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過去の記録
過去の記録 ～04/19｜本日 04/20 | 今後の予定 04/21～
東京確率論セミナー
17:00-18:30 数理科学研究科棟(駒場) 126号室
Stefan Junk 氏 (学習院大学)
Local limit theorem for directed polymer in (almost) the whole weak disorder regime (English)
Stefan Junk 氏 (学習院大学)
Local limit theorem for directed polymer in (almost) the whole weak disorder regime (English)
[ 講演概要 ]
We consider the directed polymer model in the weak disorder (high temperature) phase in spatial dimension d>2. In the case where the (normalized) partition function is L^2-bounded it is known for that time
polymer measure satisfies a local limit theorem, i.e., that the point-to-point partition function can be approximated by two point-to-plane partition functions at the start- and endpoint. We show
that this result continues to hold true if the partition function is L^p-bounded for some p>1+2/d. We furthermore show that for environments with finite support the required L^p -boundedness holds in the whole weak disorder phase, except possibly for the critical value itself.
We consider the directed polymer model in the weak disorder (high temperature) phase in spatial dimension d>2. In the case where the (normalized) partition function is L^2-bounded it is known for that time
polymer measure satisfies a local limit theorem, i.e., that the point-to-point partition function can be approximated by two point-to-plane partition functions at the start- and endpoint. We show
that this result continues to hold true if the partition function is L^p-bounded for some p>1+2/d. We furthermore show that for environments with finite support the required L^p -boundedness holds in the whole weak disorder phase, except possibly for the critical value itself.
2023年11月24日(金)
代数幾何学セミナー
14:00-15:30 数理科学研究科棟(駒場) ハイブリッド開催/056号室
Haidong Liu 氏 (Sun Yat-sen University)
On Kawamata-Miyaoka type inequality
Haidong Liu 氏 (Sun Yat-sen University)
On Kawamata-Miyaoka type inequality
[ 講演概要 ]
For klt projective varieties with nef and big canonical divisors, there exists a Miyaoka-Yau type inequality concerning the first and the second Chern classes. In this talk, I will present a Kawamata-Miyaoka type inequality for terminal Q-Fano varieties, which is a mirror version of the Miyaoka-Yau type inequality. This is a joint work with Jie Liu.
For klt projective varieties with nef and big canonical divisors, there exists a Miyaoka-Yau type inequality concerning the first and the second Chern classes. In this talk, I will present a Kawamata-Miyaoka type inequality for terminal Q-Fano varieties, which is a mirror version of the Miyaoka-Yau type inequality. This is a joint work with Jie Liu.
日仏数学拠点FJ-LMIセミナー
14:00-14:40 数理科学研究科棟(駒場) 117号室
Gwénaël MASSUYEAU 氏 (Université de Bourgogne & CNRS)
Surgery equivalence relations on 3-manifolds (English)
https://fj-lmi.cnrs.fr/seminars/
Gwénaël MASSUYEAU 氏 (Université de Bourgogne & CNRS)
Surgery equivalence relations on 3-manifolds (English)
[ 講演概要 ]
By some classical results in low-dimensional topology, any two 3-manifolds (with the “same” boundaries) are related one to the other by surgery operations. In this survey talk, we shall review this basic fact and, next, by restricting the type of surgeries, we shall consider several families of non-trivial equivalence relations on the set of (homeomorphism classes of) 3-manifolds. Those “surgery equivalence relations” are defined in terms of filtrations of the mapping class groups of surfaces, and their characterization / classification involves the notion of “finite-type invariant” which arises in quantum topology.
[ 参考URL ]By some classical results in low-dimensional topology, any two 3-manifolds (with the “same” boundaries) are related one to the other by surgery operations. In this survey talk, we shall review this basic fact and, next, by restricting the type of surgeries, we shall consider several families of non-trivial equivalence relations on the set of (homeomorphism classes of) 3-manifolds. Those “surgery equivalence relations” are defined in terms of filtrations of the mapping class groups of surfaces, and their characterization / classification involves the notion of “finite-type invariant” which arises in quantum topology.
https://fj-lmi.cnrs.fr/seminars/
2023年11月22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
山崎隆雄 氏 (中央大学)
曲面のねじれ双有理モチーフ不変量と不分岐コホモロジー (Japanese)
山崎隆雄 氏 (中央大学)
曲面のねじれ双有理モチーフ不変量と不分岐コホモロジー (Japanese)
[ 講演概要 ]
対角線の分解を許容する曲面の捻じれ双有理モチーフについて，不分岐コホモロジーが普遍的な不変量を与えるという結果について講演する．整係数Hodge予想への新たな反例についても触れる．また，正標数では単純な類似が成立し得ないことを論じる．（佐藤周友氏との共同研究）
対角線の分解を許容する曲面の捻じれ双有理モチーフについて，不分岐コホモロジーが普遍的な不変量を与えるという結果について講演する．整係数Hodge予想への新たな反例についても触れる．また，正標数では単純な類似が成立し得ないことを論じる．（佐藤周友氏との共同研究）
2023年11月21日(火)
トポロジー火曜セミナー
17:30-18:30 数理科学研究科棟(駒場) ハイブリッド開催/056号室
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。
古宇田 悠哉 氏 (慶應義塾大学)
Shadows, divides and hyperbolic volumes (JAPANESE)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
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。
古宇田 悠哉 氏 (慶應義塾大学)
Shadows, divides and hyperbolic volumes (JAPANESE)
[ 講演概要 ]
In 2008, Costantino and D.Thurston revealed that the combinatorial structure of the Stein factorizations of stable maps from 3-manifolds into the real plane can be used to describe the hyperbolic structures of the complement of the set of definite fold points, which is a link. The key was that the Stein factorizations can naturally be embedded into 4-manifolds, and nice ideal polyhedral decompositions become visible on their boundaries. In this talk, we consider divides, which are the images of a proper and generic immersions of compact 1-manifolds into the 2-disk. Due to A'Campo's theory, each divide is associated with a link in the 3-sphere. By embedding a polyhedron induced from a given divide into the 4-ball as was done to Stein factorization, we can read off the ideal polyhedral decompositions on the boundary. We then show that the complement of the link of the divide can be obtained by Dehn filling a hyperbolic 3-manifold that admits a decomposition into several ideal regular hyperbolic polyhedra, where the number of each polyhedron is determined by types of the double points of the divide. This immediately gives an upper bound of the hyperbolic volume of the links of divides, which is shown to be asymptotically sharp. As in the case of Stein factorizations, an idea from the theory of Turaev's shadows plays an important role here. This talk is based on joint work with Ryoga Furutani (Hiroshima University).
