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過去の記録 ～04/19｜本日 04/20 | 今後の予定 04/21～
2017年12月05日(火)
トポロジー火曜セミナー
17:00-18:30 数理科学研究科棟(駒場) 056号室
Tea: Common Room 16:30-17:00
川村 一宏 氏 (筑波大学)
Derivations and cohomologies of Lipschitz algebras (JAPANESE)
Tea: Common Room 16:30-17:00
川村 一宏 氏 (筑波大学)
Derivations and cohomologies of Lipschitz algebras (JAPANESE)
[ 講演概要 ]
For a compact metric space M, Lip(M) denotes the Banach algebra of all complex-valued Lipschitz functions on M. Motivated by a classical work of de Leeuw, we define a compact, not necessarily metrizable, Hausdorff space \hat{M} so that each point of \hat{M} induces a derivation on Lip(M). To some extent, \hat{M} may be regarded as "the space of directions." We study, by an elementary method, the space of derivations and continuous Hochschild cohomologies (in the sense of B.E. Johnson and A.Y. Helemskii) of Lip(M) with coefficients C(\hat{M}) and C(M). The results so obtained show that the behavior of Lip(M) is (naturally) rather different than that of the algebra of smooth/C^1 functions on M.
For a compact metric space M, Lip(M) denotes the Banach algebra of all complex-valued Lipschitz functions on M. Motivated by a classical work of de Leeuw, we define a compact, not necessarily metrizable, Hausdorff space \hat{M} so that each point of \hat{M} induces a derivation on Lip(M). To some extent, \hat{M} may be regarded as "the space of directions." We study, by an elementary method, the space of derivations and continuous Hochschild cohomologies (in the sense of B.E. Johnson and A.Y. Helemskii) of Lip(M) with coefficients C(\hat{M}) and C(M). The results so obtained show that the behavior of Lip(M) is (naturally) rather different than that of the algebra of smooth/C^1 functions on M.
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
佐藤 謙太 氏 (東大数理)
Ascending chain condition for F-pure thresholds on a fixed strongly F-regular germ (English or Japanese)
佐藤 謙太 氏 (東大数理)
Ascending chain condition for F-pure thresholds on a fixed strongly F-regular germ (English or Japanese)
[ 講演概要 ]
For a germ of a variety in positive characteristic and a non-zero ideal sheaf on the variety, we can define the F-pure threshold of the ideal by using Frobenius morphisms, which measures the singularities of the pair. In this talk, I will show that the set of all F-pure thresholds on a fixed strongly F-regular germ satisfies the ascending chain condition. This is a positive characteristic analogue of the "ascending chain condition for log canonical thresholds" in characteristic 0, which was recently proved by Hacon, McKernan, and Xu.
For a germ of a variety in positive characteristic and a non-zero ideal sheaf on the variety, we can define the F-pure threshold of the ideal by using Frobenius morphisms, which measures the singularities of the pair. In this talk, I will show that the set of all F-pure thresholds on a fixed strongly F-regular germ satisfies the ascending chain condition. This is a positive characteristic analogue of the "ascending chain condition for log canonical thresholds" in characteristic 0, which was recently proved by Hacon, McKernan, and Xu.
2017年12月04日(月)
東京確率論セミナー
16:00-17:30 数理科学研究科棟(駒場) 128号室
岡村 和樹 氏 (京都大学 数理解析研究所)
Some results for range of random walk on graph with spectral dimension two (JAPANESE)
岡村 和樹 氏 (京都大学 数理解析研究所)
Some results for range of random walk on graph with spectral dimension two (JAPANESE)
[ 講演概要 ]
We consider the range of random walk on graphs with spectral dimension two. We show that a certain weak law of large numbers hold if a recurrent graph satisfies a uniform condition. We construct a recurrent graph such that the uniform condition holds but appropriately scaled expectations fluctuate. Our result is applicable to showing LILs for lamplighter random walks in the case that the spectral dimension of the underlying graph is two.
