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過去の記録
過去の記録 ～04/17｜本日 04/18 | 今後の予定 04/19～
2023年10月19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)
格子暗号の数理 (Japanese)
高島 克幸 氏 (早大教育)
格子暗号の数理 (Japanese)
[ 講演概要 ]
本講演では，格子暗号の数理を紹介する．まず、格子上のフーリエ解析に基づくRegevの格子暗号構成フレームワークとそれに基づく具体的な構成法を順に概説する．そして，加群格子・イデアル格子といった特別な格子に基づく暗号構成の基礎付けを見た後に，時間が許せば、Cramerらによる近似Ideal-SVP 問題に対する多項式時間量子アルゴリズムを概説する．
本講演では，格子暗号の数理を紹介する．まず、格子上のフーリエ解析に基づくRegevの格子暗号構成フレームワークとそれに基づく具体的な構成法を順に概説する．そして，加群格子・イデアル格子といった特別な格子に基づく暗号構成の基礎付けを見た後に，時間が許せば、Cramerらによる近似Ideal-SVP 問題に対する多項式時間量子アルゴリズムを概説する．
2023年10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
Wansu Kim 氏 (KAIST/東京大学大学院数理科学研究科)
On Igusa varieties (English)
Wansu Kim 氏 (KAIST/東京大学大学院数理科学研究科)
On Igusa varieties (English)
[ 講演概要 ]
In this talk, we construct Igusa varieties and study some basic properties in the setting of abelian-type Shimura varieties, as well as in the analogous setting for function fields (over shtuka spaces). The is joint work with Paul Hamacher.
In this talk, we construct Igusa varieties and study some basic properties in the setting of abelian-type Shimura varieties, as well as in the analogous setting for function fields (over shtuka spaces). The is joint work with Paul Hamacher.
2023年10月17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。
奥村真善美 氏 (甲南大学知能情報学部)
空間2次元における動的境界条件下のCahn-Hilliard方程式に対する構造保存スキームについて (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。
奥村真善美 氏 (甲南大学知能情報学部)
空間2次元における動的境界条件下のCahn-Hilliard方程式に対する構造保存スキームについて (Japanese)
[ 講演概要 ]
偏微分方程式の初期値境界値問題において, 動的境界条件を課した問題が幅広く研究されている. この境界条件は, 領域内部と境界の相互作用を表現するために導入された条件であり, 条件内に未知関数の時間微分を含む. それゆえ, 代表的な境界条件と異なり, 動境界条件は, 領域内部の力学系と同時に境界上でも同種, あるいは異種の力学系を考察することができ, その境界値問題は領域内部の方程式と境界上の方程式の連立系と見なすこともできる. 近年, 相分離現象を記述するCahn-Hilliard方程式に対し, 境界上でもCahn-Hilliard方程式を考察する動的境界条件を課したモデルがGoldstein-Miranville-Schimperna (GMS)やLiu-Wu (LW)によって提唱された. 両者は化学ポテンシャルの外向き単位法線方向微分の扱いが異なっており, GMSモデルでは領域内部と境界の質量和が保存するという保存則, LWモデルでは内部と境界それぞれで質量が保存するという保存則が成り立つ. さらにはいずれのモデルにおいても領域内部と境界のエネルギーの総和が減衰するという総エネルギー散逸則が成り立つことにも注意したい. これらの性質は数値計算においても重要な意味を持ち, その構造をスキームが離散的に再現することで, 安定な計算が可能になるなどの様々な恩恵がある. 本研究では, 先行研究を踏まえ, これらの性質を離散的に再現する構造保存スキームを構成した. 本講演では, それらの構造保存スキームを紹介するとともに, GMSモデル対する構造保存スキームに焦点を当て, その可解性について得られた結果を報告する. また, 両モデルの保存則の違いに起因する, 数値解の挙動の違いも興味深く, その数値計算例も紹介する.
本研究は深尾武史氏(龍谷大学)との共同研究に基づく.
