ρ: Г→GL_d(R), we are interested in obtaining probabilistic limit theorems for the deterministic sequence of spherical averages (with respect to S-metric) for various numerical quantities (such as the operator norm) associated to elements of Г via the representation. We will discuss a general law of large numbers and more refined limit theorems such as central limit theorem and large deviations. Time permitting, connections with the results of Lubotzky–Mozes–Raghunathan and Kaimanovich–Kapovich–Schupp will also be mentioned. Joint work with Stephen Cantrell.
https://fj-lmi.cnrs.fr/seminars/
Lie群論・表現論セミナー
13:30-14:30 数理科学研究科棟(駒場) 122号室
日仏数学拠点 FJ-LMI セミナーと合同
Çağrı SERT 氏 (Univeristy of Warwick)
Counting limit theorems for representations of Gromov-hyperbolic groups (English)
日仏数学拠点 FJ-LMI セミナーと合同
Çağrı SERT 氏 (Univeristy of Warwick)
Counting limit theorems for representations of Gromov-hyperbolic groups (English)
[ 講演概要 ]
Let Г be a Gromov-hyperbolic group and S a finite symmetric generating set. The choice of S determines a metric on Г (namely the graph metric on the associated Cayley graph).
Given a representation ρ: Г→GL_d(R), we are interested in obtaining probabilistic limit theorems for the deterministic sequence of spherical averages (with respect to S-metric) for various numerical quantities (such as the operator norm) associated to elements of Г via the representation. We will discuss a general law of large numbers and more refined limit theorems such as central limit theorem and large deviations. Time permitting, connections with the results of Lubotzky–Mozes–Raghunathan and Kaimanovich–Kapovich–Schupp will also be mentioned. Joint work with Stephen Cantrell.
Let Г be a Gromov-hyperbolic group and S a finite symmetric generating set. The choice of S determines a metric on Г (namely the graph metric on the associated Cayley graph).
Given a representation ρ: Г→GL_d(R), we are interested in obtaining probabilistic limit theorems for the deterministic sequence of spherical averages (with respect to S-metric) for various numerical quantities (such as the operator norm) associated to elements of Г via the representation. We will discuss a general law of large numbers and more refined limit theorems such as central limit theorem and large deviations. Time permitting, connections with the results of Lubotzky–Mozes–Raghunathan and Kaimanovich–Kapovich–Schupp will also be mentioned. Joint work with Stephen Cantrell.
2024年08月19日(月)
博士論文発表会
14:00-15:15 数理科学研究科棟(駒場) 128号室
小原 和馬 氏 (東京大学数理科学研究科)
Hecke algebra isomorphisms for tame types
（馴分岐なタイプに付随するHecke環の同型について）
小原 和馬 氏 (東京大学数理科学研究科)
Hecke algebra isomorphisms for tame types
（馴分岐なタイプに付随するHecke環の同型について）
2024年07月29日(月)
東京無限可積分系セミナー
10:30-12:00 数理科学研究科棟(駒場) 056号室
John Alex Cruz Morales 氏 (National University of Colombia)
What would be equivariant mirror symmetry for Hitchin systems? (ENGLISH)
John Alex Cruz Morales 氏 (National University of Colombia)
What would be equivariant mirror symmetry for Hitchin systems? (ENGLISH)
[ 講演概要 ]
In some recent works Aganagic has introduced the idea of equivariant mirror symmetry for certain kind of hyperkahler manifolds. In this talk, after reviewing Aganagic's proposal, we will discuss how some parts of this framework could be used to study mirror symmetry of Hitchin systems. This is based on work in progress with O. Dumitrescu and M. Mulase.
In some recent works Aganagic has introduced the idea of equivariant mirror symmetry for certain kind of hyperkahler manifolds. In this talk, after reviewing Aganagic's proposal, we will discuss how some parts of this framework could be used to study mirror symmetry of Hitchin systems. This is based on work in progress with O. Dumitrescu and M. Mulase.
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