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過去の記録
過去の記録 ～04/26｜本日 04/27 | 今後の予定 04/28～
2019年11月18日(月)
複素解析幾何セミナー
10:30-12:00 数理科学研究科棟(駒場) 128号室
吉川 謙一 氏 (京都大学)
j-invariant and Borcherds Phi-function (Japanese)
吉川 謙一 氏 (京都大学)
j-invariant and Borcherds Phi-function (Japanese)
[ 講演概要 ]
The j-invariant is a modular function on the complex upper half plane inducing an isomorphism between the moduli space of elliptic curves and the complex plane. Besides the j-invariant itself, the difference of j-invariants has also attracted some mathematicians. In this talk, I will explain a factorization of the difference of j-invariants in terms of Borcherds Phi-function, the automorphic form on the period domain for Enriques surfaces characterizing the discriminant divisor. This is a joint work with Shu Kawaguchi and Shigeru Mukai.
The j-invariant is a modular function on the complex upper half plane inducing an isomorphism between the moduli space of elliptic curves and the complex plane. Besides the j-invariant itself, the difference of j-invariants has also attracted some mathematicians. In this talk, I will explain a factorization of the difference of j-invariants in terms of Borcherds Phi-function, the automorphic form on the period domain for Enriques surfaces characterizing the discriminant divisor. This is a joint work with Shu Kawaguchi and Shigeru Mukai.
2019年11月14日(木)
情報数学セミナー
16:50-18:35 数理科学研究科棟(駒場) 122号室
御手洗 光祐 氏 (大阪大学基礎工学研究科)
量子コンピュータを用いた量子機械学習 (Japanese)
御手洗 光祐 氏 (大阪大学基礎工学研究科)
量子コンピュータを用いた量子機械学習 (Japanese)
[ 講演概要 ]
本講義では、量子コンピュータを使って機械学習を高速化しようとする試みを概観する。まず量子誤り訂正付きの万能量子計算を用いた機械学習アルゴリズムについて、これまで提案されているアイデアの特徴をみる。そののち、今後数年で実現するとされる Noisy Intermidiate-Scale Qunatum (NISQ) デバイスを用いた機械学習アルゴリズムについて述べる。
本講義では、量子コンピュータを使って機械学習を高速化しようとする試みを概観する。まず量子誤り訂正付きの万能量子計算を用いた機械学習アルゴリズムについて、これまで提案されているアイデアの特徴をみる。そののち、今後数年で実現するとされる Noisy Intermidiate-Scale Qunatum (NISQ) デバイスを用いた機械学習アルゴリズムについて述べる。
2019年11月12日(火)
解析学火曜セミナー
16:50-18:20 数理科学研究科棟(駒場) 128号室
神本晋吾 氏 (広島大学)
Mould展開を用いたResurgence構造の解析 (Japanese)
神本晋吾 氏 (広島大学)
Mould展開を用いたResurgence構造の解析 (Japanese)
[ 講演概要 ]
Mould解析はJ. Ecalle氏により考案された解析手法であり, ベクトル場の標準形の構成や多重ゼータ値などに応用されている. Mould 解析では word による展開を用いるが, その後Ecalle氏によりtreeを用いた展開も導入された. 2017年に, F. Fauvet氏とF. Menous氏により, このtreeによる展開のConnes-Kreimer Hopf代数を用いた明確な定式化が与えられた. 本講演では, この定式化に則り, ベクトル場の線形化問題に現れるStokes現象のResurgence構造に関して議論を行う.
Mould解析はJ. Ecalle氏により考案された解析手法であり, ベクトル場の標準形の構成や多重ゼータ値などに応用されている. Mould 解析では word による展開を用いるが, その後Ecalle氏によりtreeを用いた展開も導入された. 2017年に, F. Fauvet氏とF. Menous氏により, このtreeによる展開のConnes-Kreimer Hopf代数を用いた明確な定式化が与えられた. 本講演では, この定式化に則り, ベクトル場の線形化問題に現れるStokes現象のResurgence構造に関して議論を行う.
2019年11月08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) 056号室
斎藤秀司 氏 (東大数理)
モチーフ理論と分岐理論への応用 (日本語)
斎藤秀司 氏 (東大数理)
モチーフ理論と分岐理論への応用 (日本語)
[ 講演概要 ]
モチーフ理論とは，代数多様体の普遍的コホモロジー理論の構成を目的とする理論である．
すでに1970年代にGrothendieckがさまざまなコホモロジー理論の背後に潜むものとしてその存在を予見し，1980年にBeilinsonがそれを正確に定式化し予想として提出した．
それ以来、モチーフ理論は哲学的指導原理として多くの優れた研究を導びきつつ発展してきた．
最も大きな進展は、今世紀初頭にVoevodskyが構成した特異点を持たない多様体にたいしては望まれた性質を持つモチーフ理論である（彼はその応用としてBloch-加藤予想を解決しフィールズ賞を受賞している）．
しかし一般の場合のモチーフ理論の構成(Beilinson予想)は未解決である．
本講演では、Voevodskyの理論を拡張することによりBeilinson予想の解決に向けた
最近の進展を解説し、その応用として、加藤和也氏と斎藤毅氏たちが牽引する分岐理論を新しい視点から再構成し一般化する試みを紹介したい．
モチーフ理論とは，代数多様体の普遍的コホモロジー理論の構成を目的とする理論である．
すでに1970年代にGrothendieckがさまざまなコホモロジー理論の背後に潜むものとしてその存在を予見し，1980年にBeilinsonがそれを正確に定式化し予想として提出した．
それ以来、モチーフ理論は哲学的指導原理として多くの優れた研究を導びきつつ発展してきた．
最も大きな進展は、今世紀初頭にVoevodskyが構成した特異点を持たない多様体にたいしては望まれた性質を持つモチーフ理論である（彼はその応用としてBloch-加藤予想を解決しフィールズ賞を受賞している）．
しかし一般の場合のモチーフ理論の構成(Beilinson予想)は未解決である．
本講演では、Voevodskyの理論を拡張することによりBeilinson予想の解決に向けた
最近の進展を解説し、その応用として、加藤和也氏と斎藤毅氏たちが牽引する分岐理論を新しい視点から再構成し一般化する試みを紹介したい．
2019年11月07日(木)
情報数学セミナー
16:50-18:35 数理科学研究科棟(駒場) 126号室
中川裕也 氏 (株式会社QunaSys)
量子コンピュータを用いた量子化学計算 (Japanese)
中川裕也 氏 (株式会社QunaSys)
量子コンピュータを用いた量子化学計算 (Japanese)
[ 講演概要 ]
量子計算に関する連続講義（全4回）の第2回目となる本講義では、量子コンピュータの産業応用先として最も注目されている分野の一つである量子化学計算について解説する。特に、Noisy Intermidiate-Scale Qunatum (NISQ) デバイスという、数年以内の実用化が期待されている量子コンピュータを用いた量子化学計算に関する話題を掘り下げていく。
量子計算に関する連続講義（全4回）の第2回目となる本講義では、量子コンピュータの産業応用先として最も注目されている分野の一つである量子化学計算について解説する。特に、Noisy Intermidiate-Scale Qunatum (NISQ) デバイスという、数年以内の実用化が期待されている量子コンピュータを用いた量子化学計算に関する話題を掘り下げていく。
2019年11月06日(水)
作用素環セミナー
16:45-18:15 数理科学研究科棟(駒場) 126号室
森脇湧登 氏 (東大数理)
Deformation of two-dimensional conformal field theory and vertex algebra
森脇湧登 氏 (東大数理)
Deformation of two-dimensional conformal field theory and vertex algebra
2019年11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) 056号室
Tea: Common Room 16:30-17:00
五味 清紀 氏 (東京工業大学)
Magnitude homology of geodesic space (JAPANESE)
Tea: Common Room 16:30-17:00
五味 清紀 氏 (東京工業大学)
Magnitude homology of geodesic space (JAPANESE)
[ 講演概要 ]