[ 参考URL ]In 2008, Costantino and D.Thurston revealed that the combinatorial structure of the Stein factorizations of stable maps from 3-manifolds into the real plane can be used to describe the hyperbolic structures of the complement of the set of definite fold points, which is a link. The key was that the Stein factorizations can naturally be embedded into 4-manifolds, and nice ideal polyhedral decompositions become visible on their boundaries. In this talk, we consider divides, which are the images of a proper and generic immersions of compact 1-manifolds into the 2-disk. Due to A'Campo's theory, each divide is associated with a link in the 3-sphere. By embedding a polyhedron induced from a given divide into the 4-ball as was done to Stein factorization, we can read off the ideal polyhedral decompositions on the boundary. We then show that the complement of the link of the divide can be obtained by Dehn filling a hyperbolic 3-manifold that admits a decomposition into several ideal regular hyperbolic polyhedra, where the number of each polyhedron is determined by types of the double points of the divide. This immediately gives an upper bound of the hyperbolic volume of the links of divides, which is shown to be asymptotically sharp. As in the case of Stein factorizations, an idea from the theory of Turaev's shadows plays an important role here. This talk is based on joint work with Ryoga Furutani (Hiroshima University).
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
星野真生 氏 (東大数理)
Finite index quantum subgroups of DQGs
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
星野真生 氏 (東大数理)
Finite index quantum subgroups of DQGs
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
2023年11月20日(月)
東京確率論セミナー
17:00-18:30 数理科学研究科棟(駒場) 126号室
木上淳 氏 (京都大学)
Yet another construction of “Sobolev” spaces on metric spaces (日本語)
木上淳 氏 (京都大学)
Yet another construction of “Sobolev” spaces on metric spaces (日本語)
[ 講演概要 ]
距離空間上への”ソボレフ空間”の構成については、「Lipschitz連続な関数の局所Lipschitz定数を微分の代替物としてもちいる。」という発想のもと、Hajlasz, Cheeger, Shanmugalingam らによる Newtonian 空間などの理論が研究の主流となっている。ところが、最近のKajino-Muruganの研究により、Sierpinski Carpet などの多くの自己相似集合では、この方法が通用しないことがわかってきた。本講演では、Sierpinski carpet 等を含むコンパクトな自己相似集合上に””ソボレフ””空間を構成するための新しい方法について述べる。
距離空間上への”ソボレフ空間”の構成については、「Lipschitz連続な関数の局所Lipschitz定数を微分の代替物としてもちいる。」という発想のもと、Hajlasz, Cheeger, Shanmugalingam らによる Newtonian 空間などの理論が研究の主流となっている。ところが、最近のKajino-Muruganの研究により、Sierpinski Carpet などの多くの自己相似集合では、この方法が通用しないことがわかってきた。本講演では、Sierpinski carpet 等を含むコンパクトな自己相似集合上に””ソボレフ””空間を構成するための新しい方法について述べる。
2023年11月16日(木)
情報数学セミナー
16:50-18:35 数理科学研究科棟(駒場) 128号室
山内 卓也 氏 (東北大理)
超特殊アーベル多様体上の同種グラフ: 固有値, Bruhat-Tits ビルディングおよびProperty (T) (Japanese)
山内 卓也 氏 (東北大理)
超特殊アーベル多様体上の同種グラフ: 固有値, Bruhat-Tits ビルディングおよびProperty (T) (Japanese)
[ 講演概要 ]
正整数$g$, 素数$p$, $\ell$に対して, 標数$p$の有限体上の次元$g$をもつsuperspecial abelian varietiesであって$\ell$-marking が指定されたもの全体の成す類から有限向き付き正則グラフを構成することができる. 講演ではこのグラフに対するランダムウォーク行列の性質を対応するBruhat-Tits buildingsを解析することで調べることができることを説明する. また, $g=2$のとき, 保型形式, 保型表現論の観点からランダムウォーク行列の固有値に関して何が期待されるかも説明する. 本研究は東京大学の相川 勇輔 氏、京都大学の田中 亮吉 氏との共同研究である.
