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過去の記録 ～04/24｜本日 04/25 | 今後の予定 04/26～
2023年12月06日(水)
東京無限可積分系セミナー
13:00-14:30 数理科学研究科棟(駒場) 056号室
Misha Feigin 氏 (University of Glasgow)
本講演はキャンセルとなりました
Flat coordinates of algebraic Frobenius manifolds (ENGLISH)
Misha Feigin 氏 (University of Glasgow)
本講演はキャンセルとなりました
Flat coordinates of algebraic Frobenius manifolds (ENGLISH)
[ 講演概要 ]
本講演はキャンセルとなりました
Orbit spaces of the reflection representation of finite irreducible Coxeter groups provide Frobenius manifolds with polynomial prepotentials. Flat coordinates of the corresponding flat metric, known as Saito metric, are distinguished basic invariants of the Coxeter group. They have applications in representations of Cherednik algebras. Frobenius manifolds with algebraic prepotentials remain not classified and they are typically related to quasi-Coxeter conjugacy classes in finite Coxeter groups. We obtain flat coordinates for the majority of known examples of algebraic Frobenius manifolds in dimensions up to 4. In all the cases, flat coordinates appear to be some algebraic functions on the orbit space of the Coxeter group. This is a joint work with Daniele Valeri and Johan Wright.
本講演はキャンセルとなりました
Orbit spaces of the reflection representation of finite irreducible Coxeter groups provide Frobenius manifolds with polynomial prepotentials. Flat coordinates of the corresponding flat metric, known as Saito metric, are distinguished basic invariants of the Coxeter group. They have applications in representations of Cherednik algebras. Frobenius manifolds with algebraic prepotentials remain not classified and they are typically related to quasi-Coxeter conjugacy classes in finite Coxeter groups. We obtain flat coordinates for the majority of known examples of algebraic Frobenius manifolds in dimensions up to 4. In all the cases, flat coordinates appear to be some algebraic functions on the orbit space of the Coxeter group. This is a joint work with Daniele Valeri and Johan Wright.
2023年12月05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。
北野 晃朗 氏 (創価大学)
On the Euler class for flat S1-bundles, C∞ vs Cω (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。
北野 晃朗 氏 (創価大学)
On the Euler class for flat S1-bundles, C∞ vs Cω (JAPANESE)
[ 講演概要 ]
We describe low dimensional homology groups of the real analytic, orientation preserving diffeomorphism group of S1 in terms of BΓ1 by applying a theorem of Thurston. It is an open problem whether some power of the rational Euler class vanishes for real analytic flat S1 bundles. In this talk we discuss that if it does, then the homology group should contain many torsion classes that vanish in the smooth case. Along this line we can give a new proof for the non-triviality of any power of the rational Euler class in the smooth case. If time permits, we will mention some attempts to study a Mather-Thurston map in the analytic case. This talk is based on a joint work with Shigeyuki Morita and Yoshihiko Mitsumatsu.
[ 参考URL ]We describe low dimensional homology groups of the real analytic, orientation preserving diffeomorphism group of S1 in terms of BΓ1 by applying a theorem of Thurston. It is an open problem whether some power of the rational Euler class vanishes for real analytic flat S1 bundles. In this talk we discuss that if it does, then the homology group should contain many torsion classes that vanish in the smooth case. Along this line we can give a new proof for the non-triviality of any power of the rational Euler class in the smooth case. If time permits, we will mention some attempts to study a Mather-Thurston map in the analytic case. This talk is based on a joint work with Shigeyuki Morita and Yoshihiko Mitsumatsu.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
2023年12月04日(月)
日仏数学拠点FJ-LMIセミナー
14:00- 数理科学研究科棟(駒場) 056号室
Philippe G. LEFLOCH 氏 (Sorbonne University & CNRS)
An introduction to Einstein constraints and the seed-to-solution method
https://fj-lmi.cnrs.fr/seminars/
Philippe G. LEFLOCH 氏 (Sorbonne University & CNRS)
An introduction to Einstein constraints and the seed-to-solution method
[ 講演概要 ]
I will present an introduction to the constraint equations associated with Einstein’s field equations of general relativity, and to recent developments based on the seed-to-solution method developed in collaboration with The-Cang Nguyen (Montpellier) and Bruno Le Floch (LPTHE, Sorbonne).