[ 参考URL ]偏微分方程式の初期値境界値問題において, 動的境界条件を課した問題が幅広く研究されている. この境界条件は, 領域内部と境界の相互作用を表現するために導入された条件であり, 条件内に未知関数の時間微分を含む. それゆえ, 代表的な境界条件と異なり, 動境界条件は, 領域内部の力学系と同時に境界上でも同種, あるいは異種の力学系を考察することができ, その境界値問題は領域内部の方程式と境界上の方程式の連立系と見なすこともできる. 近年, 相分離現象を記述するCahn-Hilliard方程式に対し, 境界上でもCahn-Hilliard方程式を考察する動的境界条件を課したモデルがGoldstein-Miranville-Schimperna (GMS)やLiu-Wu (LW)によって提唱された. 両者は化学ポテンシャルの外向き単位法線方向微分の扱いが異なっており, GMSモデルでは領域内部と境界の質量和が保存するという保存則, LWモデルでは内部と境界それぞれで質量が保存するという保存則が成り立つ. さらにはいずれのモデルにおいても領域内部と境界のエネルギーの総和が減衰するという総エネルギー散逸則が成り立つことにも注意したい. これらの性質は数値計算においても重要な意味を持ち, その構造をスキームが離散的に再現することで, 安定な計算が可能になるなどの様々な恩恵がある. 本研究では, 先行研究を踏まえ, これらの性質を離散的に再現する構造保存スキームを構成した. 本講演では, それらの構造保存スキームを紹介するとともに, GMSモデル対する構造保存スキームに焦点を当て, その可解性について得られた結果を報告する. また, 両モデルの保存則の違いに起因する, 数値解の挙動の違いも興味深く, その数値計算例も紹介する.
本研究は深尾武史氏(龍谷大学)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。
狩野 隼輔 氏 (東北大学 数理科学共創社会センター)
Train track combinatorics and cluster algebras (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。
狩野 隼輔 氏 (東北大学 数理科学共創社会センター)
Train track combinatorics and cluster algebras (JAPANESE)
[ 講演概要 ]
The concepts of train track was introduced by W. P. Thurston to study the measured foliations/laminations and the pseudo-Anosov mapping classes on a surface. In this talk, we translate some concepts of train tracks into the language of cluster algebras using the tropicalization of Goncharov--Shen's potential function. Using this, we translate a combinatorial property of a train track associated with a pseudo-Anosov mapping class into the combinatorial property in cluster algebras, called the sign stability which was introduced by Tsukasa Ishibashi and the speaker.
[ 参考URL ]The concepts of train track was introduced by W. P. Thurston to study the measured foliations/laminations and the pseudo-Anosov mapping classes on a surface. In this talk, we translate some concepts of train tracks into the language of cluster algebras using the tropicalization of Goncharov--Shen's potential function. Using this, we translate a combinatorial property of a train track associated with a pseudo-Anosov mapping class into the combinatorial property in cluster algebras, called the sign stability which was introduced by Tsukasa Ishibashi and the speaker.
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
紅村冬大 氏 (理研)
$*$-homomorphisms between groupoid C$^*$-algebras
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
紅村冬大 氏 (理研)
$*$-homomorphisms between groupoid C$^*$-algebras
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
2023年10月16日(月)
代数幾何学セミナー
14:00-15:30 数理科学研究科棟(駒場) 002号室
Lena Ji 氏 (University of Michigan)
Symmetries of Fano varieties
Lena Ji 氏 (University of Michigan)
Symmetries of Fano varieties
[ 講演概要 ]
Prokhorov and Shramov proved that the BAB conjecture (which Birkar later proved) implies the uniform Jordan property for automorphism groups of complex Fano varieties of fixed dimension. This property in particular gives an upper bound on the size of semi-simple groups (meaning those with no non-trivial normal abelian subgroups) acting faithfully on n-dimensional complex Fano varieties, and this bound only depends on n. In this talk, we investigate the consequences of a large action by a particular semi-simple group: the symmetric group. This work is joint with Louis Esser and Joaquín Moraga.
Prokhorov and Shramov proved that the BAB conjecture (which Birkar later proved) implies the uniform Jordan property for automorphism groups of complex Fano varieties of fixed dimension. This property in particular gives an upper bound on the size of semi-simple groups (meaning those with no non-trivial normal abelian subgroups) acting faithfully on n-dimensional complex Fano varieties, and this bound only depends on n. In this talk, we investigate the consequences of a large action by a particular semi-simple group: the symmetric group. This work is joint with Louis Esser and Joaquín Moraga.
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
辻 元 氏 (上智大学)
The limit of Kähler-Ricci flows
https://u-tokyo-ac-jp.zoom.us/meeting/register/tZEqceqsrTIjEtRxenSMdPogvCxlWzAogj5A
辻 元 氏 (上智大学)
The limit of Kähler-Ricci flows
[ 講演概要 ]
In this talk, I would like to present the (normalized) limit of Kähler-Ricci flows for compact Kähler manifolds with intermediate Kodaira dimesion under the condition that the canonical bundle is abundant.