正整数$g$, 素数$p$, $\ell$に対して, 標数$p$の有限体上の次元$g$をもつsuperspecial abelian varietiesであって$\ell$-marking が指定されたもの全体の成す類から有限向き付き正則グラフを構成することができる. 講演ではこのグラフに対するランダムウォーク行列の性質を対応するBruhat-Tits buildingsを解析することで調べることができることを説明する. また, $g=2$のとき, 保型形式, 保型表現論の観点からランダムウォーク行列の固有値に関して何が期待されるかも説明する. 本研究は東京大学の相川 勇輔 氏、京都大学の田中 亮吉 氏との共同研究である.
2023年11月14日(火)
トポロジー火曜セミナー
17:00-18:30 数理科学研究科棟(駒場) ハイブリッド開催/056号室
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。
横山 知郎 氏 (埼玉大学)
曲面上の流れの正方向と負方向の極限の振る舞いの依存性 (JAPANESE)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
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。
横山 知郎 氏 (埼玉大学)
曲面上の流れの正方向と負方向の極限の振る舞いの依存性 (JAPANESE)
[ 講演概要 ]
We discuss the dependence of a flow's positive and negative limit behaviors on a surface. In particular, I introduce the list of possible pairs of positive and negative limit behaviors that can and cannot occur. The idea of the dependence mechanism is illustrated using the dependence of the limit behavior of a toy model, a circle homeomorphism. We overview with as few prior knowledge assumptions as possible.
[ 参考URL ]We discuss the dependence of a flow's positive and negative limit behaviors on a surface. In particular, I introduce the list of possible pairs of positive and negative limit behaviors that can and cannot occur. The idea of the dependence mechanism is illustrated using the dependence of the limit behavior of a toy model, a circle homeomorphism. We overview with as few prior knowledge assumptions as possible.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
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
古川賢 氏 (理化学研究所)
いくつかの力学系とそのデータ同化による予測について (Japanese)
ハイブリッド開催です。参加の詳細は参考URLをご覧ください。
古川賢 氏 (理化学研究所)
いくつかの力学系とそのデータ同化による予測について (Japanese)
[ 講演概要 ]
データ同化による力学系の予測について得られた２つの結果を紹介する．前半では，2次元3種のオートマトンのカオス的な離散力学系を導入し，その離散力学系の時間発展を粒子フィルターによるデータ同化によって予測する方法とその結果について紹介する．後半では，プリミティブ方程式のナッジングによるデータ同化にまつわる問題について紹介する．特に，データ自身の持つ情報量とデータ同化によって得られる近似解(予測)のもつ情報量の関係性を正則性の観点から特徴づける．
[ 参考URL ]データ同化による力学系の予測について得られた２つの結果を紹介する．前半では，2次元3種のオートマトンのカオス的な離散力学系を導入し，その離散力学系の時間発展を粒子フィルターによるデータ同化によって予測する方法とその結果について紹介する．後半では，プリミティブ方程式のナッジングによるデータ同化にまつわる問題について紹介する．特に，データ自身の持つ情報量とデータ同化によって得られる近似解(予測)のもつ情報量の関係性を正則性の観点から特徴づける．
ハイブリッド開催です。参加の詳細は参考URLをご覧ください。
解析学火曜セミナー
16:15-17:15 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，日時・場所にご注意ください
Arne Jensen 氏 (Aalborg University)
Resolvent expansions for magnetic Schrödinger operators (English)
https://forms.gle/qyEUeo4kVuPL1s289
対面・オンラインハイブリッド開催，日時・場所にご注意ください
Arne Jensen 氏 (Aalborg University)
Resolvent expansions for magnetic Schrödinger operators (English)
[ 講演概要 ]
I will present some new results resolvent expansions around threshold zero for magnetic Schrödinger operators in dimension three. The magnetic field and the electric potential are assumed to decay sufficiently fast. Analogous results for Pauli operators will also be presented.
Joint work with H. Kovarik, Brescia, Italy.
[ 参考URL ]I will present some new results resolvent expansions around threshold zero for magnetic Schrödinger operators in dimension three. The magnetic field and the electric potential are assumed to decay sufficiently fast. Analogous results for Pauli operators will also be presented.
Joint work with H. Kovarik, Brescia, Italy.