We consider the range of random walk on graphs with spectral dimension two. We show that a certain weak law of large numbers hold if a recurrent graph satisfies a uniform condition. We construct a recurrent graph such that the uniform condition holds but appropriately scaled expectations fluctuate. Our result is applicable to showing LILs for lamplighter random walks in the case that the spectral dimension of the underlying graph is two.
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
Pieter Naaijkens 氏 (UC Davis)
Subfactors and wiretapping channels
(English)
Pieter Naaijkens 氏 (UC Davis)
Subfactors and wiretapping channels
(English)
2017年11月28日(火)
トポロジー火曜セミナー
17:00-18:30 数理科学研究科棟(駒場) 056号室
Tea: Common Room 16:30-17:00
Sang-hyun Kim 氏 (Seoul National University)
Diffeomorphism Groups of One-Manifolds (ENGLISH)
Tea: Common Room 16:30-17:00
Sang-hyun Kim 氏 (Seoul National University)
Diffeomorphism Groups of One-Manifolds (ENGLISH)
[ 講演概要 ]
Let a>=2 be a real number and k = [a]. We denote by Diff^a(S^1) the group of C^k diffeomorphisms such that the k--th derivatives are Hölder--continuous of exponent (a - k). For each real number a>=2, we prove that there exists a finitely generated group G < Diff^a(S^1) such that G admits no injective homomorphisms into Diff^b(S^1) for any b>a. This is joint work with Thomas Koberda.
Let a>=2 be a real number and k = [a]. We denote by Diff^a(S^1) the group of C^k diffeomorphisms such that the k--th derivatives are Hölder--continuous of exponent (a - k). For each real number a>=2, we prove that there exists a finitely generated group G < Diff^a(S^1) such that G admits no injective homomorphisms into Diff^b(S^1) for any b>a. This is joint work with Thomas Koberda.
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
田中 公 氏 (東大数理)
Kodaira vanishing theorem for Witt canonical sheaves (English)
田中 公 氏 (東大数理)
Kodaira vanishing theorem for Witt canonical sheaves (English)
[ 講演概要 ]
We establish an analogue of the Kodaira vanishing theorem in terms of de Rham-Witt complex. More specifically, given a smooth projective variety over a perfect field of positive characteristic, we prove that the higher cohomologies vanish for the tensor product of the Witt canonical sheaf and the Teichmuller lift of an ample invertible sheaf.
We establish an analogue of the Kodaira vanishing theorem in terms of de Rham-Witt complex. More specifically, given a smooth projective variety over a perfect field of positive characteristic, we prove that the higher cohomologies vanish for the tensor product of the Witt canonical sheaf and the Teichmuller lift of an ample invertible sheaf.
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
小山大介 氏 (電気通信大学大学院情報理工学研究科)
Hybrid discontinuous Galerkin methods for nearly incompressible elasticity problems
(Japanese)
小山大介 氏 (電気通信大学大学院情報理工学研究科)
Hybrid discontinuous Galerkin methods for nearly incompressible elasticity problems
(Japanese)
[ 講演概要 ]
A Hybrid discontinuous Galerkin (HDG) method for linear elasticity problems has been introduced by Kikuchi et al. [Theor. Appl. Mech. Japan, vol.57, 395--404 (2009)], [RIMS Kokyuroku, vol.1971, 28--46 (2015)]. We consider to seek numerical solutions of the plane strain problem by the HDG method, especially in the case when materials are nearly incompressible, that is, when the first Lam\'e parameter $\lambda$ is large. In this talk, we consider two cases when the HDG method uses a lifting term and does not use it. When the lifting term is used, the method can be free of volumetric locking. On the other hand, when the lifting term is not used, we have to take an interior penalty parameter of order $\lambda$ as $\lambda$ tends to infinity, in order to guarantee the coercivity of the bilinear form. Taking such an interior penalty parameter causes volumetric locking phenomena. We thus conclude that the lifting term is essential for avoiding the volumetric locking in the HDG method.
