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過去の記録
過去の記録 ～04/24｜本日 04/25 | 今後の予定 04/26～
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
高田土満 氏 (東大数理)
An infinite-dimensional index theory and the Higson-Kasparov-Trout algebra
高田土満 氏 (東大数理)
An infinite-dimensional index theory and the Higson-Kasparov-Trout algebra
2019年12月03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
Anton Zeitlin 氏 (Louisiana State University)
Homotopy Gerstenhaber algebras, Courant algebroids, and Field Equations (ENGLISH)
Tea: Common Room 16:30-17:00
Anton Zeitlin 氏 (Louisiana State University)
Homotopy Gerstenhaber algebras, Courant algebroids, and Field Equations (ENGLISH)
[ 講演概要 ]
I will talk about the underlying homotopical structures within field equations, which emerge in string theory as conformal invariance conditions for sigma models. I will show how these, often hidden, structures emerge from the homotopy Gerstenhaber algebra associated to vertex and Courant algebroids, thus making all such equations the natural objects within vertex algebra theory.
I will talk about the underlying homotopical structures within field equations, which emerge in string theory as conformal invariance conditions for sigma models. I will show how these, often hidden, structures emerge from the homotopy Gerstenhaber algebra associated to vertex and Courant algebroids, thus making all such equations the natural objects within vertex algebra theory.
代数幾何学セミナー
14:30-16:00 数理科学研究科棟(駒場) 056号室
普段と曜日・時間・部屋が異なりますのでご注意ください。The room and time are different from our usual.
Gavril Farkas 氏 (Humboldt Univ. Berlin)
Moduli of K3 surfaces via cubic 4-folds (English)
普段と曜日・時間・部屋が異なりますのでご注意ください。The room and time are different from our usual.
Gavril Farkas 氏 (Humboldt Univ. Berlin)
Moduli of K3 surfaces via cubic 4-folds (English)
[ 講演概要 ]
In a celebrated series of papers, Mukai established structure theorems for polarized K3 surfaces of all genera g<21, with the exception of the case g=14. Using the identification between certain moduli spaces of polarized K3 surfaces of genera 14 and the moduli space of special cubic fourfolds of given discriminant, we discuss a novel approach to moduli spaces of K3 surfaces. As an application, we establish the rationality of the universal K3 surface of these genus 14,22. This is joint work with A. Verra.
In a celebrated series of papers, Mukai established structure theorems for polarized K3 surfaces of all genera g<21, with the exception of the case g=14. Using the identification between certain moduli spaces of polarized K3 surfaces of genera 14 and the moduli space of special cubic fourfolds of given discriminant, we discuss a novel approach to moduli spaces of K3 surfaces. As an application, we establish the rationality of the universal K3 surface of these genus 14,22. This is joint work with A. Verra.