https://forms.gle/qyEUeo4kVuPL1s289
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
森迪也 氏 (東大数理)
On the Scottish Book Problem 155 by Mazur and Sternbach
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
森迪也 氏 (東大数理)
On the Scottish Book Problem 155 by Mazur and Sternbach
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
2023年11月09日(木)
情報数学セミナー
16:50-18:35 数理科学研究科棟(駒場) 128号室
高島 克幸 氏 (早大教育)
同種写像暗号の数理 (Japanese)
高島 克幸 氏 (早大教育)
同種写像暗号の数理 (Japanese)
[ 講演概要 ]
耐量子計算機暗号の一つである同種写像暗号は，楕円曲線間の同種写像を使った鍵共有や署名方式であり，CGLハッシュ関数，SIDH鍵共有，SQIsign署名などが基本的な方式として知られてきた．また、種数1の楕円曲線だけでなく，種数2曲線同種写像暗号の研究も進んでいる．本講演では，まず，それらの概要を報告するとともに，種数2 Richelot同種写像グラフに関する桂利行氏との共同研究成果も簡単に紹介する．
2022年に，Castryck–Decruに始まる一連の研究によって「補助点情報」を巧みに使ったSIDH 鍵共有に対する多項式時間攻撃法が発表された．種数1同種写像暗号に対するこれらの攻撃法においても，高次元アーベル多様体の同種写像が基本的な役割を果たしている．本講演後半では，種数2 Richelot同種写像を使ったCastryck–Decruの攻撃法を紹介して，Robertの8次元アーベル多様体を使った攻撃法にも簡単に触れる予定である．
耐量子計算機暗号の一つである同種写像暗号は，楕円曲線間の同種写像を使った鍵共有や署名方式であり，CGLハッシュ関数，SIDH鍵共有，SQIsign署名などが基本的な方式として知られてきた．また、種数1の楕円曲線だけでなく，種数2曲線同種写像暗号の研究も進んでいる．本講演では，まず，それらの概要を報告するとともに，種数2 Richelot同種写像グラフに関する桂利行氏との共同研究成果も簡単に紹介する．
2022年に，Castryck–Decruに始まる一連の研究によって「補助点情報」を巧みに使ったSIDH 鍵共有に対する多項式時間攻撃法が発表された．種数1同種写像暗号に対するこれらの攻撃法においても，高次元アーベル多様体の同種写像が基本的な役割を果たしている．本講演後半では，種数2 Richelot同種写像を使ったCastryck–Decruの攻撃法を紹介して，Robertの8次元アーベル多様体を使った攻撃法にも簡単に触れる予定である．
2023年11月07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
田中聖人 氏 (名大)
A quantum analogue of the special linear group and its proper cocycle
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
田中聖人 氏 (名大)
A quantum analogue of the special linear group and its proper cocycle
[ 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
17:00-18:30 数理科学研究科棟(駒場) ハイブリッド開催/056号室
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。
Florent Schaffhauser 氏 (Heidelberg University)
Hodge numbers of moduli spaces of principal bundles on curves (ENGLISH)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
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。
Florent Schaffhauser 氏 (Heidelberg University)
Hodge numbers of moduli spaces of principal bundles on curves (ENGLISH)
[ 講演概要 ]
The Poincaré series of moduli stacks of semistable G-bundles on curves has been computed by Laumon and Rapoport. In this joint work with Melissa Liu, we show that the Hodge-Poincaré series of these moduli stacks can be computed in a similar way. As an application, we obtain a new proof of a joint result of the speaker with Erwan Brugallé, on the maximality on moduli spaces of vector bundles over real algebraic curves.
[ 参考URL ]The Poincaré series of moduli stacks of semistable G-bundles on curves has been computed by Laumon and Rapoport. In this joint work with Melissa Liu, we show that the Hodge-Poincaré series of these moduli stacks can be computed in a similar way. As an application, we obtain a new proof of a joint result of the speaker with Erwan Brugallé, on the maximality on moduli spaces of vector bundles over real algebraic curves.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
2023年11月02日(木)
情報数学セミナー
16:50-18:35 数理科学研究科棟(駒場) 128号室
安田 雅哉 氏 (立教大学)
格子問題の求解アルゴリズムとその応用 (Japanese)
安田 雅哉 氏 (立教大学)
格子問題の求解アルゴリズムとその応用 (Japanese)
[ 講演概要 ]
本講演では、格子問題を解くための必須の技術であるLLLやBKZなどの
格子アルゴリズムを紹介する。また、LWEやNTRUの格子問題への適用
方法を説明すると共に、素因数分解問題への応用についても述べる。
本講演では、格子問題を解くための必須の技術であるLLLやBKZなどの
格子アルゴリズムを紹介する。また、LWEやNTRUの格子問題への適用
方法を説明すると共に、素因数分解問題への応用についても述べる。
2023年11月01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
Alex Youcis 氏 (東京大学大学院数理科学研究科)
Prismatic realization functor for Shimura varieties of abelian type (English)
Alex Youcis 氏 (東京大学大学院数理科学研究科)
Prismatic realization functor for Shimura varieties of abelian type (English)
[ 講演概要 ]
Shimura varieties are certain classes of schemes which play an important role in various studies of number theory. The Langlands program is one of such examples. While far from known in general, it is expected that Shimura varieties are moduli spaces of certain motives with extra structure. In this talk I discuss joint work with Naoki Imai and Hiroki Kato, which constructs prismatic objects on the integral canonical models of Shimura varieties of abelian type at hyperspecial level. These may be thought of as the prismatic realization of such a hypothetical universal motive. I will also discuss how one can use this object to characterize these integral models, even at finite level.
Shimura varieties are certain classes of schemes which play an important role in various studies of number theory. The Langlands program is one of such examples. While far from known in general, it is expected that Shimura varieties are moduli spaces of certain motives with extra structure. In this talk I discuss joint work with Naoki Imai and Hiroki Kato, which constructs prismatic objects on the integral canonical models of Shimura varieties of abelian type at hyperspecial level. These may be thought of as the prismatic realization of such a hypothetical universal motive. I will also discuss how one can use this object to characterize these integral models, even at finite level.