[ 参考URL ]I will present an introduction to the constraint equations associated with Einstein’s field equations of general relativity, and to recent developments based on the seed-to-solution method developed in collaboration with The-Cang Nguyen (Montpellier) and Bruno Le Floch (LPTHE, Sorbonne).
https://fj-lmi.cnrs.fr/seminars/
2023年11月30日(木)
応用解析セミナー
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
Philippe G. LeFloch 氏 (Sorbonne University and CNRS)
Einstein spacetimes: dispersion, localization, collapse, and bouncing (English)
https://forms.gle/HPsYinKweUW3AQGv9
対面・オンラインハイブリッド開催
Philippe G. LeFloch 氏 (Sorbonne University and CNRS)
Einstein spacetimes: dispersion, localization, collapse, and bouncing (English)
[ 講演概要 ]
I will overview recent developments on Einstein's field equations of general relativity, especially the global evolution problem from initial data sets. A variety of phenomena may arise in this evolution: gravitational waves, dispersion, collapse, formation of singularities, and bouncing. While many problems remain widely open and very challenging, in the past decades major mathematical advances were made for several classes of spacetimes. I will review recent results on the (1) nonlinear stability of Minkowski spacetime, (2) localization problem at infinity, (3) collapse of spherically symmetric fields, and (4) scattering through quiescent singularity. This talk is based on joint work with Y. Ma (Xi'an), T.-C. Nguyen (Montpellier), F. Mena (Lisbon), B. Le Floch (Paris), and G. Veneziano (Geneva).
Blog: philippelefloch.org
[ 参考URL ]I will overview recent developments on Einstein's field equations of general relativity, especially the global evolution problem from initial data sets. A variety of phenomena may arise in this evolution: gravitational waves, dispersion, collapse, formation of singularities, and bouncing. While many problems remain widely open and very challenging, in the past decades major mathematical advances were made for several classes of spacetimes. I will review recent results on the (1) nonlinear stability of Minkowski spacetime, (2) localization problem at infinity, (3) collapse of spherically symmetric fields, and (4) scattering through quiescent singularity. This talk is based on joint work with Y. Ma (Xi'an), T.-C. Nguyen (Montpellier), F. Mena (Lisbon), B. Le Floch (Paris), and G. Veneziano (Geneva).
Blog: philippelefloch.org
https://forms.gle/HPsYinKweUW3AQGv9
2023年11月28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。
Gwénaël Massuyeau 氏 (Université de Bourgogne)
An analogue of the Johnson-Morita theory for the handlebody group (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。
Gwénaël Massuyeau 氏 (Université de Bourgogne)
An analogue of the Johnson-Morita theory for the handlebody group (ENGLISH)
[ 講演概要 ]
The Johnson-Morita theory provides an approach for the mapping class group of a surface by considering its actions on the successive nilpotent quotients of the fundamental group of the surface. In this talk, after an outline of the original theory, we will present an analogue of the Johnson-Morita theory for the handlebody group, i.e. the mapping class group of a handlebody. This is joint work with Kazuo Habiro; as we shall explain if time allows, our motivation is to recover the "tree reduction" of a certain functor on the category of bottom tangles in handlebodies that we introduced (a few years ago) using the Kontsevich integral.
[ 参考URL ]The Johnson-Morita theory provides an approach for the mapping class group of a surface by considering its actions on the successive nilpotent quotients of the fundamental group of the surface. In this talk, after an outline of the original theory, we will present an analogue of the Johnson-Morita theory for the handlebody group, i.e. the mapping class group of a handlebody. This is joint work with Kazuo Habiro; as we shall explain if time allows, our motivation is to recover the "tree reduction" of a certain functor on the category of bottom tangles in handlebodies that we introduced (a few years ago) using the Kontsevich integral.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
日仏数学拠点FJ-LMIセミナー
16:00- 数理科学研究科棟(駒場) 117号室
Maud DELATTRE 氏 (Université Paris-Saclay, INRAE)
Some contributions on variable selection in nonlinear mixed-effects models
https://fj-lmi.cnrs.fr/seminars/
Maud DELATTRE 氏 (Université Paris-Saclay, INRAE)
Some contributions on variable selection in nonlinear mixed-effects models
[ 講演概要 ]
In the first part of this presentation, we will introduce the general formalism of nonlinear mixed effects models (NLMEM) that are specifically designed models to describe dynamic phenomena from repeated data on several subjects. In the second part, we will focus on specific variable selection technics for NLMEM through two contributions. In the first one, we will discuss the proper definition and use of the Bayesian information criterion (BIC) for variable selection in a low dimensional setting. High dimensional variable selection is the subject of the second contribution.