2019年12月02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
本多 宣博 氏 (東京工業大学)
Moishezonツイスター空間の分類に向けて
本多 宣博 氏 (東京工業大学)
Moishezonツイスター空間の分類に向けて
[ 講演概要 ]
ツイスター空間は4次元共形幾何から生じる3次元複素多様体であり、コンパクトな場合、ほとんどが非ケーラーであることが知られている。一方、コンパクトなツイスター空間でMoishezonであるものの例は数多く知られている。そのような空間の位相構造はかなり限定されたものになるため、Moishezonツイスター空間を分類しそれらの構造を記述することは必ずしも不可能とは言えないと思われる。本講演では、ある単純な仮定を満たすMoishezonツイスター空間の分類結果についてお話しする。なお、この仮定を満たさないMoishezonツイスター空間の例は知られていない。
ツイスター空間は4次元共形幾何から生じる3次元複素多様体であり、コンパクトな場合、ほとんどが非ケーラーであることが知られている。一方、コンパクトなツイスター空間でMoishezonであるものの例は数多く知られている。そのような空間の位相構造はかなり限定されたものになるため、Moishezonツイスター空間を分類しそれらの構造を記述することは必ずしも不可能とは言えないと思われる。本講演では、ある単純な仮定を満たすMoishezonツイスター空間の分類結果についてお話しする。なお、この仮定を満たさないMoishezonツイスター空間の例は知られていない。
2019年11月29日(金)
作用素環セミナー
15:00-17:00 数理科学研究科棟(駒場) 126号室
戸松玲治 氏 (北海道大学)
Subfactor理論のまとめ V
戸松玲治 氏 (北海道大学)
Subfactor理論のまとめ V
2019年11月28日(木)
作用素環セミナー
15:00-17:00 数理科学研究科棟(駒場) 117号室
戸松玲治 氏 (北海道大学)
Subfactor理論のまとめ IV
戸松玲治 氏 (北海道大学)
Subfactor理論のまとめ IV
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
水上民夫 氏 (長浜バイオ大学、フロンティアファーマ)
AIを使ったデジタル細胞画像処理 ～「細胞の見える化」技術の開発～ (Japanese)
水上民夫 氏 (長浜バイオ大学、フロンティアファーマ)
AIを使ったデジタル細胞画像処理 ～「細胞の見える化」技術の開発～ (Japanese)
[ 講演概要 ]
蛍光顕微鏡は、細胞の生死や分化状態などを観察するための基盤的な研究機器である。しかし細胞の蛍光標識や励起光照射によるダメージにより継続的な細胞観察ができないという問題がある。この問題を解決するために、私たちはディープラーニングの敵対的生成ネットワークを利用し、「細胞の見える化」技術を開発した。本技術では、蛍光標識した教師細胞画像とそれに対応する明視野細胞画像の関係性を精緻に学習させたモデルにより、通常顕微鏡の明視野細胞画像から95％以上の正解性で細胞の生死が識別でき、さらに、細胞数や面積等の計測が可能となっている。
また、通常顕微鏡の明視野画像がリアルタイムに蛍光画像に変換され、細胞の性状を蛍光標識等の実験作業なしに観察できる「細胞の見える化顕微鏡」の開発にも成功している。
本講義では、生命科学において新たに登場したこれらのテクノロジーを紹介した後、数理科学人財と産業ニーズの結合を促す意義と方策を議論したい。
蛍光顕微鏡は、細胞の生死や分化状態などを観察するための基盤的な研究機器である。しかし細胞の蛍光標識や励起光照射によるダメージにより継続的な細胞観察ができないという問題がある。この問題を解決するために、私たちはディープラーニングの敵対的生成ネットワークを利用し、「細胞の見える化」技術を開発した。本技術では、蛍光標識した教師細胞画像とそれに対応する明視野細胞画像の関係性を精緻に学習させたモデルにより、通常顕微鏡の明視野細胞画像から95％以上の正解性で細胞の生死が識別でき、さらに、細胞数や面積等の計測が可能となっている。
また、通常顕微鏡の明視野画像がリアルタイムに蛍光画像に変換され、細胞の性状を蛍光標識等の実験作業なしに観察できる「細胞の見える化顕微鏡」の開発にも成功している。
本講義では、生命科学において新たに登場したこれらのテクノロジーを紹介した後、数理科学人財と産業ニーズの結合を促す意義と方策を議論したい。
2019年11月27日(水)
作用素環セミナー
17:15-18:45 数理科学研究科棟(駒場) 126号室
曽我部太郎 氏 (京都大学)
The homotopy groups of the automorphism groups of Cuntz-Toeplitz algebras
曽我部太郎 氏 (京都大学)
The homotopy groups of the automorphism groups of Cuntz-Toeplitz algebras
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
Ahmed Abbes 氏 (CNRS & IHÉS)
The relative Hodge-Tate spectral sequence (ENGLISH)
Ahmed Abbes 氏 (CNRS & IHÉS)
The relative Hodge-Tate spectral sequence (ENGLISH)
[ 講演概要 ]
It is well known that the p-adic étale cohomology of a smooth and proper variety over a p-adic field admits a Hodge-Tate decomposition and that it is the abutment of a spectral sequence called Hodge-Tate; these two properties are incidentally equivalent. The Hodge-Tate decomposition was generalized in higher dimensions to Hodge-Tate local systems by Hyodo, and was studied by Faltings, Tsuji and others. But the generalization of the Hodge-Tate spectral sequence to a relative situation has not yet been considered (not even conjectured), with the exception of a special case of abelian schemes by Hyodo. This has now been done in a joint work with Michel Gros. The relative Hodge-Tate spectral sequence that we construct takes place in the Faltings topos, but its construction requires the introduction of a relative variant of this topos which is the main novelty of our work. The relative Hodge-Tate spectral sequence sheds new light on the fact that the relative p-adic étale cohomology is Hodge-Tate, but the two properties are not equivalent in general.