[ 参考URL ]In this talk, I would like to present the (normalized) limit of Kähler-Ricci flows for compact Kähler manifolds with intermediate Kodaira dimesion under the condition that the canonical bundle is abundant.
https://u-tokyo-ac-jp.zoom.us/meeting/register/tZEqceqsrTIjEtRxenSMdPogvCxlWzAogj5A
2023年10月12日(木)
東京名古屋代数セミナー
10:30-12:00 オンライン開催
任 鑫 氏 (関西大学)
q-deformed rational numbers, Farey sum and a 2-Calabi-Yau category of A_2 quiver (English)
http://www.math.nagoya-u.ac.jp/~aaron.chan/TNAseminar.html
任 鑫 氏 (関西大学)
q-deformed rational numbers, Farey sum and a 2-Calabi-Yau category of A_2 quiver (English)
[ 講演概要 ]
Let q be a positive real number. The left and right q-deformed rational numbers were introduced by Bapat, Becker and Licata via regular continued fractions, and the right q-deformed rational number is exactly q-deformed rational number considered by Morier-Genoud and Ovsienko, when q is a formal parameter. They gave a homological interpretation for left and right q-deformed rational numbers by considering a special 2-Calabi–Yau category associated to the A_2 quiver.
In this talk, we begin by introducing the above definitions and related results. Then we give a formula for computing the q-deformed Farey sum of the left q-deformed rational numbers based on the negative continued fractions. We combine the homological interpretation of the left and right q-deformed rational numbers and the q-deformed Farey sum, and give a homological interpretation of the q-deformed Farey sum. We also apply the above results to real quadratic irrational numbers with periodic type.
[ 参考URL ]Let q be a positive real number. The left and right q-deformed rational numbers were introduced by Bapat, Becker and Licata via regular continued fractions, and the right q-deformed rational number is exactly q-deformed rational number considered by Morier-Genoud and Ovsienko, when q is a formal parameter. They gave a homological interpretation for left and right q-deformed rational numbers by considering a special 2-Calabi–Yau category associated to the A_2 quiver.
In this talk, we begin by introducing the above definitions and related results. Then we give a formula for computing the q-deformed Farey sum of the left q-deformed rational numbers based on the negative continued fractions. We combine the homological interpretation of the left and right q-deformed rational numbers and the q-deformed Farey sum, and give a homological interpretation of the q-deformed Farey sum. We also apply the above results to real quadratic irrational numbers with periodic type.
http://www.math.nagoya-u.ac.jp/~aaron.chan/TNAseminar.html
2023年10月10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。
見村 万佐人 氏 (東北大学)
不変擬準同型と scl の粗い幾何 (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。
見村 万佐人 氏 (東北大学)
不変擬準同型と scl の粗い幾何 (JAPANESE)
[ 講演概要 ]
10/9〜13 の集中講義では Green--Tao の定理とその数体への一般化について話しますが、本講演の内容はそれとは完全に独立しています。川崎盛通氏（北海道大学）、木村満晃氏（京都大学）、松下尚弘氏（信州大学）、丸山修平氏（金沢大学）との一連の共同研究の話をします。群上の擬準同型（quasimorphism）は双曲幾何などとの関係から大変興味深いものですが、多くの面白い群に対し擬準同型全体のなすベクトル空間がつまらないか無限次元かの二択となってしまいます。1 つの群ではなく群と正規部分群の組の設定で不変擬準同型を考えることで、面白い例で非ゼロな有限次元ベクトル空間を取り出すことができることをお話しします。Bavard の双対定理はこの枠組みに拡張され、この結果は安定交換子長（scl）の粗い幾何（coarse geometry）への応用ももちます。一連の理論の発展をあまり予備知識を仮定せず概観したいと思います。
[ 参考URL ]10/9〜13 の集中講義では Green--Tao の定理とその数体への一般化について話しますが、本講演の内容はそれとは完全に独立しています。川崎盛通氏（北海道大学）、木村満晃氏（京都大学）、松下尚弘氏（信州大学）、丸山修平氏（金沢大学）との一連の共同研究の話をします。群上の擬準同型（quasimorphism）は双曲幾何などとの関係から大変興味深いものですが、多くの面白い群に対し擬準同型全体のなすベクトル空間がつまらないか無限次元かの二択となってしまいます。1 つの群ではなく群と正規部分群の組の設定で不変擬準同型を考えることで、面白い例で非ゼロな有限次元ベクトル空間を取り出すことができることをお話しします。Bavard の双対定理はこの枠組みに拡張され、この結果は安定交換子長（scl）の粗い幾何（coarse geometry）への応用ももちます。一連の理論の発展をあまり予備知識を仮定せず概観したいと思います。
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
2023年10月05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
岡本 龍明 氏 (NTT)
暗号とブロックチェーン (Japanese)
岡本 龍明 氏 (NTT)
暗号とブロックチェーン (Japanese)
[ 講演概要 ]
ブロックチェーンは分散環境下で多人数により合意形成を行う方式であり、基本的な暗号機能を用いて実現される。本講演では、その基本的なコンセプトの解説を行うとともに、最近の動向についても紹介する。
ブロックチェーンは分散環境下で多人数により合意形成を行う方式であり、基本的な暗号機能を用いて実現される。本講演では、その基本的なコンセプトの解説を行うとともに、最近の動向についても紹介する。
2023年10月03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
Alexander Ivanov 氏 (Imperial College London)
The VOA origins of Majorana theory
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
Alexander Ivanov 氏 (Imperial College London)
The VOA origins of Majorana theory
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
2023年09月25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
Jimmy He 氏 (MIT)
Boundary current fluctuations for the half space ASEP (English)
Jimmy He 氏 (MIT)
Boundary current fluctuations for the half space ASEP (English)
[ 講演概要 ]
The half space asymmetric simple exclusion process (ASEP) is an interacting particle system on the half line, with particles allowed to enter/exit at the boundary. I will discuss recent work on understanding fluctuations for the number of particles in the half space ASEP started with no particles, which exhibits the Baik-Rains phase transition between GSE, GOE, and Gaussian fluctuations as the boundary rates vary. As part of the proof, we find new distributional identities relating this system to two other models, the half space Hall-Littlewood process, and the free boundary Schur process, which allows exact formulas to be computed.