Magnitude is an invariant which counts `effective number of points' on a metric space. Its categorification is magnitude homology. This notion is first formulated for metric spaces associated to simple graphs by Hepworth and Willerton, and then for any metric spaces by Leinster and Shulman. The definition of the magnitude homology is easy, but its calculation is rather difficult. For example, the magnitude homology of the circle with geodesic metric was known partially. In my talk, I will explain my result that fully determines the magnitude homology of any geodesic metric space subject to a certain non-branching assumption. In this result, the magnitude homology is described in terms of geodesics. Complete and connected Riemannian manifolds are examples of the geodesic metric spaces satisfying the assumption.
Magnitude is an invariant which counts `effective number of points' on a metric space. Its categorification is magnitude homology. This notion is first formulated for metric spaces associated to simple graphs by Hepworth and Willerton, and then for any metric spaces by Leinster and Shulman. The definition of the magnitude homology is easy, but its calculation is rather difficult. For example, the magnitude homology of the circle with geodesic metric was known partially. In my talk, I will explain my result that fully determines the magnitude homology of any geodesic metric space subject to a certain non-branching assumption. In this result, the magnitude homology is described in terms of geodesics. Complete and connected Riemannian manifolds are examples of the geodesic metric spaces satisfying the assumption.
解析学火曜セミナー
16:50-18:20 数理科学研究科棟(駒場) 128号室
Ngô Quốc Anh 氏 (ベトナム国家大学ハノイ校 / 東京大学)
Exhaustive existence and non-existence results for some prototype polyharmonic equations in the whole space (English)
Ngô Quốc Anh 氏 (ベトナム国家大学ハノイ校 / 東京大学)
Exhaustive existence and non-existence results for some prototype polyharmonic equations in the whole space (English)
[ 講演概要 ]
This talk concerns entire, non-trivial, non-negative solutions and/or entire, positive solutions to the simplest models of polyharmonic equations with power-type nonlinearity \[\Delta^m u = \pm u^\alpha\] in $\mathbb R^n$ with $n \geqslant 1$, $m \geqslant 1$, and $\alpha \in \mathbb R$. For small $m$, the above equations arise in many physical phenomena and applied mathematics. They also arise from several prescribing geometric curvture problems in conformal geometry such as the Yamabe problem, the scalar curvature problem, and the Q-curvature problem for the Paneitz operator. Higher-order cases also arise from the Q-curvature problem for the GJMS operator. In this talk, I will present a complete picture of the existence and non-existence of solutions to the above equations in the full rage of the parameters $n$, $m$, and $\alpha$. This is joint work with V.H. Nguyen, Q.H. Phan, and D. Ye.
This talk concerns entire, non-trivial, non-negative solutions and/or entire, positive solutions to the simplest models of polyharmonic equations with power-type nonlinearity \[\Delta^m u = \pm u^\alpha\] in $\mathbb R^n$ with $n \geqslant 1$, $m \geqslant 1$, and $\alpha \in \mathbb R$. For small $m$, the above equations arise in many physical phenomena and applied mathematics. They also arise from several prescribing geometric curvture problems in conformal geometry such as the Yamabe problem, the scalar curvature problem, and the Q-curvature problem for the Paneitz operator. Higher-order cases also arise from the Q-curvature problem for the GJMS operator. In this talk, I will present a complete picture of the existence and non-existence of solutions to the above equations in the full rage of the parameters $n$, $m$, and $\alpha$. This is joint work with V.H. Nguyen, Q.H. Phan, and D. Ye.
2019年10月31日(木)
応用解析セミナー
16:00-17:30 数理科学研究科棟(駒場) 128 (TBD)号室
Marius Ghergu 氏 (University College Dublin)
Behaviour around the isolated singularity for solutions of some nonlinear elliptic inequalities and systems (English)
Marius Ghergu 氏 (University College Dublin)
Behaviour around the isolated singularity for solutions of some nonlinear elliptic inequalities and systems (English)
[ 講演概要 ]
We present some results on the behaviour around the isolated singularity for solutions of nonlinear elliptic inequalities driven by the Laplace operator. We derive optimal conditions that imply either a blow-up or the existence of pointwise bounds for solutions. We obtain that whenever a pointwise bound exists, then an optimal bound is given by the fundamental solution of the Laplace operator. This situation changes in case of systems of inequalities where other types of optimal bounds may occur. The approach relies on integral representation of solutions combined with various nonlinear potential estimates. Further extensions to the parabolic case will be presented. This talk is based on joint works with S. Taliaferro (Texas A&M University) and I. Verbitsky (Missouri University).