It is well known that the p-adic étale cohomology of a smooth and proper variety over a p-adic field admits a Hodge-Tate decomposition and that it is the abutment of a spectral sequence called Hodge-Tate; these two properties are incidentally equivalent. The Hodge-Tate decomposition was generalized in higher dimensions to Hodge-Tate local systems by Hyodo, and was studied by Faltings, Tsuji and others. But the generalization of the Hodge-Tate spectral sequence to a relative situation has not yet been considered (not even conjectured), with the exception of a special case of abelian schemes by Hyodo. This has now been done in a joint work with Michel Gros. The relative Hodge-Tate spectral sequence that we construct takes place in the Faltings topos, but its construction requires the introduction of a relative variant of this topos which is the main novelty of our work. The relative Hodge-Tate spectral sequence sheds new light on the fact that the relative p-adic étale cohomology is Hodge-Tate, but the two properties are not equivalent in general.
作用素環セミナー
15:00-17:00 数理科学研究科棟(駒場) 126号室
戸松玲治 氏 (北海道大学)
Subfactor理論のまとめ III (日本語)
戸松玲治 氏 (北海道大学)
Subfactor理論のまとめ III (日本語)
2019年11月26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
蘆田聡平 氏 (学習院大学)
Accurate lower bounds for eigenvalues of electronic Hamiltonians (Japanese)
蘆田聡平 氏 (学習院大学)
Accurate lower bounds for eigenvalues of electronic Hamiltonians (Japanese)
[ 講演概要 ]
Electronic Hamiltonians are differential operators depending on relative positions of nuclei as parameters. When we regard an eigenvalues of an electronic Hamiltonian as a function of relative positions of nuclei, minimum points correspond to shapes of molecules. Upper bounds for eigenvalues are obtained by variational methods. However, since the physical information as minimum points does not change when a reference point of energy changes, physical information can not be obtained by variational methods only. Combining lower and upper bounds physical information is obtained.
In this talk we discuss the Weinstein-Arnszajn intermediate problem methods for lower bounds of eigenvalues based on comparison of operators. A method for lower bounds of one-electronic Hamiltonians is also introduced. Some computations for two kinds of hydrogen molecule-ion are shown.
Electronic Hamiltonians are differential operators depending on relative positions of nuclei as parameters. When we regard an eigenvalues of an electronic Hamiltonian as a function of relative positions of nuclei, minimum points correspond to shapes of molecules. Upper bounds for eigenvalues are obtained by variational methods. However, since the physical information as minimum points does not change when a reference point of energy changes, physical information can not be obtained by variational methods only. Combining lower and upper bounds physical information is obtained.
In this talk we discuss the Weinstein-Arnszajn intermediate problem methods for lower bounds of eigenvalues based on comparison of operators. A method for lower bounds of one-electronic Hamiltonians is also introduced. Some computations for two kinds of hydrogen molecule-ion are shown.