The half space asymmetric simple exclusion process (ASEP) is an interacting particle system on the half line, with particles allowed to enter/exit at the boundary. I will discuss recent work on understanding fluctuations for the number of particles in the half space ASEP started with no particles, which exhibits the Baik-Rains phase transition between GSE, GOE, and Gaussian fluctuations as the boundary rates vary. As part of the proof, we find new distributional identities relating this system to two other models, the half space Hall-Littlewood process, and the free boundary Schur process, which allows exact formulas to be computed.
2023年09月14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
Michał Łasica 氏 (The Polish Academy of Sciences)
Bounds on the gradient of minimizers in variational denoising (English)
https://forms.gle/C39ZLdQNVHyVmJ4j8
対面・オンラインハイブリッド開催
Michał Łasica 氏 (The Polish Academy of Sciences)
Bounds on the gradient of minimizers in variational denoising (English)
[ 講演概要 ]
We consider minimization problem for a class of convex integral functionals composed of two terms:
-- a regularizing term of linear growth in the gradient,
-- and a fidelity term penalizing the distance from a given function.
To ensure that such functionals attain their minima, one needs to extend their domain to the BV space. In particular minimizers may exhibit jump discontinuities. I will discuss estimates on the gradient of minimizers in terms of the data, focusing on singular part of the gradient measure.
The talk is based on joint works with P. Rybka, Z. Grochulska and A. Chambolle.
[ 参考URL ]We consider minimization problem for a class of convex integral functionals composed of two terms:
-- a regularizing term of linear growth in the gradient,
-- and a fidelity term penalizing the distance from a given function.
To ensure that such functionals attain their minima, one needs to extend their domain to the BV space. In particular minimizers may exhibit jump discontinuities. I will discuss estimates on the gradient of minimizers in terms of the data, focusing on singular part of the gradient measure.
The talk is based on joint works with P. Rybka, Z. Grochulska and A. Chambolle.
https://forms.gle/C39ZLdQNVHyVmJ4j8
2023年09月07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
Samuel Mercer 氏 (Delft University of Technology)
Uniform Convergence of Gradient Flows on a Stack of Banach Spaces (English)
https://forms.gle/T8yWr2gDTYzj8vkE7
対面・オンラインハイブリッド開催
Samuel Mercer 氏 (Delft University of Technology)
Uniform Convergence of Gradient Flows on a Stack of Banach Spaces (English)
[ 講演概要 ]
Within this talk I will recall the classical result: Given a sequence of convex functionals on a Hilbert space, Gamma-convergence of this sequence implies uniform convergence on finite time-intervals for their gradient flows. I will then discuss a generalisation for this result. In particular our functionals are defined on a sequence of distinct Banach spaces that can be stacked together inside of a unifying space. We will study a kind of gradient flow for our functionals inside their respective Banach space and ask the following question. What structure is necessary within our unifying space to attain uniform convergence of gradient flows?
