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過去の記録
過去の記録 ～12/13｜本日 12/14 | 今後の予定 12/15～
2019年12月12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
渡辺克也 氏 (株式会社インターネット総合研究所 (IRI))
５Gとは？ (Japanese)
渡辺克也 氏 (株式会社インターネット総合研究所 (IRI))
５Gとは？ (Japanese)
[ 講演概要 ]
5G時代に向けたモバイルブロードバンドの進展と今後の展望について、事例も踏まえながらお話をさせていただければと考えております。
5G時代に向けたモバイルブロードバンドの進展と今後の展望について、事例も踏まえながらお話をさせていただければと考えております。
2019年12月11日(水)
複素解析幾何セミナー
16:00-17:00 数理科学研究科棟(駒場) 156号室
Joel Merker 氏 (Paris Sud)
Einstein-Weyl structures (English)
Joel Merker 氏 (Paris Sud)
Einstein-Weyl structures (English)
[ 講演概要 ]
On a conformal 3D manifold with electromagnetic field, Einstein-Weyl equations are the counterpart of Einstein's classical field equations. In 1943, Elie Cartan showed, using abstract arguments, that the general solution depends on 4 functions of 2 variables. I will present families of explicit solutions depending on 9 functions of 1 variable, much beyond what was known before. Such solutions are generic in the sense that the Cotton tensor is nonzero. This is joint work with Pawel Nurowski.
On a conformal 3D manifold with electromagnetic field, Einstein-Weyl equations are the counterpart of Einstein's classical field equations. In 1943, Elie Cartan showed, using abstract arguments, that the general solution depends on 4 functions of 2 variables. I will present families of explicit solutions depending on 9 functions of 1 variable, much beyond what was known before. Such solutions are generic in the sense that the Cotton tensor is nonzero. This is joint work with Pawel Nurowski.
2019年12月10日(火)
作用素環セミナー
17:00-18:30 数理科学研究科棟(駒場) 122号室
Zhenghan Wang 氏 (Microsoft Station Q)
On gauging symmetries of topological phases of matter (English)
Zhenghan Wang 氏 (Microsoft Station Q)
On gauging symmetries of topological phases of matter (English)
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
小木曽 岳義 氏 (城西大学)
q-Deformation of a continued fraction and its applications (JAPANESE)
Tea: Common Room 16:30-17:00
小木曽 岳義 氏 (城西大学)
q-Deformation of a continued fraction and its applications (JAPANESE)
[ 講演概要 ]
Morier-Genoud と Ovsienko によって連分数のある種の q-変形が導入された。このq-変形の最大の応用はそれを用いて向きづけられた有理絡み目の Jones 多項式がそれから直接求めることができることである。またこの連分数のq-変形は結び目理論への応用以外にも、2次無理数論、組み合わせ論への応用もあり、それについても紹介する。
一方、Lee-Schiffler の snake graph を用いる方法や Kogiso-Wakui による Conway-Coxeter frieze を持ちいる方法で Jones 多項式を計算するレシピが与えられている。そのことから、Morier-Genoud and Ovsienko の結果のそれらの観点からの別証明が考えられるが、それについて紹介し、さらに, Kogiso-Wakui の研究で用いた Ancestoral triangles の観点から連分数のq-変形をさらに一般化でき、連分数の cluster-variable 変形が出来ることを紹介する。
Morier-Genoud と Ovsienko によって連分数のある種の q-変形が導入された。このq-変形の最大の応用はそれを用いて向きづけられた有理絡み目の Jones 多項式がそれから直接求めることができることである。またこの連分数のq-変形は結び目理論への応用以外にも、2次無理数論、組み合わせ論への応用もあり、それについても紹介する。
一方、Lee-Schiffler の snake graph を用いる方法や Kogiso-Wakui による Conway-Coxeter frieze を持ちいる方法で Jones 多項式を計算するレシピが与えられている。そのことから、Morier-Genoud and Ovsienko の結果のそれらの観点からの別証明が考えられるが、それについて紹介し、さらに, Kogiso-Wakui の研究で用いた Ancestoral triangles の観点から連分数のq-変形をさらに一般化でき、連分数の cluster-variable 変形が出来ることを紹介する。
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
Tobias Barker 氏 (École Normale Supérieure)
Vorticity alignment vs vorticity creation at the boundary (English)
Tobias Barker 氏 (École Normale Supérieure)
Vorticity alignment vs vorticity creation at the boundary (English)
[ 講演概要 ]
The Navier-Stokes are used as a model for viscous incompressible fluids such as water. The question as to whether or not the equations in three dimensions form singularities is an open Millennium prize problem. In their celebrated paper in 1993, Constantin and Fefferman showed that (in the whole plane) if the vorticity is sufficiently well aligned in regions of high vorticity then the Navier-Stokes equations remain smooth. For the half-space it is commonly assumed that viscous fluids `stick' to the boundary, which generates vorticity at the boundary. In such a setting, it is open as to whether Constantin and Fefferman's result remains to be true. In my talk I will present recent results in this direction. Joint work with Christophe Prange (CNRS, Université de Bordeaux)