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
Marco De Renzi 氏 (早稲田大学)
$2+1$-TQFTs from non-semisimple modular categories (ENGLISH)
Tea: Common Room 16:30-17:00
Marco De Renzi 氏 (早稲田大学)
$2+1$-TQFTs from non-semisimple modular categories (ENGLISH)
[ 講演概要 ]
Non-semisimple constructions have substantially generalized the standard approach of Witten, Reshetikhin, and Turaev to quantum topology, producing powerful invariants and TQFTs with unprecedented properties. We will explain how to use the theory of modified traces to renormalize Lyubashenko’s closed 3-manifold invariants coming from finite twist non-degenerate unimodular ribbon categories. Under the additional assumption of factorizability, our renormalized invariants extend to $2+1$-TQFTs, unlike Lyubashenko’s original ones. This general framework encompasses important examples of non-semisimple modular categories which were left out of previous non-semisimple TQFT constructions.
Based on a joint work with Azat Gainutdinov, Nathan Geer, Bertrand Patureau, and Ingo Runkel.
Non-semisimple constructions have substantially generalized the standard approach of Witten, Reshetikhin, and Turaev to quantum topology, producing powerful invariants and TQFTs with unprecedented properties. We will explain how to use the theory of modified traces to renormalize Lyubashenko’s closed 3-manifold invariants coming from finite twist non-degenerate unimodular ribbon categories. Under the additional assumption of factorizability, our renormalized invariants extend to $2+1$-TQFTs, unlike Lyubashenko’s original ones. This general framework encompasses important examples of non-semisimple modular categories which were left out of previous non-semisimple TQFT constructions.
Based on a joint work with Azat Gainutdinov, Nathan Geer, Bertrand Patureau, and Ingo Runkel.
作用素環セミナー
15:00-17:00 数理科学研究科棟(駒場) 126号室
戸松玲治 氏 (北海道大学)
Subfactor理論のまとめ II (日本語)
戸松玲治 氏 (北海道大学)
Subfactor理論のまとめ II (日本語)
PDE実解析研究会
10:30-11:30 数理科学研究科棟(駒場) 056号室
Dan Tiba 氏 (Institute of Mathematics of the Romanian Academy / Academy of Romanian Scientists)
A Hamiltonian approach with penalization in shape and topology optimization (English)
Dan Tiba 氏 (Institute of Mathematics of the Romanian Academy / Academy of Romanian Scientists)
A Hamiltonian approach with penalization in shape and topology optimization (English)
[ 講演概要 ]
General geometric optimization problems involve boundary and topology variations. This research area has already almost fifty years of history and very rich applications in computer aided industrial design. Recently, a new representation of manifolds, using iterated Hamiltonian systems, has been introduced in arbitrary dimension and co-dimension. Combining this technique with a penalization procedure for the boundary conditions, a comprehensive approximation method for optimal design problems associated to elliptic equations, is obtained. It reduces shape and topology optimization problems to optimal control problems, in a general setting. It enters the category of fixed domain methods in variable/unknown domain problems and it has consistent advantages at the computational level. It allows "free" changes of the boundary and/or the topology, during the iterations. This methodology, based on iterated Hamiltonian systems and implicit parametrizations, was also applied to nonlinear programming problems in arbitrary dimension.
General geometric optimization problems involve boundary and topology variations. This research area has already almost fifty years of history and very rich applications in computer aided industrial design. Recently, a new representation of manifolds, using iterated Hamiltonian systems, has been introduced in arbitrary dimension and co-dimension. Combining this technique with a penalization procedure for the boundary conditions, a comprehensive approximation method for optimal design problems associated to elliptic equations, is obtained. It reduces shape and topology optimization problems to optimal control problems, in a general setting. It enters the category of fixed domain methods in variable/unknown domain problems and it has consistent advantages at the computational level. It allows "free" changes of the boundary and/or the topology, during the iterations. This methodology, based on iterated Hamiltonian systems and implicit parametrizations, was also applied to nonlinear programming problems in arbitrary dimension.