We present some results on the behaviour around the isolated singularity for solutions of nonlinear elliptic inequalities driven by the Laplace operator. We derive optimal conditions that imply either a blow-up or the existence of pointwise bounds for solutions. We obtain that whenever a pointwise bound exists, then an optimal bound is given by the fundamental solution of the Laplace operator. This situation changes in case of systems of inequalities where other types of optimal bounds may occur. The approach relies on integral representation of solutions combined with various nonlinear potential estimates. Further extensions to the parabolic case will be presented. This talk is based on joint works with S. Taliaferro (Texas A&M University) and I. Verbitsky (Missouri University).
FMSPレクチャーズ
13:00-15:05 数理科学研究科棟(駒場) 002号室
全6回：9/26～10/31の毎週（木）13:00-15:05
Chung-jun Tsai 氏 (National Taiwan University)
Topic on minimal submanifolds (6/6) (ENGLISH)
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Tsai.pdf
全6回：9/26～10/31の毎週（木）13:00-15:05
Chung-jun Tsai 氏 (National Taiwan University)
Topic on minimal submanifolds (6/6) (ENGLISH)
[ 講演概要 ]
The main theme of these lectures will be theory about minimal submanifolds, which are higher dimensional generalizations of geodesics. A naive motivation is that one tries to understand the geometry from its special submanifolds (minimal, etc.).
For minimal submanifolds, the equations are no longer ODEs, but elliptic PDEs. This increases the difficulties. The study are very good examples for the application of methods from PDEs and calculus of variations. We will try to explain some important results in this theory, which stimulate many of the researches today.
Here are some specific materials we plan to cover: Simon’s work based on the second variational formula, Sacks - Uhlenback theorem on the existence of minimal 2-spheres, the theory of stable minimal hypersurfaces by Schoen-Simon-Yau.
[ 参考URL ]The main theme of these lectures will be theory about minimal submanifolds, which are higher dimensional generalizations of geodesics. A naive motivation is that one tries to understand the geometry from its special submanifolds (minimal, etc.).
For minimal submanifolds, the equations are no longer ODEs, but elliptic PDEs. This increases the difficulties. The study are very good examples for the application of methods from PDEs and calculus of variations. We will try to explain some important results in this theory, which stimulate many of the researches today.
Here are some specific materials we plan to cover: Simon’s work based on the second variational formula, Sacks - Uhlenback theorem on the existence of minimal 2-spheres, the theory of stable minimal hypersurfaces by Schoen-Simon-Yau.
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Tsai.pdf
情報数学セミナー
16:50-18:35 数理科学研究科棟(駒場) 122号室
鈴木泰成 氏 (NTTセキュアプラットフォーム研究所)
量子計算の基礎 (Japanese)
鈴木泰成 氏 (NTTセキュアプラットフォーム研究所)
量子計算の基礎 (Japanese)
[ 講演概要 ]
近年の量子デバイスの発展で実用的な量子計算機の実現が現実味を帯びてきたことから、量子計算に関する研究開発が現在世界的に過熱している。量子計算の研究開発の次なる目標として、計算機の拡張に必須となる量子誤り訂正の実現と、量子誤り訂正を使わずとも可能な有用なアプリケーションを探求するNISQ(Noisy intermediate-scale quantum)アルゴリズムの実現の二つが特に注目を集めている。
4回構成の本講義ではまず1回目に量子計算の基礎的な枠組みを学んだ後、2,3回目でNISQアルゴリズムとして有望視される量子化学計算と機械学習への量子計算機の応用についてそれぞれ解説し、4回目に量子誤り訂正について解説を行う。
初回となる本講義では、量子計算を記述する基本的枠組み、物理実装や計算量などに関する基礎的な事実、そして近年の量子計算の発展の概要について解説する。
近年の量子デバイスの発展で実用的な量子計算機の実現が現実味を帯びてきたことから、量子計算に関する研究開発が現在世界的に過熱している。量子計算の研究開発の次なる目標として、計算機の拡張に必須となる量子誤り訂正の実現と、量子誤り訂正を使わずとも可能な有用なアプリケーションを探求するNISQ(Noisy intermediate-scale quantum)アルゴリズムの実現の二つが特に注目を集めている。
4回構成の本講義ではまず1回目に量子計算の基礎的な枠組みを学んだ後、2,3回目でNISQアルゴリズムとして有望視される量子化学計算と機械学習への量子計算機の応用についてそれぞれ解説し、4回目に量子誤り訂正について解説を行う。
初回となる本講義では、量子計算を記述する基本的枠組み、物理実装や計算量などに関する基礎的な事実、そして近年の量子計算の発展の概要について解説する。
2019年10月30日(水)
代数幾何学セミナー
15:30-17:00 数理科学研究科棟(駒場) 122号室
Andrew Macpherson 氏 (IPMU)
A Tannakian perspective on rigid analytic geometry (English)
Andrew Macpherson 氏 (IPMU)
A Tannakian perspective on rigid analytic geometry (English)
[ 講演概要 ]
Raynaud's conception of analytic geometry contends that the category of analytic spaces over a non-Archimedean field is a (suitably "geometric") localisation of the category of formal schemes over the ring of integers at a class of modifications "along the central fibre". Unfortunately, as with all existing presentations of non-Archimedean geometry, this viewpoint is confounded by a proliferation of technical difficulties if one does not impose absolute finiteness conditions on the formal schemes under consideration.
I will argue that by combining Raynaud's idea with a Tannakian perspective which prioritises the module category, we can obtain a reasonable framework for rigid analytic geometry with no absolute finiteness hypotheses whatsoever, but which has descent for finitely presented modules.