2023年10月31日(火)
トポロジー火曜セミナー
17:30-18:30 数理科学研究科棟(駒場) ハイブリッド開催/056号室
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。
千吉良 直紀 氏 (熊本大学)
原田予想IIについて (JAPANESE)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
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。
千吉良 直紀 氏 (熊本大学)
原田予想IIについて (JAPANESE)
[ 講演概要 ]
有限群の指標表は非常に多くの情報を含んでいる。本講演では、原田耕一郎氏による既約指標の次数の積と共役類の元の個数の積に関する予想（原田予想II）についてこれまでの概要と最近の進展について講演する。
[ 参考URL ]有限群の指標表は非常に多くの情報を含んでいる。本講演では、原田耕一郎氏による既約指標の次数の積と共役類の元の個数の積に関する予想（原田予想II）についてこれまでの概要と最近の進展について講演する。
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
古典解析セミナー
10:30-14:30 数理科学研究科棟(駒場) 126号室
Benedetta Facciotti 氏 (University of Birmingham) 10:30-11:30
The Wild Riemann-Hilbert Correspondence via Groupoid Representations (ENGLISH)
The Wild Riemann-Hilbert Correspondence via Groupoid Representations (ENGLISH)
Benedetta Facciotti 氏 (University of Birmingham) 10:30-11:30
The Wild Riemann-Hilbert Correspondence via Groupoid Representations (ENGLISH)
[ 講演概要 ]
In this talk, through simple examples, I will explain the basic idea behind the Riemann-Hilbert correspondence. It is a correspondence between two different moduli spaces: the de Rham moduli space parametrizing meromorphic differential equations, and the Betti moduli space describing local systems of solutions and the representations of the fundamental group defined by them. We will see why such a correspondence breaks down for higher order poles.
Nikita Nikolaev 氏 (University of Birmingham) 13:30-14:30In this talk, through simple examples, I will explain the basic idea behind the Riemann-Hilbert correspondence. It is a correspondence between two different moduli spaces: the de Rham moduli space parametrizing meromorphic differential equations, and the Betti moduli space describing local systems of solutions and the representations of the fundamental group defined by them. We will see why such a correspondence breaks down for higher order poles.
The Wild Riemann-Hilbert Correspondence via Groupoid Representations (ENGLISH)
[ 講演概要 ]
I will explain an approach to extending the Riemann-Hilbert correspondence to the setting of equations with higher-order poles using the representation theory of holomorphic Lie groupoids. Each Riemann-Hilbert problem is associated with a suitable Lie algebroid that is integrable to a holomorphic Lie groupoid that can be explicitly constructed as a blowup of the fundamental groupoid. Then the Riemann-Hilbert correspondence can be formulated in rather familiar Lie theoretic terms as the correspondence between representations of algebroids and groupoids. An advantage of this approach is that groupoid representations can be investigated geometrically. Based on joint work with Benedetta Facciotti (Birmingham) and Marta Mazzocco (Birmingham), as well as joint work with Francis Bischoff (Regina) and Marco Gualtieri (Toronto).
I will explain an approach to extending the Riemann-Hilbert correspondence to the setting of equations with higher-order poles using the representation theory of holomorphic Lie groupoids. Each Riemann-Hilbert problem is associated with a suitable Lie algebroid that is integrable to a holomorphic Lie groupoid that can be explicitly constructed as a blowup of the fundamental groupoid. Then the Riemann-Hilbert correspondence can be formulated in rather familiar Lie theoretic terms as the correspondence between representations of algebroids and groupoids. An advantage of this approach is that groupoid representations can be investigated geometrically. Based on joint work with Benedetta Facciotti (Birmingham) and Marta Mazzocco (Birmingham), as well as joint work with Francis Bischoff (Regina) and Marco Gualtieri (Toronto).
2023年10月30日(月)
東京確率論セミナー
16:00-18:50 数理科学研究科棟(駒場) 126号室
いつもと開始時間が異なります。この日は３つの講演があります。
Chenlin Gu 氏 (Tsinghua University) 16:00-16:50
Quantitative homogenization of interacting particle systems (English)
https://chenlin-gu.github.io/index.html
Lorenzo Dello-Schiavio 氏 (Institute of Science and Technology Austria (ISTA)) 17:00-17:50
Wasserstein geometry and Ricci curvature bounds for Poisson spaces (English)
https://lzdsmath.github.io
鈴木康平 氏 (Durham University) 18:00-18:50
Curvature Bound of the Dyson Brownian Motion (English)
https://www.durham.ac.uk/staff/kohei-suzuki/
いつもと開始時間が異なります。この日は３つの講演があります。
Chenlin Gu 氏 (Tsinghua University) 16:00-16:50
Quantitative homogenization of interacting particle systems (English)
[ 講演概要 ]
This talk presents that, for a class of interacting particle systems in continuous space, the finite-volume approximations of the bulk diffusion matrix converge at an algebraic rate. The models we consider are reversible with respect to the Poisson measures with constant density, and are of non-gradient type. This approach is inspired by recent progress in the quantitative homogenization of elliptic equations. Along the way, a modified Caccioppoli inequality and a multiscale Poincare inequality are developed, which are of independent interest. The talk is based on a joint work with Arianna Giunti and Jean-Christophe Mourrat.