[ 参考URL ]Within this talk I will recall the classical result: Given a sequence of convex functionals on a Hilbert space, Gamma-convergence of this sequence implies uniform convergence on finite time-intervals for their gradient flows. I will then discuss a generalisation for this result. In particular our functionals are defined on a sequence of distinct Banach spaces that can be stacked together inside of a unifying space. We will study a kind of gradient flow for our functionals inside their respective Banach space and ask the following question. What structure is necessary within our unifying space to attain uniform convergence of gradient flows?
https://forms.gle/T8yWr2gDTYzj8vkE7
2023年08月30日(水)
離散数理モデリングセミナー
16:30-17:30 数理科学研究科棟(駒場) 370号室
Joshua Capel 氏 (University of New South Wales)
Classical structure theory for second-order semi-degenerate super-integrable systems (English)
Joshua Capel 氏 (University of New South Wales)
Classical structure theory for second-order semi-degenerate super-integrable systems (English)
[ 講演概要 ]
Second-order superintegrable systems have long been a subject of interest in the study of integral systems, primarily due to their close connection with separation of variables. Among these, the 'non-degenerate' second-order systems on constant curvature spaces have been particularly well studies, and are mostly understood.
A non-degenerate system in n-dimensions comprises an (n+1)-dimensional vector space of potentials, along with 2n-1 second-order constants that commute with the Hamiltonian of the system.
In contrast, a semi-degenerate system is characterised by having fewer than n+1 parameters. In this talk, we will discuss the structure theory of truly n-dimensional potentials (meaning potentials that are not just restrictions of (n+1)-dimensional counterparts). We will see that the classical structure theory appears just as rich as the non-degenerate case.
This talk is joint work with Jeremy Nugent and Jonathan Kress.
Second-order superintegrable systems have long been a subject of interest in the study of integral systems, primarily due to their close connection with separation of variables. Among these, the 'non-degenerate' second-order systems on constant curvature spaces have been particularly well studies, and are mostly understood.
A non-degenerate system in n-dimensions comprises an (n+1)-dimensional vector space of potentials, along with 2n-1 second-order constants that commute with the Hamiltonian of the system.
In contrast, a semi-degenerate system is characterised by having fewer than n+1 parameters. In this talk, we will discuss the structure theory of truly n-dimensional potentials (meaning potentials that are not just restrictions of (n+1)-dimensional counterparts). We will see that the classical structure theory appears just as rich as the non-degenerate case.
This talk is joint work with Jeremy Nugent and Jonathan Kress.
2023年08月25日(金)
博士論文発表会
13:00-14:15 数理科学研究科棟(駒場) 123号室
北村 侃 氏 (東京大学大学院数理科学研究科)
Discrete quantum subgroups of quantum doubles
(量子ダブルの離散部分量子群について)
北村 侃 氏 (東京大学大学院数理科学研究科)
Discrete quantum subgroups of quantum doubles
(量子ダブルの離散部分量子群について)
2023年08月24日(木)
東京名古屋代数セミナー
10:30-12:00 オンライン開催
淺井 聡太 氏 (東京大学)
TF equivalence on the real Grothendieck group (Japanese)
http://www.math.nagoya-u.ac.jp/~aaron.chan/TNAseminar.html
淺井 聡太 氏 (東京大学)
TF equivalence on the real Grothendieck group (Japanese)
[ 講演概要 ]
$A$を体$K$上の有限次元多元環とするとき、有限生成射影加群圏の実Grothendieck群$K_0(\mathsf{proj} A)_\mathbb{R}$は、Euclid空間と同一視できる。Baumann-Kamnitzer-Tingleyは、各元$\theta \in K_0(\mathsf{proj} A)_\mathbb{R}$に対し、商加群や部分加群に関する線型不等式を用いて、有限生成加群圏$\mathsf{mod} A$の半安定ねじれ対を定めており、これをもとに私は、$K_0(\mathsf{proj} A)_\mathbb{R}$上の同値関係「TF同値」を導入した。TF同値類の典型例として、ホモトピー圏$\mathsf{K}^\mathrm{b}(\mathsf{proj} A)$の2-term presilting complex $U$の直既約因子が定める錐$C^\circ(U)$が挙げられ、これを$U$のsilting coneと呼ぶ。TF同値の研究には、silting coneのみならず、その適切な近傍をとることが有効であり、私はやはり半安定ねじれ対を用いて、各2-term presilting complex $U$に対し、「区間近傍」と呼ばれる$C^\circ(U)$の開近傍$N_U$を定め、この$N_U$が様々な良い性質を満たしていることを証明した。この講演では、上記の概念について、じっくりと時間をかけて解説する。一部の内容は、伊山修氏（東京大学）との共同研究に基づく。