Raynaud's conception of analytic geometry contends that the category of analytic spaces over a non-Archimedean field is a (suitably "geometric") localisation of the category of formal schemes over the ring of integers at a class of modifications "along the central fibre". Unfortunately, as with all existing presentations of non-Archimedean geometry, this viewpoint is confounded by a proliferation of technical difficulties if one does not impose absolute finiteness conditions on the formal schemes under consideration.
I will argue that by combining Raynaud's idea with a Tannakian perspective which prioritises the module category, we can obtain a reasonable framework for rigid analytic geometry with no absolute finiteness hypotheses whatsoever, but which has descent for finitely presented modules.
Lie群論・表現論セミナー
16:30-18:00 数理科学研究科棟(駒場) 128号室
Quentin Labriet 氏 (Reims University)
On holographic transform (English)
Quentin Labriet 氏 (Reims University)
On holographic transform (English)
[ 講演概要 ]
In representation theory, decomposing the restriction of a given representation $¥pi$ of a Lie group $G$ to an appropriate subgroup $G'$ is an important issue referred to as a branching law. In this context,one can define symmetry breaking operators, as $G'$-intertwining operators between the restriction $¥pi¥vert_{G'}$ and its irreducible components. Going in the opposite direction gives rise to holographic operators and the notion of holographic transform.
I will illustrate this construction by two examples :
- the diagonal case where one considers the restriction problem for $¥pi$ being an outer product of two holomorphic discrete series representations, $G=SL(2,R)¥times SL(2,R)$ and $G'=SL(2,R)$.
- the conformal case for the restriction of a scalar valued holomorphic discrete series representation $¥pi$ of $G=SO(2,n)$ to $G'=SO(2,n-1)$.
I will then explain different methods for an explicit construction of such holographic operators in these cases, and present some of my results and open problems in this direction.
In representation theory, decomposing the restriction of a given representation $¥pi$ of a Lie group $G$ to an appropriate subgroup $G'$ is an important issue referred to as a branching law. In this context,one can define symmetry breaking operators, as $G'$-intertwining operators between the restriction $¥pi¥vert_{G'}$ and its irreducible components. Going in the opposite direction gives rise to holographic operators and the notion of holographic transform.
I will illustrate this construction by two examples :
- the diagonal case where one considers the restriction problem for $¥pi$ being an outer product of two holomorphic discrete series representations, $G=SL(2,R)¥times SL(2,R)$ and $G'=SL(2,R)$.
- the conformal case for the restriction of a scalar valued holomorphic discrete series representation $¥pi$ of $G=SO(2,n)$ to $G'=SO(2,n-1)$.
I will then explain different methods for an explicit construction of such holographic operators in these cases, and present some of my results and open problems in this direction.
2019年10月29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) 056号室
Tea: Common Room 16:30-17:00
Chung-Jun Tsai 氏 (National Taiwan University)
Strong stability of minimal submanifolds (ENGLISH)
Tea: Common Room 16:30-17:00
Chung-Jun Tsai 氏 (National Taiwan University)
Strong stability of minimal submanifolds (ENGLISH)
[ 講演概要 ]
It is well known that the distance function to a totally geodesic submanifold of a negatively curved ambient manifold is a convex function. One can identify a strong stability condition on minimal submanifolds that generalizes the above scenario. Besides a strong local uniqueness property, a strongly stable minimal submanifold is also Lipschitz stable under the mean curvature flow. We will also discuss some famous local (complete, non-compact) models. This is based on a joint work with Mu-Tao Wang.
It is well known that the distance function to a totally geodesic submanifold of a negatively curved ambient manifold is a convex function. One can identify a strong stability condition on minimal submanifolds that generalizes the above scenario. Besides a strong local uniqueness property, a strongly stable minimal submanifold is also Lipschitz stable under the mean curvature flow. We will also discuss some famous local (complete, non-compact) models. This is based on a joint work with Mu-Tao Wang.
2019年10月28日(月)
複素解析幾何セミナー
10:30-12:00 数理科学研究科棟(駒場) 128号室
野口 潤次郎 氏 (東京大学)
On Kiyoshi Oka's unpublished papers 1943 (Japanese)
野口 潤次郎 氏 (東京大学)
On Kiyoshi Oka's unpublished papers 1943 (Japanese)
[ 講演概要 ]
いわゆる岡の解決した不分岐リーマン領域に対する3大問題(Oka IX, 1953)は、実はこの未発表論文(VII～XI)で終わっている。 Oka VII、VIIIで示された連接性、不定域イデアルの理論はこれ等を、分岐リーマン領域へ確立しようとする試みより生まれたことが、この未発表論文から明らかになる。この講演では、この未発表論文で擬凸問題がどのように解決されたかを紹介する。 分岐リーマン領域の場合の擬凸問題は、Fornaessによる反例が与えられたとはいえ、情況は不明で未解決問題として今も残っている（岡の夢）ことにも言及したい。
いわゆる岡の解決した不分岐リーマン領域に対する3大問題(Oka IX, 1953)は、実はこの未発表論文(VII～XI)で終わっている。 Oka VII、VIIIで示された連接性、不定域イデアルの理論はこれ等を、分岐リーマン領域へ確立しようとする試みより生まれたことが、この未発表論文から明らかになる。この講演では、この未発表論文で擬凸問題がどのように解決されたかを紹介する。 分岐リーマン領域の場合の擬凸問題は、Fornaessによる反例が与えられたとはいえ、情況は不明で未解決問題として今も残っている（岡の夢）ことにも言及したい。
2019年10月25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) 123号室
Yves Benoist 氏 ( CNRS, Paris-Sud)
Arithmeticity of discrete subgroups (英語)
Yves Benoist 氏 ( CNRS, Paris-Sud)
Arithmeticity of discrete subgroups (英語)
[ 講演概要 ]
By a theorem of Borel and Harish-Chandra,
an arithmetic group in a semisimple Lie group is a lattice.
Conversely, by a celebrated theorem of Margulis,
in a higher rank semisimple Lie group G
any irreducible lattice is an arithmetic group.
The aim of this lecture is to survey an
arithmeticity criterium for discrete subgroups
which are not assumed to be lattices.