The Navier-Stokes are used as a model for viscous incompressible fluids such as water. The question as to whether or not the equations in three dimensions form singularities is an open Millennium prize problem. In their celebrated paper in 1993, Constantin and Fefferman showed that (in the whole plane) if the vorticity is sufficiently well aligned in regions of high vorticity then the Navier-Stokes equations remain smooth. For the half-space it is commonly assumed that viscous fluids `stick' to the boundary, which generates vorticity at the boundary. In such a setting, it is open as to whether Constantin and Fefferman's result remains to be true. In my talk I will present recent results in this direction. Joint work with Christophe Prange (CNRS, Université de Bordeaux)
FMSPレクチャーズ
17:00-18:00 数理科学研究科棟(駒場) 118号室
Anatoly G. Yagola 氏 (Lomonosov Moscow State University)
A priori and a posteriori error estimation for solutions of ill-posed problems (ENGLISH)
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_AnatolyYagola.pdf
Anatoly G. Yagola 氏 (Lomonosov Moscow State University)
A priori and a posteriori error estimation for solutions of ill-posed problems (ENGLISH)
[ 講演概要 ]
In order to calculate a priori or a posteriori error estimates for solutions of an ill-posed operator equation with an injective operator we need to describe a set of approximate solutions that contains an exact solution. After that we have to calculate a diameter of this set or maximal distance from a fixed approximate solution to any element of this set. I will describe three approaches for constructing error estimates and also their practical applications.
[ 講演参考URL ]In order to calculate a priori or a posteriori error estimates for solutions of an ill-posed operator equation with an injective operator we need to describe a set of approximate solutions that contains an exact solution. After that we have to calculate a diameter of this set or maximal distance from a fixed approximate solution to any element of this set. I will describe three approaches for constructing error estimates and also their practical applications.
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_AnatolyYagola.pdf
2019年12月09日(月)
数値解析セミナー
16:50-18:20 数理科学研究科棟(駒場) 117号室
劉雪峰 氏 (新潟大学理学部)
ポアソン方程式の有限要素解の各点誤差評価---加藤・藤田の方法への再検討 (Japanese)
劉雪峰 氏 (新潟大学理学部)
ポアソン方程式の有限要素解の各点誤差評価---加藤・藤田の方法への再検討 (Japanese)
[ 講演概要 ]
In 1950s, H. Fujita proposed a method to provide the upper and lower bounds in boundary value problems, which is based on the T*T theory of T. Kato about differential equations. Such a method can be regarded a different formulation of the hypercircle method from Prage-Synge's theorem.
Recently, the speaker extended Kato-Fujita's method to the case of the finite element solution of Poisson's equation and proposed a guaranteed point-wise error estimation. The newly proposed error estimation can be applied to problems defined over domains of general shapes along with general boundary conditions.
In 1950s, H. Fujita proposed a method to provide the upper and lower bounds in boundary value problems, which is based on the T*T theory of T. Kato about differential equations. Such a method can be regarded a different formulation of the hypercircle method from Prage-Synge's theorem.
Recently, the speaker extended Kato-Fujita's method to the case of the finite element solution of Poisson's equation and proposed a guaranteed point-wise error estimation. The newly proposed error estimation can be applied to problems defined over domains of general shapes along with general boundary conditions.