[ 参考URL ]$A$を体$K$上の有限次元多元環とするとき、有限生成射影加群圏の実Grothendieck群$K_0(\mathsf{proj} A)_\mathbb{R}$は、Euclid空間と同一視できる。Baumann-Kamnitzer-Tingleyは、各元$\theta \in K_0(\mathsf{proj} A)_\mathbb{R}$に対し、商加群や部分加群に関する線型不等式を用いて、有限生成加群圏$\mathsf{mod} A$の半安定ねじれ対を定めており、これをもとに私は、$K_0(\mathsf{proj} A)_\mathbb{R}$上の同値関係「TF同値」を導入した。TF同値類の典型例として、ホモトピー圏$\mathsf{K}^\mathrm{b}(\mathsf{proj} A)$の2-term presilting complex $U$の直既約因子が定める錐$C^\circ(U)$が挙げられ、これを$U$のsilting coneと呼ぶ。TF同値の研究には、silting coneのみならず、その適切な近傍をとることが有効であり、私はやはり半安定ねじれ対を用いて、各2-term presilting complex $U$に対し、「区間近傍」と呼ばれる$C^\circ(U)$の開近傍$N_U$を定め、この$N_U$が様々な良い性質を満たしていることを証明した。この講演では、上記の概念について、じっくりと時間をかけて解説する。一部の内容は、伊山修氏（東京大学）との共同研究に基づく。
http://www.math.nagoya-u.ac.jp/~aaron.chan/TNAseminar.html
2023年08月22日(火)
解析学火曜セミナー
16:00-17:30 数理科学研究科棟(駒場) 126号室
対面・オンラインハイブリッド開催，通常とは場所が異なります
Daniel Parra 氏 (Universidad de Santiago de Chile)
Towards a Levinson's Theorem for Discrete Magnetic operators on tubes under finite rank perturbations (English)
https://forms.gle/VBp4nSnYYKVpXFhB9
対面・オンラインハイブリッド開催，通常とは場所が異なります
Daniel Parra 氏 (Universidad de Santiago de Chile)
Towards a Levinson's Theorem for Discrete Magnetic operators on tubes under finite rank perturbations (English)
[ 講演概要 ]
In this talk we study a family of magnetic Hamiltonians on discrete tubes under a finite rank perturbation supported on its border. We go into detail for the case of rank $2$ and show how the eigenvalues can be related to the scattering matrix to exhibit an index theorem in the tradition of Levison’s theorem. We then turn to the general case, discuss the different spectral scenarios that can occur and explain the C*-algebraic framework that could allow us to treat this case. This is an ongoing work with S. Richard (名大), V. Austen (名大) and A. Rennie (Wollongong).
[ 参考URL ]In this talk we study a family of magnetic Hamiltonians on discrete tubes under a finite rank perturbation supported on its border. We go into detail for the case of rank $2$ and show how the eigenvalues can be related to the scattering matrix to exhibit an index theorem in the tradition of Levison’s theorem. We then turn to the general case, discuss the different spectral scenarios that can occur and explain the C*-algebraic framework that could allow us to treat this case. This is an ongoing work with S. Richard (名大), V. Austen (名大) and A. Rennie (Wollongong).
https://forms.gle/VBp4nSnYYKVpXFhB9
2023年08月21日(月)
古典解析セミナー
10:00-17:30 数理科学研究科棟(駒場) 123号室
Xiaomeng Xu 氏 (BICMR, China) 10:00-11:30
Stokes matrices of confluent hypergeometric systems and the isomonodromy deformation equations (ENGLISH)
Stokes matrices of quantum confluent hypergeometric systems and the representation of quantum groups (ENGLISH)
The WKB approximation of (quantum) confluent hypergeometric systems, Cauchy interlacing inequality and crystal basis (ENGLISH)
Xiaomeng Xu 氏 (BICMR, China) 10:00-11:30
Stokes matrices of confluent hypergeometric systems and the isomonodromy deformation equations (ENGLISH)
[ 講演概要 ]
This talk first gives an introduction to the Stokes matrices of a linear meromorphic system of Poncaré rank 1, and the associated nonlinear isomonodromy deformation equation. The nonlinear equation naturally arises from the theory of Frobenius manifolds, stability conditions, Poisson-Lie groups and so on, and can be seen as a higher rank generalizations of the sixth Painlevé equation. The talk then gives a parameterization of the asymptotics of the solutions of the isomonodromy equation at a critical point, the explicit formula of the monodromy/Stokes matrices of the linear problem via the parameterization, as well as a connection formula between two differential critical points. It can be seen as a generalization of Jimbo's work for the sixth Painlevé equation to a higher rank case. It is partially based on a joint work with Qian Tang.
Xiaomeng Xu 氏 (BICMR, China) 14:00-15:30This talk first gives an introduction to the Stokes matrices of a linear meromorphic system of Poncaré rank 1, and the associated nonlinear isomonodromy deformation equation. The nonlinear equation naturally arises from the theory of Frobenius manifolds, stability conditions, Poisson-Lie groups and so on, and can be seen as a higher rank generalizations of the sixth Painlevé equation. The talk then gives a parameterization of the asymptotics of the solutions of the isomonodromy equation at a critical point, the explicit formula of the monodromy/Stokes matrices of the linear problem via the parameterization, as well as a connection formula between two differential critical points. It can be seen as a generalization of Jimbo's work for the sixth Painlevé equation to a higher rank case. It is partially based on a joint work with Qian Tang.