2019年11月25日(月)
作用素環セミナー
15:00-17:00 数理科学研究科棟(駒場) 128号室
戸松玲治 氏 (北海道大学)
Subfactor理論のまとめ I (日本語)
戸松玲治 氏 (北海道大学)
Subfactor理論のまとめ I (日本語)
2019年11月22日(金)
離散数理モデリングセミナー
17:00-18:00 数理科学研究科棟(駒場) 056号室
Adam Doliwa 氏 (University of Warmia and Mazury)
The Hopf algebra structure of coloured non-commutative symmetric functions
Adam Doliwa 氏 (University of Warmia and Mazury)
The Hopf algebra structure of coloured non-commutative symmetric functions
[ 講演概要 ]
The Hopf algebra of symmetric functions (Sym), especially its Schur function basis, plays an important role in the theory of KP hierarchy. The Hopf algebra of non-commutative symmetric functions (NSym) was introduced by Gelfand, Krob, Lascoux, Leclerc, Retakh and Thibon. In my talk I would like to present its "A-coloured" version NSym_A and its graded dual - the Hopf algebra QSym_A of coloured quasi-symmetric functions. It turns out that these two algebras are both non-commutative and non-cocommutative (for |A|>1), and their product and coproduct operations allow for simple combinatorial meaning. I will also show how the structure of the poset of sentences over alphabet A (A-coloured compositions) gives rise to a description of the corresponding coloured version of the ribbon Schur basis of NSym_A.
The Hopf algebra of symmetric functions (Sym), especially its Schur function basis, plays an important role in the theory of KP hierarchy. The Hopf algebra of non-commutative symmetric functions (NSym) was introduced by Gelfand, Krob, Lascoux, Leclerc, Retakh and Thibon. In my talk I would like to present its "A-coloured" version NSym_A and its graded dual - the Hopf algebra QSym_A of coloured quasi-symmetric functions. It turns out that these two algebras are both non-commutative and non-cocommutative (for |A|>1), and their product and coproduct operations allow for simple combinatorial meaning. I will also show how the structure of the poset of sentences over alphabet A (A-coloured compositions) gives rise to a description of the corresponding coloured version of the ribbon Schur basis of NSym_A.
2019年11月21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
鈴木泰成 氏 (NTTセキュアプラットフォーム研究所)
量子誤り訂正 (Japanese)
鈴木泰成 氏 (NTTセキュアプラットフォーム研究所)
量子誤り訂正 (Japanese)
[ 講演概要 ]
本講義では2048bitの素因数分解などの大規模な量子計算の実現において必須となる、量子誤り訂正技術について解説する。まず量子計算と通常の計算機の違いから誤り訂正の仕組みにどのような要請の違いが生じるのかを解説し、量子誤り訂正の構造と難しさを概観する。続けて、量子誤り訂正および誤り耐性量子計算の全体像と、その実現に向けた最近の取り組みを紹介する。
本講義では2048bitの素因数分解などの大規模な量子計算の実現において必須となる、量子誤り訂正技術について解説する。まず量子計算と通常の計算機の違いから誤り訂正の仕組みにどのような要請の違いが生じるのかを解説し、量子誤り訂正の構造と難しさを概観する。続けて、量子誤り訂正および誤り耐性量子計算の全体像と、その実現に向けた最近の取り組みを紹介する。
基礎論セミナー
13:30-15:00 数理科学研究科棟(駒場) 156号室
佐藤憲太郎 氏
Self-referential Theorems for Finitist Arithmetic
佐藤憲太郎 氏
Self-referential Theorems for Finitist Arithmetic
[ 講演概要 ]
The finitist logic excludes,on the syntax level, unbounded quantifiers
and accommodates only bounded quantifiers.