This criterium, obtained with Miquel,
generalizes works of Selberg and Hee Oh
and solves a conjecture of Margulis. It says:
a discrete irreducible Zariski-dense subgroup
of G that intersects cocompactly at least one
horospherical subgroup of G is an arithmetic group.
By a theorem of Borel and Harish-Chandra,
an arithmetic group in a semisimple Lie group is a lattice.
Conversely, by a celebrated theorem of Margulis,
in a higher rank semisimple Lie group G
any irreducible lattice is an arithmetic group.
The aim of this lecture is to survey an
arithmeticity criterium for discrete subgroups
which are not assumed to be lattices.
This criterium, obtained with Miquel,
generalizes works of Selberg and Hee Oh
and solves a conjecture of Margulis. It says:
a discrete irreducible Zariski-dense subgroup
of G that intersects cocompactly at least one
horospherical subgroup of G is an arithmetic group.
2019年10月24日(木)
FMSPレクチャーズ
13:00-15:05 数理科学研究科棟(駒場) 002号室
全6回：9/26～10/31の毎週（木）13:00-15:05
Chung-jun Tsai 氏 (National Taiwan University)
Topic on minimal submanifolds (5/6) (ENGLISH)
全6回：9/26～10/31の毎週（木）13:00-15:05
Chung-jun Tsai 氏 (National Taiwan University)
Topic on minimal submanifolds (5/6) (ENGLISH)
[ 講演概要 ]
The main theme of these lectures will be theory about minimal submanifolds, which are higher dimensional generalizations of geodesics. A naive motivation is that one tries to understand the geometry from its special submanifolds (minimal, etc.).
For minimal submanifolds, the equations are no longer ODEs, but elliptic PDEs. This increases the difficulties. The study are very good examples for the application of methods from PDEs and calculus of variations. We will try to explain some important results in this theory, which stimulate many of the researches today.
Here are some specific materials we plan to cover: Simon’s work based on the second variational formula, Sacks - Uhlenback theorem on the existence of minimal 2-spheres, the theory of stable minimal hypersurfaces by Schoen-Simon-Yau.
The main theme of these lectures will be theory about minimal submanifolds, which are higher dimensional generalizations of geodesics. A naive motivation is that one tries to understand the geometry from its special submanifolds (minimal, etc.).
For minimal submanifolds, the equations are no longer ODEs, but elliptic PDEs. This increases the difficulties. The study are very good examples for the application of methods from PDEs and calculus of variations. We will try to explain some important results in this theory, which stimulate many of the researches today.
Here are some specific materials we plan to cover: Simon’s work based on the second variational formula, Sacks - Uhlenback theorem on the existence of minimal 2-spheres, the theory of stable minimal hypersurfaces by Schoen-Simon-Yau.
基礎論セミナー
13:30-15:00 数理科学研究科棟(駒場) 156号室
大川 裕矢 氏 (千葉大学)
部分保存性に対する，Bennet の結果の一般化について (JAPANESE)
大川 裕矢 氏 (千葉大学)
部分保存性に対する，Bennet の結果の一般化について (JAPANESE)
[ 講演概要 ]
文 $\varphi$ が理論 $T$ 上 $\Gamma$-保存的であるとは,
任意の $\Gamma$ 文 $\psi$ について,
$T + \varphi \vdash \psi$ ならば $T \vdash \psi$ が成立することをいう.
1979 年 Guaspari は複数の理論に対して,
同時に $\Gamma$-保存的であり,
各理論では証明できない文の存在に関する部分的な議論を行ったが,
その一般的な状況を解明するという問いを残していた.
この問いに対し, 1986年 Bennet は特に2つの理論に対する分析を行い,
存在条件をある程度特徴付けることに成功した.
今回木更津工業高等専門学校の倉橋太志講師との共同研究により ,
この Bennet の結果は任意有限個の理論に拡張可能であることが判明した.
本講演ではその拡張した結果を紹介する.
文 $\varphi$ が理論 $T$ 上 $\Gamma$-保存的であるとは,
任意の $\Gamma$ 文 $\psi$ について,
$T + \varphi \vdash \psi$ ならば $T \vdash \psi$ が成立することをいう.
1979 年 Guaspari は複数の理論に対して,
同時に $\Gamma$-保存的であり,
各理論では証明できない文の存在に関する部分的な議論を行ったが,
その一般的な状況を解明するという問いを残していた.
この問いに対し, 1986年 Bennet は特に2つの理論に対する分析を行い,
存在条件をある程度特徴付けることに成功した.
今回木更津工業高等専門学校の倉橋太志講師との共同研究により ,
この Bennet の結果は任意有限個の理論に拡張可能であることが判明した.
本講演ではその拡張した結果を紹介する.
応用解析セミナー
16:00-17:30 数理科学研究科棟(駒場) 128号室
オム ジュンヨン 氏 (東京大学)
非線形放物型方程式系に対するODE型解の漸近展開 (Japanese)
オム ジュンヨン 氏 (東京大学)
非線形放物型方程式系に対するODE型解の漸近展開 (Japanese)
[ 講演概要 ]
本講演では, 弱連立非線形放物型方程式系を考え，常微分方程式系の解の様に振る舞う解(ODE型解)の時間大域挙動を調べる．ODE解の挙動によって誘発されるある変換によって導かれる方程式系はある特別な構造を持ち，その構造とスカラー方程式の解の高次漸近展開理論を用いてODE型解の漸近挙動はある熱方程式の解を用いて表現できる．結果としてODE型解の漸近挙動はシステム特有の性質を有することが証明できる．本講演は石毛和弘氏(東京大学)との共同研究に基づく．
本講演では, 弱連立非線形放物型方程式系を考え，常微分方程式系の解の様に振る舞う解(ODE型解)の時間大域挙動を調べる．ODE解の挙動によって誘発されるある変換によって導かれる方程式系はある特別な構造を持ち，その構造とスカラー方程式の解の高次漸近展開理論を用いてODE型解の漸近挙動はある熱方程式の解を用いて表現できる．結果としてODE型解の漸近挙動はシステム特有の性質を有することが証明できる．本講演は石毛和弘氏(東京大学)との共同研究に基づく．
2019年10月23日(水)
Lie群論・表現論セミナー
16:30-18:00 数理科学研究科棟(駒場) 128号室
Clemens Weiske 氏 (Aarhus University)
Symmetry breaking and unitary branching laws for finite-multiplicity pairs of rank one (English)
Clemens Weiske 氏 (Aarhus University)
Symmetry breaking and unitary branching laws for finite-multiplicity pairs of rank one (English)
[ 講演概要 ]
Let (G,G’) be a real reductive finite multiplicity pair of rank one, i.e. a rank one real reductive group G with reductive subgroup G’, such that the space of symmetry breaking operators (SBOs) between all (smooth admissible) irreducible representations is finite dimensional.