Stokes matrices of quantum confluent hypergeometric systems and the representation of quantum groups (ENGLISH)
[ 講演概要 ]
This talk studies a quantum analog of Stokes matrices of confluent hypergeometric systems. It first gives an introduction to the Stokes phenomenon of an irregular Knizhnik–Zamolodchikov at a second order pole, associated to a regular semisimple element u and a representation $L(\lambda)$ of $gl_n$. It then shows that the Stokes matrices of the
irregular Knizhnik–Zamolodchikov equation define representation of $U_q(gl_n)$ on $L(\lambda)$. In then end, using the isomonodromy approach, it derives an explicit expression of the regularized limit of the Stokes matrices as the regular semisimple element u goes to the caterpillar point in the wonderful compactification.
Xiaomeng Xu 氏 (BICMR, China) 16:00-17:30This talk studies a quantum analog of Stokes matrices of confluent hypergeometric systems. It first gives an introduction to the Stokes phenomenon of an irregular Knizhnik–Zamolodchikov at a second order pole, associated to a regular semisimple element u and a representation $L(\lambda)$ of $gl_n$. It then shows that the Stokes matrices of the
irregular Knizhnik–Zamolodchikov equation define representation of $U_q(gl_n)$ on $L(\lambda)$. In then end, using the isomonodromy approach, it derives an explicit expression of the regularized limit of the Stokes matrices as the regular semisimple element u goes to the caterpillar point in the wonderful compactification.
The WKB approximation of (quantum) confluent hypergeometric systems, Cauchy interlacing inequality and crystal basis (ENGLISH)
[ 講演概要 ]
This talk studies the WKB approximation of the linear meromorphic systems of Poncaré rank 1 appearing in talk 1 and 2, via the isomonodromy approach. In the classical case, it unveils a relation between the WKB approximation, the Cauchy interlacing inequality and cluster algebras with the help of the spectral network; in the quantum case, motivated by the crystal limit of the quantum groups, it shows a relation between the WKB approximation and the gl_n-crystal structures. It is partially based on a joint work with
Anton Alekseev, Andrew Neitzke and Yan Zhou.
This talk studies the WKB approximation of the linear meromorphic systems of Poncaré rank 1 appearing in talk 1 and 2, via the isomonodromy approach. In the classical case, it unveils a relation between the WKB approximation, the Cauchy interlacing inequality and cluster algebras with the help of the spectral network; in the quantum case, motivated by the crystal limit of the quantum groups, it shows a relation between the WKB approximation and the gl_n-crystal structures. It is partially based on a joint work with
Anton Alekseev, Andrew Neitzke and Yan Zhou.
2023年08月08日(火)
講演会
14:00-15:00 数理科学研究科棟(駒場) 123号室
Dror Bar-Natan 氏 (University of Toronto)
Cars, Interchanges, Traffic Counters, and some Pretty Darned Good Knot Invariants (English)
http://www.math.toronto.edu/~drorbn/Talks/Tokyo-230808/
Dror Bar-Natan 氏 (University of Toronto)
Cars, Interchanges, Traffic Counters, and some Pretty Darned Good Knot Invariants (English)
[ 講演概要 ]
Reporting on joint work with Roland van der Veen, I'll tell you some stories about ρ_1, an easy to define, strong, fast to compute, homomorphic, and well-connected knot invariant. ρ_1 was first studied by Rozansky and Overbay, it is dominated by the coloured Jones polynomial (but it isn't lesser!), it has far-reaching generalizations, and I wish I understood it.
[ 参考URL ]Reporting on joint work with Roland van der Veen, I'll tell you some stories about ρ_1, an easy to define, strong, fast to compute, homomorphic, and well-connected knot invariant. ρ_1 was first studied by Rozansky and Overbay, it is dominated by the coloured Jones polynomial (but it isn't lesser!), it has far-reaching generalizations, and I wish I understood it.
http://www.math.toronto.edu/~drorbn/Talks/Tokyo-230808/
講演会
15:30-16:30 数理科学研究科棟(駒場) 123号室
Dror Bar-Natan 氏 (University of Toronto)
Shifted Partial Quadratics, their Pushwards, and Signature Invariants for Tangles (English)
http://www.math.toronto.edu/~drorbn/Talks/Tokyo-230808/
Dror Bar-Natan 氏 (University of Toronto)
Shifted Partial Quadratics, their Pushwards, and Signature Invariants for Tangles (English)
[ 講演概要 ]
Following a general discussion of the computation of zombians of unfinished columbaria (with examples), I will tell you about my recent joint work with Jessica Liu on what we feel is the "textbook" extension of knot signatures to tangles, which for unknown reasons, is not in any of the textbooks that we know.