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
北岡 旦 氏 (東京大学)
Analytic torsions associated with the Rumin complex on contact spheres (Japanese)
北岡 旦 氏 (東京大学)
Analytic torsions associated with the Rumin complex on contact spheres (Japanese)
[ 講演概要 ]
Rumin 複体は接触多様体上に定まる，実数体の定数層の分解であり，実数体のde Rham 複体の部分複体である．本講演では，球面上のRumin ラプラシアンの固有値を書き下し，Rumin 複体の解析的捩率関数がRiemann のゼータ関数を用いて書き表されることを示す．特に，その関数の原点で消滅していることと，その解析的捩率が具体的に計算できることを紹介する．
Rumin 複体は接触多様体上に定まる，実数体の定数層の分解であり，実数体のde Rham 複体の部分複体である．本講演では，球面上のRumin ラプラシアンの固有値を書き下し，Rumin 複体の解析的捩率関数がRiemann のゼータ関数を用いて書き表されることを示す．特に，その関数の原点で消滅していることと，その解析的捩率が具体的に計算できることを紹介する．
2019年12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) 118号室
荻野明仁 氏 (株式会社エーアイスクエア)
自然言語処理AIの事業化 (Japanese)
荻野明仁 氏 (株式会社エーアイスクエア)
自然言語処理AIの事業化 (Japanese)
[ 講演概要 ]
（株）エーアイスクエアでの活動を基に自然言語処理AIを題材として、事業化に際しての留意点と実際の商用化事例を紹介する。
（株）エーアイスクエアでの活動を基に自然言語処理AIを題材として、事業化に際しての留意点と実際の商用化事例を紹介する。
2019年12月04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
竹内 大智 氏 (東京大学数理科学研究科)
Characteristic epsilon cycles of l-adic sheaves on varieties (ENGLISH)
竹内 大智 氏 (東京大学数理科学研究科)
Characteristic epsilon cycles of l-adic sheaves on varieties (ENGLISH)
[ 講演概要 ]
For l-adic sheaves on varieties over finite fields, the constant terms of the functional equations of the L-functions, called global epsilon factors, are important arithmetic invariants. When the varieties are curves, Deligne and Laumon show that they admit product formulae in terms of local epsilon factors.
In this talk, I will explain that, attaching some coefficients to irreducible components of singular supports, we can define refinements of characteristic cycles. We will see that, after taking modulo roots of unity, they give product formulae of global epsilon factors for higher dimensional varieties.
I will also explain that these results can be generalized to arbitrary perfect fields of any characteristic.
For l-adic sheaves on varieties over finite fields, the constant terms of the functional equations of the L-functions, called global epsilon factors, are important arithmetic invariants. When the varieties are curves, Deligne and Laumon show that they admit product formulae in terms of local epsilon factors.
In this talk, I will explain that, attaching some coefficients to irreducible components of singular supports, we can define refinements of characteristic cycles. We will see that, after taking modulo roots of unity, they give product formulae of global epsilon factors for higher dimensional varieties.
I will also explain that these results can be generalized to arbitrary perfect fields of any characteristic.
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。
基礎論セミナー
13:00-14:30 数理科学研究科棟(駒場) 156号室
池上 大祐 氏 (芝浦工業大学)
On supercompactness of $\omega_1$
池上 大祐 氏 (芝浦工業大学)
On supercompactness of $\omega_1$
[ 講演概要 ]
In ZFC, all the large cardinals are much bigger than $\omega_1$, the least uncountable cardinal,
while without assuming the Axiom of Choice, $\omega_1$ could have some large cardinal properties.
Jech and Takeuti independently proved that if the axiom system ZFC + There is a measurable cardinal is consistent,
then so is ZF + $\omega_1$ is a measurable cardinal.
Takeuti also proved that one can replace "measurable cardinal" above with "supercompact cardinal" as well as some other large cardinals.
Woodin proved that one can reduce the assumption, i.e., the consistency of ZFC + a supercompact cardinal,
to that of ZFC + There are proper class many Woodin cardinals which are limits of Woodin cardinals,
to obtain the consistency of ZF + $\omega_1$ is a supercompact cardinal.
Furthermore, the model he constructed also satisfies the Axiom of Determinacy (AD).
In this talk, after giving some background on the connections between large cardinals and determinacy, we discuss some consequences of the axiom system ZF + $\omega_1$ is a supercompact cardinal.
This is joint work with Nam Trang.
In ZFC, all the large cardinals are much bigger than $\omega_1$, the least uncountable cardinal,
while without assuming the Axiom of Choice, $\omega_1$ could have some large cardinal properties.
Jech and Takeuti independently proved that if the axiom system ZFC + There is a measurable cardinal is consistent,
then so is ZF + $\omega_1$ is a measurable cardinal.
Takeuti also proved that one can replace "measurable cardinal" above with "supercompact cardinal" as well as some other large cardinals.
Woodin proved that one can reduce the assumption, i.e., the consistency of ZFC + a supercompact cardinal,
to that of ZFC + There are proper class many Woodin cardinals which are limits of Woodin cardinals,
to obtain the consistency of ZF + $\omega_1$ is a supercompact cardinal.
Furthermore, the model he constructed also satisfies the Axiom of Determinacy (AD).
In this talk, after giving some background on the connections between large cardinals and determinacy, we discuss some consequences of the axiom system ZF + $\omega_1$ is a supercompact cardinal.
This is joint work with Nam Trang.
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.
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