References
[1] Delattre, M., Lavielle, M. and Poursat, M.A. (2014) A note on BIC in mixed effects models, Electronic Journal of Statistics 8(1) p. 456-475.
[2] Delattre, M. and Poursat, M.A. (2020) An iterative algorithm for joint covariate and random effect selection in mixed effects models., The International Journal of Biostatistics 16(2), 20190082.
[3] Naveau, M., Kon Kam King, G., Rincent, R., Sansonnet, L. and Delattre, M. Bayesian high dimensional covariate selection in non-linear mixed-effects models using the SAEM algorithm. hal-03685060.
[ 参考URL ]In the first part of this presentation, we will introduce the general formalism of nonlinear mixed effects models (NLMEM) that are specifically designed models to describe dynamic phenomena from repeated data on several subjects. In the second part, we will focus on specific variable selection technics for NLMEM through two contributions. In the first one, we will discuss the proper definition and use of the Bayesian information criterion (BIC) for variable selection in a low dimensional setting. High dimensional variable selection is the subject of the second contribution.
References
[1] Delattre, M., Lavielle, M. and Poursat, M.A. (2014) A note on BIC in mixed effects models, Electronic Journal of Statistics 8(1) p. 456-475.
[2] Delattre, M. and Poursat, M.A. (2020) An iterative algorithm for joint covariate and random effect selection in mixed effects models., The International Journal of Biostatistics 16(2), 20190082.
[3] Naveau, M., Kon Kam King, G., Rincent, R., Sansonnet, L. and Delattre, M. Bayesian high dimensional covariate selection in non-linear mixed-effects models using the SAEM algorithm. hal-03685060.
https://fj-lmi.cnrs.fr/seminars/
2023年11月27日(月)
複素解析幾何セミナー
11:00-12:30 数理科学研究科棟(駒場) 128号室
小川 智史 氏 (大阪公立大学)
On a holomorphic tubular neighborhood of a compact complex curve and Brjuno condition (Japanese)
https://u-tokyo-ac-jp.zoom.us/meeting/register/tZEqceqsrTIjEtRxenSMdPogvCxlWzAogj5A
小川 智史 氏 (大阪公立大学)
On a holomorphic tubular neighborhood of a compact complex curve and Brjuno condition (Japanese)
[ 講演概要 ]
Let $C$ be a compact complex curve holomorphically embedded in a non-singular complex surface $M$ with a unitary flat normal bundle $N_{C/M}$ and let $\mathcal{U}$ be a finite open cover of $C$. Gong--Stolovitch posed a sufficient condition for the existence of a holomorphic tubular neighborhood of $C$ in $M$ expressed with operator norms of Čech coboundary maps $\delta$ on $\check{C}^0(\mathcal{U}, \mathcal{O}_C(N_{C/M}^\nu))$ and $\check{C}^0(\mathcal{U}, \mathcal{O}_C(T_C \otimes N_{C/M}^\nu))$.
In this talk, we introduce some estimates of the operator norms of $\delta$. As a result, we see the Brjuno condition appears as a sufficient condition for the existence of a holomorphic tubular neighborhood.
[ 参考URL ]Let $C$ be a compact complex curve holomorphically embedded in a non-singular complex surface $M$ with a unitary flat normal bundle $N_{C/M}$ and let $\mathcal{U}$ be a finite open cover of $C$. Gong--Stolovitch posed a sufficient condition for the existence of a holomorphic tubular neighborhood of $C$ in $M$ expressed with operator norms of Čech coboundary maps $\delta$ on $\check{C}^0(\mathcal{U}, \mathcal{O}_C(N_{C/M}^\nu))$ and $\check{C}^0(\mathcal{U}, \mathcal{O}_C(T_C \otimes N_{C/M}^\nu))$.
In this talk, we introduce some estimates of the operator norms of $\delta$. As a result, we see the Brjuno condition appears as a sufficient condition for the existence of a holomorphic tubular neighborhood.
https://u-tokyo-ac-jp.zoom.us/meeting/register/tZEqceqsrTIjEtRxenSMdPogvCxlWzAogj5A
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
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