[ 参考URL ]This talk presents that, for a class of interacting particle systems in continuous space, the finite-volume approximations of the bulk diffusion matrix converge at an algebraic rate. The models we consider are reversible with respect to the Poisson measures with constant density, and are of non-gradient type. This approach is inspired by recent progress in the quantitative homogenization of elliptic equations. Along the way, a modified Caccioppoli inequality and a multiscale Poincare inequality are developed, which are of independent interest. The talk is based on a joint work with Arianna Giunti and Jean-Christophe Mourrat.
https://chenlin-gu.github.io/index.html
Lorenzo Dello-Schiavio 氏 (Institute of Science and Technology Austria (ISTA)) 17:00-17:50
Wasserstein geometry and Ricci curvature bounds for Poisson spaces (English)
[ 講演概要 ]
Let Υ be the configuration space over a complete and separable metric base space, endowed with the Poisson measure π. We study the geometry of Υ from the point of view of optimal transport and Ricci-lower bounds. To do so, we define a formal Riemannian structure on P_1(Y), the space of probability measures over Υ with finite first moment, and we construct an extended distance W on P_1(Y). The distance W corresponds, in our setting, to the Benamou–Brenier variational formulation of the Wasserstein distance. Our main technical tool is a non-local continuity equation defined via the difference operator on the Poisson space. We show that the closure of the domain of the relative entropy is a complete geodesic space, when endowed with W. We establish non-local infinite-dimensional analogues of results regarding the geometry of the Wasserstein space over a metric measure space with synthetic Ricci curvature bounded below. In particular, we obtain that: (a) the Ornstein–Uhlenbeck semi-group is the gradient flow of the relative entropy; (b) the Poisson space has Ricci curvature bounded below by 1 in the entropic sense; (c) the distance W satisfies an HWI inequality.
Base on joint work arXiv:2303.00398 with Ronan Herry (Rennes 1) and Kohei Suzuki (Durham)
[ 参考URL ]Let Υ be the configuration space over a complete and separable metric base space, endowed with the Poisson measure π. We study the geometry of Υ from the point of view of optimal transport and Ricci-lower bounds. To do so, we define a formal Riemannian structure on P_1(Y), the space of probability measures over Υ with finite first moment, and we construct an extended distance W on P_1(Y). The distance W corresponds, in our setting, to the Benamou–Brenier variational formulation of the Wasserstein distance. Our main technical tool is a non-local continuity equation defined via the difference operator on the Poisson space. We show that the closure of the domain of the relative entropy is a complete geodesic space, when endowed with W. We establish non-local infinite-dimensional analogues of results regarding the geometry of the Wasserstein space over a metric measure space with synthetic Ricci curvature bounded below. In particular, we obtain that: (a) the Ornstein–Uhlenbeck semi-group is the gradient flow of the relative entropy; (b) the Poisson space has Ricci curvature bounded below by 1 in the entropic sense; (c) the distance W satisfies an HWI inequality.
Base on joint work arXiv:2303.00398 with Ronan Herry (Rennes 1) and Kohei Suzuki (Durham)
https://lzdsmath.github.io
鈴木康平 氏 (Durham University) 18:00-18:50
Curvature Bound of the Dyson Brownian Motion (English)
[ 講演概要 ]
The Dyson Brownian Motion (DBM) is an eigenvalue process of a particular Hermitian matrix-valued Brownian motion introduced by Freeman Dyson in 1962, which has been one of the central subjects in the random matrix theory. In this talk, we study the DBM from a geometric perspective. We show that the infinite particle DBM possesses a lower bound of the Ricci curvature à la Bakry-Émery. As a consequence, we obtain various quantitative estimates of the transition probability of the DBM (e.g., the local spectral gap, the local log-Sobolev, and the dimension-free Harnack inequalities) as well as the characterisation of the DBM as the gradient flow of the Boltzmann entropy in a particular Wasserstein-type space, the latter of which provides a new viewpoint of the Dyson Brownian motion.
[ 参考URL ]The Dyson Brownian Motion (DBM) is an eigenvalue process of a particular Hermitian matrix-valued Brownian motion introduced by Freeman Dyson in 1962, which has been one of the central subjects in the random matrix theory. In this talk, we study the DBM from a geometric perspective. We show that the infinite particle DBM possesses a lower bound of the Ricci curvature à la Bakry-Émery. As a consequence, we obtain various quantitative estimates of the transition probability of the DBM (e.g., the local spectral gap, the local log-Sobolev, and the dimension-free Harnack inequalities) as well as the characterisation of the DBM as the gradient flow of the Boltzmann entropy in a particular Wasserstein-type space, the latter of which provides a new viewpoint of the Dyson Brownian motion.
https://www.durham.ac.uk/staff/kohei-suzuki/
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
松村慎一 氏 (東北大学)
The Nonvanishing problem for varieties with nef anticanonical bundle
https://u-tokyo-ac-jp.zoom.us/meeting/register/tZEqceqsrTIjEtRxenSMdPogvCxlWzAogj5A
松村慎一 氏 (東北大学)
The Nonvanishing problem for varieties with nef anticanonical bundle
[ 講演概要 ]
一般化された極小モデル理論(generalized MMP)の枠組みではアバンダンス予想は成立しない. しかし, 一般化された非消滅予想(generalized nonvanishing conjecture)の成立は期待されている. この予想は適切な標準因子の数値的同値類が有効因子で代表できるかを問う予想である. 本講演では３次元の一般化されたLC対に対する非消滅予想について議論し, ネフ反標準因子に対して予想が正しいことを証明する.
この講演はV. Lazic, Th. Peternell, N. Tsakanikas, Z. Xieとの共同研究に基づく.
[ 参考URL ]一般化された極小モデル理論(generalized MMP)の枠組みではアバンダンス予想は成立しない. しかし, 一般化された非消滅予想(generalized nonvanishing conjecture)の成立は期待されている. この予想は適切な標準因子の数値的同値類が有効因子で代表できるかを問う予想である. 本講演では３次元の一般化されたLC対に対する非消滅予想について議論し, ネフ反標準因子に対して予想が正しいことを証明する.