We give a classification of SBOs between spherical principal series representations of G and G’, essentially generalizing the results on (O(1,n+1),O(1,n)) of Kobayashi—Speh (2015). Moreover we show how to decompose unitary representations occurring in (not necessarily) spherical principal series representations of G in terms of unitary G’ representations, by making use of the knowledge gathered in the classification of the SBOs and the structure of the open P’orbit in G/P as a homogenous G’-space, where P’ is a minimal parabolic in G’ and P is a minimal parabolic in G. This includes the construction of discrete spectra in the restriction of complementary series representations and unitarizable composition factors.
Let (G,G’) be a real reductive finite multiplicity pair of rank one, i.e. a rank one real reductive group G with reductive subgroup G’, such that the space of symmetry breaking operators (SBOs) between all (smooth admissible) irreducible representations is finite dimensional.
We give a classification of SBOs between spherical principal series representations of G and G’, essentially generalizing the results on (O(1,n+1),O(1,n)) of Kobayashi—Speh (2015). Moreover we show how to decompose unitary representations occurring in (not necessarily) spherical principal series representations of G in terms of unitary G’ representations, by making use of the knowledge gathered in the classification of the SBOs and the structure of the open P’orbit in G/P as a homogenous G’-space, where P’ is a minimal parabolic in G’ and P is a minimal parabolic in G. This includes the construction of discrete spectra in the restriction of complementary series representations and unitarizable composition factors.
2019年10月21日(月)
複素解析幾何セミナー
10:30-12:00 数理科学研究科棟(駒場) 128号室
松本 佳彦 氏 (大阪大学)
Canonical almost complex structures on ACH Einstein manifolds
松本 佳彦 氏 (大阪大学)
Canonical almost complex structures on ACH Einstein manifolds
[ 講演概要 ]
Einstein ACH (asymptotically complex hyperbolic) manifolds are seen as a device that establishes a correspondence between CR geometry on the boundary and Riemannian geometry in “the bulk.” This talk concerns an idea of enriching the geometric structure of the bulk by adding some almost complex structure compatible with the metric. I will introduce an energy functional of almost complex structures and discuss an existence result of critical points when the given ACH Einstein metric is a small perturbation of the Cheng-Yau complete K?hler-Einstein metric on a bounded strictly pseudoconvex domain. The renormalized Chern-Gauss-Bonnet formula is also planned to be discussed.
Einstein ACH (asymptotically complex hyperbolic) manifolds are seen as a device that establishes a correspondence between CR geometry on the boundary and Riemannian geometry in “the bulk.” This talk concerns an idea of enriching the geometric structure of the bulk by adding some almost complex structure compatible with the metric. I will introduce an energy functional of almost complex structures and discuss an existence result of critical points when the given ACH Einstein metric is a small perturbation of the Cheng-Yau complete K?hler-Einstein metric on a bounded strictly pseudoconvex domain. The renormalized Chern-Gauss-Bonnet formula is also planned to be discussed.
2019年10月17日(木)
FMSPレクチャーズ
13:00-15:05 数理科学研究科棟(駒場) 002号室
全6回：9/26～10/31の毎週（木）13:00-15:05
Chung-jun Tsai 氏 (National Taiwan University)
Topic on minimal submanifolds (4/6) (ENGLISH)
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Tsai.pdf
全6回：9/26～10/31の毎週（木）13:00-15:05
Chung-jun Tsai 氏 (National Taiwan University)
Topic on minimal submanifolds (4/6) (ENGLISH)
[ 講演概要 ]
The main theme of these lectures will be theory about minimal submanifolds, which are higher dimensional generalizations of geodesics. A naive motivation is that one tries to understand the geometry from its special submanifolds (minimal, etc.).
For minimal submanifolds, the equations are no longer ODEs, but elliptic PDEs. This increases the difficulties. The study are very good examples for the application of methods from PDEs and calculus of variations. We will try to explain some important results in this theory, which stimulate many of the researches today.
Here are some specific materials we plan to cover: Simon’s work based on the second variational formula, Sacks - Uhlenback theorem on the existence of minimal 2-spheres, the theory of stable minimal hypersurfaces by Schoen-Simon-Yau.
[ 参考URL ]The main theme of these lectures will be theory about minimal submanifolds, which are higher dimensional generalizations of geodesics. A naive motivation is that one tries to understand the geometry from its special submanifolds (minimal, etc.).
For minimal submanifolds, the equations are no longer ODEs, but elliptic PDEs. This increases the difficulties. The study are very good examples for the application of methods from PDEs and calculus of variations. We will try to explain some important results in this theory, which stimulate many of the researches today.
Here are some specific materials we plan to cover: Simon’s work based on the second variational formula, Sacks - Uhlenback theorem on the existence of minimal 2-spheres, the theory of stable minimal hypersurfaces by Schoen-Simon-Yau.