The following two self-referential theorems for arithmetic theories
over the finitist logic will be considered:
Tarski's impossibility of naive truth predicate and
Goedel's incompleteness theorem.
Particularly, it will be briefly explained that
(i) the naive truth theory over the finitist arithmetic with summation and multiplication
is consistent and proves its own consistency, and that
(ii) by the use of finitist arithmetic, the hierarchy of consistency strengths,
based on Goedel's second incompleteness theorem,
can be extended downward (to the area not reachable by first order predicate arithmetic).
This is a joint work with Jan Walker, and overlaps significantly with his doctoral dissertation.
The finitist logic excludes,on the syntax level, unbounded quantifiers
and accommodates only bounded quantifiers.
The following two self-referential theorems for arithmetic theories
over the finitist logic will be considered:
Tarski's impossibility of naive truth predicate and
Goedel's incompleteness theorem.
Particularly, it will be briefly explained that
(i) the naive truth theory over the finitist arithmetic with summation and multiplication
is consistent and proves its own consistency, and that
(ii) by the use of finitist arithmetic, the hierarchy of consistency strengths,
based on Goedel's second incompleteness theorem,
can be extended downward (to the area not reachable by first order predicate arithmetic).
This is a joint work with Jan Walker, and overlaps significantly with his doctoral dissertation.
2019年11月20日(水)
代数学コロキウム
18:00-19:00 数理科学研究科棟(駒場) 056号室
Vasudevan Srinivas 氏 (Tata Institute of Fundamental Research)
Algebraic versus topological entropy for surfaces over finite fields (ENGLISH)
Vasudevan Srinivas 氏 (Tata Institute of Fundamental Research)
Algebraic versus topological entropy for surfaces over finite fields (ENGLISH)
[ 講演概要 ]
For an automorphism of an algebraic variety, we consider some properties of eigenvalues of the induced linear transformation on l-adic cohomology, motivated by some results from complex dynamics, related to the notion of entropy. This is a report on joint work with Hélène Esnault, and some subsequent work of K. Shuddhodan.
（本講演は「東京北京パリ数論幾何セミナー」として，インターネットによる東大数理，Morningside Center of Mathematics と IHES の双方向同時中継で行います．今回は東京からの中継です．）
For an automorphism of an algebraic variety, we consider some properties of eigenvalues of the induced linear transformation on l-adic cohomology, motivated by some results from complex dynamics, related to the notion of entropy. This is a report on joint work with Hélène Esnault, and some subsequent work of K. Shuddhodan.
（本講演は「東京北京パリ数論幾何セミナー」として，インターネットによる東大数理，Morningside Center of Mathematics と IHES の双方向同時中継で行います．今回は東京からの中継です．）
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
Stefan Hollands 氏 (Univ. Leipzig)
Modular theory and entanglement in CFT
Stefan Hollands 氏 (Univ. Leipzig)
Modular theory and entanglement in CFT
2019年11月19日(火)
PDE実解析研究会
10:30-11:30 数理科学研究科棟(駒場) 056号室
Peter Topping 氏 (University of Warwick)
Starting Ricci flow with rough initial data (English)
Peter Topping 氏 (University of Warwick)
Starting Ricci flow with rough initial data (English)
[ 講演概要 ]
Ricci flow is a nonlinear PDE that is traditionally used to deform a manifold we would like to understand into a manifold we already understand. For example, Hamilton showed that a simply connected closed 3-manifold with positive Ricci curvature is deformed into a manifold of constant sectional curvature, thus allowing us to identify it as topologically a sphere.
In this talk we take a look at a different use of Ricci flow. We would like to exploit the regularising effect of parabolic PDE to turn a rough space into a smooth space by running the Ricci flow. In practice, this revolves around proving good a priori estimates on solutions, and taking unorthodox approaches to solving parabolic PDE. We will see some theory, first in 2D, then in higher dimension, and some applications.