この講演はV. Lazic, Th. Peternell, N. Tsakanikas, Z. Xieとの共同研究に基づく.
https://u-tokyo-ac-jp.zoom.us/meeting/register/tZEqceqsrTIjEtRxenSMdPogvCxlWzAogj5A
2023年10月27日(金)
談話会・数理科学講演会
15:30-16:30 数理科学研究科棟(駒場) 大講義室(auditorium)号室
数理科学研究科所属以外の方は、[参考URL]から参加登録をお願いいたします。
Jenn-Nan Wang 氏 (National Taiwan University)
Increasing stability and decreasing instability estimates for an inverse boundary value problem (English)
https://forms.gle/9xDcHfHXFFHPfsKW6
数理科学研究科所属以外の方は、[参考URL]から参加登録をお願いいたします。
Jenn-Nan Wang 氏 (National Taiwan University)
Increasing stability and decreasing instability estimates for an inverse boundary value problem (English)
[ 講演概要 ]
According to Hadamard’s definition, a well-posed problem satisfies three criteria: existence, uniqueness, and continuous dependence on the data. Most of forward problems (e.g., the boundary value problem or Calderón’s problem) can be proved to be well-posed. However, many inverse problems are known to be ill-posed, for example, the inverse boundary value problem in which one would like to determine unknown parameters from the boundary measurements. The failure of the continuous dependence on the data in Hadamard’s sense makes the feasible determination of unknown parameters rather difficult in practice. However, if one restricts the unknown parameters in a suitable subspace, one can restore the continuous dependence or stability. Nonetheless, the ill-posedness nature of the inverse problem may give rise a logarithmic type modulus of continuity. For Calderón’s problem, such logarithmic stability estimate was derived by Alessandrini and Mandache showed that this estimate is optimal by proving an instability estimate of exponential type. When we consider the time-harmonic equation, it was first proved by Isakov that the stability increases as the frequency increases. In this talk, I would like to discuss a refinement of Mandache’s idea aiming to derive explicitly the dependence of the instability estimate on the frequency. If time allows, I also want to discuss the increasing stability phenomenon from the statistical viewpoint based on the Bayes approach. The aim is to show that the posterior distribution contracts around the true parameter at a rate closely related to the decreasing instability estimate derived above.
[ 参考URL ]According to Hadamard’s definition, a well-posed problem satisfies three criteria: existence, uniqueness, and continuous dependence on the data. Most of forward problems (e.g., the boundary value problem or Calderón’s problem) can be proved to be well-posed. However, many inverse problems are known to be ill-posed, for example, the inverse boundary value problem in which one would like to determine unknown parameters from the boundary measurements. The failure of the continuous dependence on the data in Hadamard’s sense makes the feasible determination of unknown parameters rather difficult in practice. However, if one restricts the unknown parameters in a suitable subspace, one can restore the continuous dependence or stability. Nonetheless, the ill-posedness nature of the inverse problem may give rise a logarithmic type modulus of continuity. For Calderón’s problem, such logarithmic stability estimate was derived by Alessandrini and Mandache showed that this estimate is optimal by proving an instability estimate of exponential type. When we consider the time-harmonic equation, it was first proved by Isakov that the stability increases as the frequency increases. In this talk, I would like to discuss a refinement of Mandache’s idea aiming to derive explicitly the dependence of the instability estimate on the frequency. If time allows, I also want to discuss the increasing stability phenomenon from the statistical viewpoint based on the Bayes approach. The aim is to show that the posterior distribution contracts around the true parameter at a rate closely related to the decreasing instability estimate derived above.
https://forms.gle/9xDcHfHXFFHPfsKW6
2023年10月25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
Linus Hamann 氏 (Stanford University)
Geometric Eisenstein Series over the Fargues-Fontaine curve (English)
Linus Hamann 氏 (Stanford University)
Geometric Eisenstein Series over the Fargues-Fontaine curve (English)
[ 講演概要 ]
Geometric Eisenstein series were first studied extensively by Braverman-Gaitsgory, Laumon, and Drinfeld, in the context of function field geometric Langlands. For a Levi subgroup M inside a connected reductive group G, they are functors which send Hecke eigensheaves on the moduli stack of M-bundles to Hecke eigensheaves on the moduli stack of G-bundles via certain relative compactifications of the moduli stack of P-bundles. We will discuss what this theory has to offer in the context of the recent Fargues-Scholze geometric Langlands program. Namely, motivated by the results in the function field setting, we will explicate what the analogous results tell us in this setting of the Fargues-Scholze program, as well as discuss various consequences for the cohmology of local and global Shimura varieties, via the relation between local Shimura varieties and the p-adic shtukas appearing in the Fargues-Scholze program.
Geometric Eisenstein series were first studied extensively by Braverman-Gaitsgory, Laumon, and Drinfeld, in the context of function field geometric Langlands. For a Levi subgroup M inside a connected reductive group G, they are functors which send Hecke eigensheaves on the moduli stack of M-bundles to Hecke eigensheaves on the moduli stack of G-bundles via certain relative compactifications of the moduli stack of P-bundles. We will discuss what this theory has to offer in the context of the recent Fargues-Scholze geometric Langlands program. Namely, motivated by the results in the function field setting, we will explicate what the analogous results tell us in this setting of the Fargues-Scholze program, as well as discuss various consequences for the cohmology of local and global Shimura varieties, via the relation between local Shimura varieties and the p-adic shtukas appearing in the Fargues-Scholze program.