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Tsai.pdf
情報数学セミナー
16:50-18:35 数理科学研究科棟(駒場) 122号室
AIと量子計算（暗号理論を含む）を主題とする
藤原 洋 氏 (株式会社ブロードバンドタワー)
CASE+AI時代の５Gデータセンター (Japanese)
AIと量子計算（暗号理論を含む）を主題とする
藤原 洋 氏 (株式会社ブロードバンドタワー)
CASE+AI時代の５Gデータセンター (Japanese)
[ 講演概要 ]
今日の情報科学および情報工学における発展トレンドの大きな流れは、「実用化
段階に入ったAI（人工知能）」、「演算速度のさらなる高速化」、「増大するサ
イバーセキュリティの重要性」の３つがあげられる。本連携講座では、このトレ
ンドに沿って、「AIと量子計算」を主テーマとし暗号理論の最前線にも触れなが
ら議論を深めていきたいと考えている。今回は、その第1回として、情報社会に
おいて情報収集拠点と共に情報発信拠点であるデータセンターの最新事情につい
て述べる。ここで起きている産業のデジタル化の中で、自動車産業が「CASE」
（Connected、Autonomous、Sharing & Services、Electrification）へと大転換
していることを取り上げデータセンターとの関係について述べることとする。
今日の情報科学および情報工学における発展トレンドの大きな流れは、「実用化
段階に入ったAI（人工知能）」、「演算速度のさらなる高速化」、「増大するサ
イバーセキュリティの重要性」の３つがあげられる。本連携講座では、このトレ
ンドに沿って、「AIと量子計算」を主テーマとし暗号理論の最前線にも触れなが
ら議論を深めていきたいと考えている。今回は、その第1回として、情報社会に
おいて情報収集拠点と共に情報発信拠点であるデータセンターの最新事情につい
て述べる。ここで起きている産業のデジタル化の中で、自動車産業が「CASE」
（Connected、Autonomous、Sharing & Services、Electrification）へと大転換
していることを取り上げデータセンターとの関係について述べることとする。
数理人口学・数理生物学セミナー
14:00-16:00 数理科学研究科棟(駒場) 052号室
Merlin C. Koehnke 氏 (Institute of Environmental Systems Research, School of Mathematics/Computer Science, Osnabrueck University) 14:00-15:00
Complex spatiotemporal dynamics in a simple predator-prey model (ENGLISH)
Functional response of competing populations to environmental variability (ENGLISH)
Merlin C. Koehnke 氏 (Institute of Environmental Systems Research, School of Mathematics/Computer Science, Osnabrueck University) 14:00-15:00
Complex spatiotemporal dynamics in a simple predator-prey model (ENGLISH)
[ 講演概要 ]
A simple reaction-diffusion predator-prey model with Holling type IV functional response
and logistic growth in the prey is considered. The functional response can be interpreted as
a group defense mechanism, i.e., the predation rate decreases with resource density when the
prey density is high enough [1]. Such a mechanism has been described in diverse biological
interactions [2,3]. For instance, high densities of filamentous algae can decrease filtering
rates of filter feeders [4].
The model will be described and linked to plankton dynamics. Nonspatial considerations reveal that the zooplankton may go extinct or coexistence (stationary or oscillatory) between
zoo- and phytoplankton may emerge depending on the choice of parameters. However,
including space, the dynamics are more complex. In particular, spatiotemporal irregular
oscillations can rescue the predator from extinction. These oscillations can be characterized
as spatiotemporal chaos. The results provide a simple mechanism not only for the emergence
of inhomogeneous plankton distributions [5] but also for the occurrence of chaos in plankton communities [6]. Possible underlying mechanisms for this phenomenon will be discussed.
References
[1] Freedman, H. I., Wolkowicz, G. S. (1986). Predator-prey systems with group defence: the
paradox of enrichment revisited. Bulletin of Mathematical Biology, 48(5-6), 493–508.
[2] Tener, J. S.. Muskoxen in Canada: a biological and taxonomic review. Vol. 2. Dept. of Northern
Affairs and National Resources, Canadian Wildlife Service, 1965.
[3] Holmes, J. C. (1972). Modification of intermediate host behaviour by parasites. Behavioural
aspects of parasite transmission.
[4] Davidowicz, P., Gliwicz, Z. M., Gulati, R. D. (1988). Can Daphnia prevent a blue-green algal
bloom in hypertrophic lakes? A laboratory test. Limnologica. Jena, 19(1), 21–26.
[5] Abbott, M., 1993. Phytoplankton patchiness: ecological implicationsand observation methods.
In: Levin, S.A., Powell, T.M., Steele, J.H.(Eds.), Patch Dynamics. Lecture Notes in Biomathematics, vol. 96. Springer-Verlag, Berlin, pp. 37–49.
[6] Beninc`a, E. et al. (2008). Chaos in a long-term experiment with a plankton community. Nature,
451(7180), 822.
Horst Malchow 氏 (Institute of Environmental Systems Research, School of Mathematics/Computer Science, Osnabrueck University) 15:00-16:00A simple reaction-diffusion predator-prey model with Holling type IV functional response
and logistic growth in the prey is considered. The functional response can be interpreted as
a group defense mechanism, i.e., the predation rate decreases with resource density when the
prey density is high enough [1]. Such a mechanism has been described in diverse biological
interactions [2,3]. For instance, high densities of filamentous algae can decrease filtering
rates of filter feeders [4].
The model will be described and linked to plankton dynamics. Nonspatial considerations reveal that the zooplankton may go extinct or coexistence (stationary or oscillatory) between
zoo- and phytoplankton may emerge depending on the choice of parameters. However,
including space, the dynamics are more complex. In particular, spatiotemporal irregular
oscillations can rescue the predator from extinction. These oscillations can be characterized
as spatiotemporal chaos. The results provide a simple mechanism not only for the emergence
of inhomogeneous plankton distributions [5] but also for the occurrence of chaos in plankton communities [6]. Possible underlying mechanisms for this phenomenon will be discussed.
References
[1] Freedman, H. I., Wolkowicz, G. S. (1986). Predator-prey systems with group defence: the
paradox of enrichment revisited. Bulletin of Mathematical Biology, 48(5-6), 493–508.
[2] Tener, J. S.. Muskoxen in Canada: a biological and taxonomic review. Vol. 2. Dept. of Northern
Affairs and National Resources, Canadian Wildlife Service, 1965.
[3] Holmes, J. C. (1972). Modification of intermediate host behaviour by parasites. Behavioural
aspects of parasite transmission.
[4] Davidowicz, P., Gliwicz, Z. M., Gulati, R. D. (1988). Can Daphnia prevent a blue-green algal
bloom in hypertrophic lakes? A laboratory test. Limnologica. Jena, 19(1), 21–26.