[ 参考URL ]Following a general discussion of the computation of zombians of unfinished columbaria (with examples), I will tell you about my recent joint work with Jessica Liu on what we feel is the "textbook" extension of knot signatures to tangles, which for unknown reasons, is not in any of the textbooks that we know.
http://www.math.toronto.edu/~drorbn/Talks/Tokyo-230808/
2023年08月07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) 123号室
いつもと教室が異なります.
Freddy Delbaen 氏 (Professor emeritus at ETH Zurich)
Approximation of Random Variables by Elements that are independent of a given sigma algebra (English)
いつもと教室が異なります.
Freddy Delbaen 氏 (Professor emeritus at ETH Zurich)
Approximation of Random Variables by Elements that are independent of a given sigma algebra (English)
[ 講演概要 ]
Given a square integrable m-dimensional random variable $X$ on a probability space $(\Omega,\mathcal{F},\mathbb{P})$ and a sub sigma algebra $\mathcal{A}$, we show that there exists another m-dimensional random variable $Y$, independent of $\mathcal{A}$ and minimising the $L^2$ distance to $X$. Such results have an importance to fairness and bias reduction in Artificial Intelligence, Machine Learning and Network Theory. The proof needs elements from transportation theory, a parametric version due to Dudley and Blackwell of the Skorohod theorem, selection theorems, … The problem also triggers other approximation problems. (joint work with C. Majumdar)
Given a square integrable m-dimensional random variable $X$ on a probability space $(\Omega,\mathcal{F},\mathbb{P})$ and a sub sigma algebra $\mathcal{A}$, we show that there exists another m-dimensional random variable $Y$, independent of $\mathcal{A}$ and minimising the $L^2$ distance to $X$. Such results have an importance to fairness and bias reduction in Artificial Intelligence, Machine Learning and Network Theory. The proof needs elements from transportation theory, a parametric version due to Dudley and Blackwell of the Skorohod theorem, selection theorems, … The problem also triggers other approximation problems. (joint work with C. Majumdar)
2023年07月31日(月)
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
Roberto Longo 氏 (ローマ大学)
Operator Algebras and Quantum Field Theory: introductory elements
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
Roberto Longo 氏 (ローマ大学)
Operator Algebras and Quantum Field Theory: introductory elements
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
2023年07月28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) ハイブリッド開催/002号室
(7/11更新) 中止となりました。来学期への延期を検討しています。
石井 志保子 氏 (東京大学)
TBA
(7/11更新) 中止となりました。来学期への延期を検討しています。
石井 志保子 氏 (東京大学)
TBA
2023年07月21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) ハイブリッド開催/056号室
普段と部屋が異なります。
江尻 祥 氏 (大阪公立大学)
The Demailly--Peternell--Schneider conjecture is true in positive characteristic
普段と部屋が異なります。
江尻 祥 氏 (大阪公立大学)
The Demailly--Peternell--Schneider conjecture is true in positive characteristic
[ 講演概要 ]
In 1993, Demailly, Peternell and Schneider conjectured that the Albanese morphism of a compact K\"{a}hler manifold with nef anti-canonical divisor is surjective. For smooth projective varieties of characteristic zero, the conjecture was verified by Zhang in 1996. In positive characteristic, the conjecture was solved under the assumption that the geometric generic fiber F of the Albanese morphism has only mild singularities. However, F may have bad singularities even if we restrict ourselves to the case when the anti-canonical divisor is nef. In this talk, we prove the conjecture in positive characteristic without any extra assumption. We also discuss properties of the Albanese morphism, such as flatness or local isotriviality. This talk is based on joint work with Zsolt Patakfalvi.
In 1993, Demailly, Peternell and Schneider conjectured that the Albanese morphism of a compact K\"{a}hler manifold with nef anti-canonical divisor is surjective. For smooth projective varieties of characteristic zero, the conjecture was verified by Zhang in 1996. In positive characteristic, the conjecture was solved under the assumption that the geometric generic fiber F of the Albanese morphism has only mild singularities. However, F may have bad singularities even if we restrict ourselves to the case when the anti-canonical divisor is nef. In this talk, we prove the conjecture in positive characteristic without any extra assumption. We also discuss properties of the Albanese morphism, such as flatness or local isotriviality. This talk is based on joint work with Zsolt Patakfalvi.
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