2023年10月24日(火)
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
ハイブリッド開催です。参加の詳細は参考URLをご覧ください。
田中一成 氏 (早稲田大学国際理工学センター)
ニューラルネットワークによる微分方程式解の包含と優解劣解法の再考 (Japanese)
https://sites.google.com/g.ecc.u-tokyo.ac.jp/utnas-bulletin-board/
ハイブリッド開催です。参加の詳細は参考URLをご覧ください。
田中一成 氏 (早稲田大学国際理工学センター)
ニューラルネットワークによる微分方程式解の包含と優解劣解法の再考 (Japanese)
[ 講演概要 ]
講演の前半では、微分方程式の解をニューラルネットワークを用いて厳密に包含する手法を紹介する。
この手法は、特定のコスト関数で方程式の優解劣解を学習し、その結果として得られるニューラルネットワークで表現された関数の組が真の解を包み込むことを事後的に確認するものである。
手法の紹介は常微分方程式の初期値問題や境界値問題を例に展開するが、楕円型・放物型偏微分方程式に対しても適用可能であることを示す。
前半の内容は矢田部浩平氏（東京農工大学）との共同研究に基づくものである。
講演の後半では楕円型境界値問題に対する優解劣解法そのものに焦点を当てる。
伝統的な優解劣解の定義では、暗に関数の滑らかさが要求されるため、優解劣解を区分線形関数を用いることができなかった。
この課題を克服するためには、優解劣解が満たすべき条件を緩めることが必要である。
そこで、変分不等式と限定されたテスト関数を使用して優解劣解を再定義し、単純な線形補間を用いて真解を包含する優解劣解が構築可能であることを示す。
これはReLUのような必ずしも滑らかでない活性化関数を用いる場合でも、前半で紹介した手法が有効であることを示唆する。
後半の内容は松江要氏（九州大学）ならびに落合啓之氏（九州大学）との共同研究に基づく。
[ 参考URL ]講演の前半では、微分方程式の解をニューラルネットワークを用いて厳密に包含する手法を紹介する。
この手法は、特定のコスト関数で方程式の優解劣解を学習し、その結果として得られるニューラルネットワークで表現された関数の組が真の解を包み込むことを事後的に確認するものである。
手法の紹介は常微分方程式の初期値問題や境界値問題を例に展開するが、楕円型・放物型偏微分方程式に対しても適用可能であることを示す。
前半の内容は矢田部浩平氏（東京農工大学）との共同研究に基づくものである。
講演の後半では楕円型境界値問題に対する優解劣解法そのものに焦点を当てる。
伝統的な優解劣解の定義では、暗に関数の滑らかさが要求されるため、優解劣解を区分線形関数を用いることができなかった。
この課題を克服するためには、優解劣解が満たすべき条件を緩めることが必要である。
そこで、変分不等式と限定されたテスト関数を使用して優解劣解を再定義し、単純な線形補間を用いて真解を包含する優解劣解が構築可能であることを示す。
これはReLUのような必ずしも滑らかでない活性化関数を用いる場合でも、前半で紹介した手法が有効であることを示唆する。
後半の内容は松江要氏（九州大学）ならびに落合啓之氏（九州大学）との共同研究に基づく。
https://sites.google.com/g.ecc.u-tokyo.ac.jp/utnas-bulletin-board/
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。
林 晋 氏 (青山学院大学)
Index theory for quarter-plane Toeplitz operators via extended symbols (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。
林 晋 氏 (青山学院大学)
Index theory for quarter-plane Toeplitz operators via extended symbols (JAPANESE)
[ 講演概要 ]
We consider index theory for some Toeplitz operators on a discrete quarter-plane. Index theory for such operators has been investigated by Simonenko, Douglas-Howe, Park and index formulas are obtained by Coburn-Douglas-Singer, Duducava. In this talk, we revisit Duducava’s idea and discuss an index formula for quarter-plane Toeplitz operators of two-variable rational matrix function symbols from a geometric viewpoint. By using Gohberg-Krein theory for matrix factorizations and analytic continuation, we see that the symbols of Fredholm quarter-plane Toeplitz operators defined originally on a two-dimensional torus can canonically be extended to some three-sphere, and show that their Fredholm indices coincides with the three-dimensional winding number of extended symbols. If time permits, we briefly mention a contact with a topic in condensed matter physics, called (higher-order) topological insulators.
[ 参考URL ]We consider index theory for some Toeplitz operators on a discrete quarter-plane. Index theory for such operators has been investigated by Simonenko, Douglas-Howe, Park and index formulas are obtained by Coburn-Douglas-Singer, Duducava. In this talk, we revisit Duducava’s idea and discuss an index formula for quarter-plane Toeplitz operators of two-variable rational matrix function symbols from a geometric viewpoint. By using Gohberg-Krein theory for matrix factorizations and analytic continuation, we see that the symbols of Fredholm quarter-plane Toeplitz operators defined originally on a two-dimensional torus can canonically be extended to some three-sphere, and show that their Fredholm indices coincides with the three-dimensional winding number of extended symbols. If time permits, we briefly mention a contact with a topic in condensed matter physics, called (higher-order) topological insulators.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
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