[5] Abbott, M., 1993. Phytoplankton patchiness: ecological implicationsand observation methods.
In: Levin, S.A., Powell, T.M., Steele, J.H.(Eds.), Patch Dynamics. Lecture Notes in Biomathematics, vol. 96. Springer-Verlag, Berlin, pp. 37–49.
[6] Beninc`a, E. et al. (2008). Chaos in a long-term experiment with a plankton community. Nature,
451(7180), 822.
Functional response of competing populations to environmental variability (ENGLISH)
[ 講演概要 ]
The possible control of competitive invasion by infection of the invader and multiplicative
noise is studied. The basic model is the Lotka-Volterra competition system with emergent
carrying capacities. Several stationary solutions of the non-infected and infected system are
identi ed as well as parameter ranges of bistability. The latter are used for the numerical
study of di usive invasion phenomena. The Fickian di usivities, the infection but in particular the white and colored multiplicative noise are the control parameters. It is shown
that not only competition, possible infection and mobilities are important drivers of the
invasive dynamics but also the noise and especially its color and the functional response of
populations to the emergence of noise.
The variability of the environment can additionally be modelled by applying Fokker-Planck
instead of Fickian di usion. An interesting feature of Fokker-Planck di usion is that for spatially varying di usion coecients the stationary solution is not a homogeneous distribution.
Instead, the densities accumulate in regions of low di usivity and tend to lower levels for
areas of high di usivity. Thus, the stationary distribution of the Fokker-Planck di usion can
be interpreted as a re
ection of di erent levels of habitat quality [1-5]. The latter recalls the
seminal papers on environmental density, cf. [6-7]. Appropriate examples will be presented.
References
[1] Bengfort, M., Malchow, H., Hilker, F.M. (2016). The Fokker-Planck law of diffusion and
pattern formation in heterogeneous media. Journal of Mathematical Biology 73(3), 683-704.
[2] Siekmann, I., Malchow, H. (2016). Fighting enemies and noise: Competition of residents
and invaders in a stochastically fluctuating environment. Mathematical Modelling of Natural
Phenomena 11(5), 120-140.
[3] Siekmann, I., Bengfort, M., Malchow, H. (2017). Coexistence of competitors mediated by
nonlinear noise. European Physical Journal Special Topics 226(9), 2157-2170.
[4] Kohnke, M.C., Malchow, H. (2017). Impact of parameter variability and environmental noise
on the Klausmeier model of vegetation pattern formation. Mathematics 5, 69 (19 pages).
[5] Bengfort, M., Siekmann, I., Malchow, H. (2018). Invasive competition with Fokker-Planck
di usion and noise. Ecological Complexity 34, 134-13.
[6] Morisita, M. (1971). Measuring of habitat value by the \environmental density" method. In:
Spatial patterns and statistical distributions (Patil, C.D., Pielou, E.C., Waters, W.E., eds.),
Statistical Ecology, vol. 1, pp. 379-401. Pennsylvania State University Press, University Park.
[7] N. Shigesada, N., Kawasaki, K., Teramoto, E. (1979). Spatial segregation of interacting species.
Journal of Theoretical Biology 79, 83-99.
The possible control of competitive invasion by infection of the invader and multiplicative
noise is studied. The basic model is the Lotka-Volterra competition system with emergent
carrying capacities. Several stationary solutions of the non-infected and infected system are
identi ed as well as parameter ranges of bistability. The latter are used for the numerical
study of di usive invasion phenomena. The Fickian di usivities, the infection but in particular the white and colored multiplicative noise are the control parameters. It is shown
that not only competition, possible infection and mobilities are important drivers of the
invasive dynamics but also the noise and especially its color and the functional response of
populations to the emergence of noise.
The variability of the environment can additionally be modelled by applying Fokker-Planck
instead of Fickian di usion. An interesting feature of Fokker-Planck di usion is that for spatially varying di usion coecients the stationary solution is not a homogeneous distribution.
Instead, the densities accumulate in regions of low di usivity and tend to lower levels for
areas of high di usivity. Thus, the stationary distribution of the Fokker-Planck di usion can
be interpreted as a re
ection of di erent levels of habitat quality [1-5]. The latter recalls the
seminal papers on environmental density, cf. [6-7]. Appropriate examples will be presented.
References
[1] Bengfort, M., Malchow, H., Hilker, F.M. (2016). The Fokker-Planck law of diffusion and
pattern formation in heterogeneous media. Journal of Mathematical Biology 73(3), 683-704.
[2] Siekmann, I., Malchow, H. (2016). Fighting enemies and noise: Competition of residents
and invaders in a stochastically fluctuating environment. Mathematical Modelling of Natural
Phenomena 11(5), 120-140.
[3] Siekmann, I., Bengfort, M., Malchow, H. (2017). Coexistence of competitors mediated by
nonlinear noise. European Physical Journal Special Topics 226(9), 2157-2170.
[4] Kohnke, M.C., Malchow, H. (2017). Impact of parameter variability and environmental noise
on the Klausmeier model of vegetation pattern formation. Mathematics 5, 69 (19 pages).
[5] Bengfort, M., Siekmann, I., Malchow, H. (2018). Invasive competition with Fokker-Planck
di usion and noise. Ecological Complexity 34, 134-13.
[6] Morisita, M. (1971). Measuring of habitat value by the \environmental density" method. In:
Spatial patterns and statistical distributions (Patil, C.D., Pielou, E.C., Waters, W.E., eds.),
Statistical Ecology, vol. 1, pp. 379-401. Pennsylvania State University Press, University Park.
[7] N. Shigesada, N., Kawasaki, K., Teramoto, E. (1979). Spatial segregation of interacting species.
Journal of Theoretical Biology 79, 83-99.
2019年10月16日(水)
作用素環セミナー
16:45-18:15 数理科学研究科棟(駒場) 126号室
氷上忍 氏 (沖縄科学技術大学院大学)
Developments in conformal bootstrap analysis
氷上忍 氏 (沖縄科学技術大学院大学)
Developments in conformal bootstrap analysis
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