Ricci flow is a nonlinear PDE that is traditionally used to deform a manifold we would like to understand into a manifold we already understand. For example, Hamilton showed that a simply connected closed 3-manifold with positive Ricci curvature is deformed into a manifold of constant sectional curvature, thus allowing us to identify it as topologically a sphere.
In this talk we take a look at a different use of Ricci flow. We would like to exploit the regularising effect of parabolic PDE to turn a rough space into a smooth space by running the Ricci flow. In practice, this revolves around proving good a priori estimates on solutions, and taking unorthodox approaches to solving parabolic PDE. We will see some theory, first in 2D, then in higher dimension, and some applications.
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
Ramón Barral Lijó 氏 (立命館大学)
The smooth Gromov space and the realization problem (ENGLISH)
Tea: Common Room 16:30-17:00
Ramón Barral Lijó 氏 (立命館大学)
The smooth Gromov space and the realization problem (ENGLISH)
[ 講演概要 ]
The n-dimensional smooth Gromov space consists of the pointed isometry classes of complete Riemannian n-manifolds. In this talk we will present the definition and basic properties of this space as well as two different applications: The first addresses the following classical problem in foliation theory.
Realization problem: what kind of manifolds can be leaves of compact foliations?
Our joint work with Álvarez López has produced the following solution in the context of foliated spaces.
Theorem. Every Riemannian manifold of bounded geometry is a leaf in a compact foliated space X endowed with a metric tensor. Moreover, we can assume that X has trivial holonomy and is transversely Cantor.
The second application is the recent research by Abert and Biringer on the subject of unimodular random Riemannian manifolds.
The n-dimensional smooth Gromov space consists of the pointed isometry classes of complete Riemannian n-manifolds. In this talk we will present the definition and basic properties of this space as well as two different applications: The first addresses the following classical problem in foliation theory.
Realization problem: what kind of manifolds can be leaves of compact foliations?
Our joint work with Álvarez López has produced the following solution in the context of foliated spaces.
Theorem. Every Riemannian manifold of bounded geometry is a leaf in a compact foliated space X endowed with a metric tensor. Moreover, we can assume that X has trivial holonomy and is transversely Cantor.
The second application is the recent research by Abert and Biringer on the subject of unimodular random Riemannian manifolds.
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
Wenjia Jing 氏 (清華大学)
Quantitative homogenization for the Dirichlet problem of Stokes system in periodic perforated domain - a unified approach (English)
Wenjia Jing 氏 (清華大学)
Quantitative homogenization for the Dirichlet problem of Stokes system in periodic perforated domain - a unified approach (English)
[ 講演概要 ]
We present a new unified approach for the quantitative homogenization of the Stokes system in periodically perforated domains, that is domains outside a periodic array of holes, with Dirichlet data at the boundary of the holes. The method is based on the (rescaled) cell-problem and is adaptive to the ratio between the typical distance and the typical side length of the holes; in particular, for the critical ratio identified by Cioranescu-Murat, we recover the “strange term from nowhere”termed by them, which, in the context of Stokes system, corresponds to the Brinkman’s law. An advantage of the method is that it can be systematically quantified using the periodic layer potential technique. We will also report some new correctors to the homogenization problem using this approach. The talk is based on joint work with Yong Lu and Christophe Prange.
We present a new unified approach for the quantitative homogenization of the Stokes system in periodically perforated domains, that is domains outside a periodic array of holes, with Dirichlet data at the boundary of the holes. The method is based on the (rescaled) cell-problem and is adaptive to the ratio between the typical distance and the typical side length of the holes; in particular, for the critical ratio identified by Cioranescu-Murat, we recover the “strange term from nowhere”termed by them, which, in the context of Stokes system, corresponds to the Brinkman’s law. An advantage of the method is that it can be systematically quantified using the periodic layer potential technique. We will also report some new correctors to the homogenization problem using this approach. The talk is based on joint work with Yong Lu and Christophe Prange.
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。
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