A Hybrid discontinuous Galerkin (HDG) method for linear elasticity problems has been introduced by Kikuchi et al. [Theor. Appl. Mech. Japan, vol.57, 395--404 (2009)], [RIMS Kokyuroku, vol.1971, 28--46 (2015)]. We consider to seek numerical solutions of the plane strain problem by the HDG method, especially in the case when materials are nearly incompressible, that is, when the first Lam\'e parameter $\lambda$ is large. In this talk, we consider two cases when the HDG method uses a lifting term and does not use it. When the lifting term is used, the method can be free of volumetric locking. On the other hand, when the lifting term is not used, we have to take an interior penalty parameter of order $\lambda$ as $\lambda$ tends to infinity, in order to guarantee the coercivity of the bilinear form. Taking such an interior penalty parameter causes volumetric locking phenomena. We thus conclude that the lifting term is essential for avoiding the volumetric locking in the HDG method.
2017年11月27日(月)
東京確率論セミナー
16:00-17:30 数理科学研究科棟(駒場) 128号室
Antar Bandyopadhyay 氏 (Indian Statistical Institute)
Random Recursive Tree, Branching Markov Chains and Urn Models (ENGLISH)
Antar Bandyopadhyay 氏 (Indian Statistical Institute)
Random Recursive Tree, Branching Markov Chains and Urn Models (ENGLISH)
[ 講演概要 ]
In this talk, we will establish a connection between random recursive tree, branching Markov chain and urn model. Exploring the connection further we will derive fairly general scaling limits for urn models with colors indexed by a Polish Space and show that several exiting results on classical/non-classical urn schemes can be easily derived out of such general asymptotic. We will further show that the connection can be used to derive exact asymptotic for the sizes of the connected components of a "random recursive forest", obtained by removing the root of a random recursive tree.
[This is a joint work with Debleena Thacker]
In this talk, we will establish a connection between random recursive tree, branching Markov chain and urn model. Exploring the connection further we will derive fairly general scaling limits for urn models with colors indexed by a Polish Space and show that several exiting results on classical/non-classical urn schemes can be easily derived out of such general asymptotic. We will further show that the connection can be used to derive exact asymptotic for the sizes of the connected components of a "random recursive forest", obtained by removing the root of a random recursive tree.
[This is a joint work with Debleena Thacker]
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
細野 元気 氏 (東京大学)
On the proof of the optimal $L^2$ extension theorem by Berndtsson-Lempert and related results
細野 元気 氏 (東京大学)
On the proof of the optimal $L^2$ extension theorem by Berndtsson-Lempert and related results
[ 講演概要 ]
We will present the recent progress on the Ohsawa-Takegoshi $L^2$ extension theorem. A version of the Ohsawa-Takegoshi $L^2$ extension with a optimal estimate has been proved by Blocki and Guan-Zhou. After that, by Berndtsson-Lempert, a new proof of the optimal $L^2$ extension theorem was given. In this talk, we will show an optimal $L^2$ extension theorem for jets of holomorphic functions by the Berndtsson-Lempert method. We will also explain the recent result about jet extensions by McNeal-Varolin. Their proof is also based on Berndtsson-Lempert, but there are some differences.
We will present the recent progress on the Ohsawa-Takegoshi $L^2$ extension theorem. A version of the Ohsawa-Takegoshi $L^2$ extension with a optimal estimate has been proved by Blocki and Guan-Zhou. After that, by Berndtsson-Lempert, a new proof of the optimal $L^2$ extension theorem was given. In this talk, we will show an optimal $L^2$ extension theorem for jets of holomorphic functions by the Berndtsson-Lempert method. We will also explain the recent result about jet extensions by McNeal-Varolin. Their proof is also based on Berndtsson-Lempert, but there are some differences.
2017年11月24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) 002号室
伊藤由佳理 氏 (IPMU, 名古屋大学)
特異点解消とマッカイ対応 (JAPANESE)
伊藤由佳理 氏 (IPMU, 名古屋大学)
特異点解消とマッカイ対応 (JAPANESE)
[ 講演概要 ]
本講演では、2次元有理二重点の特異点解消と1979年にJohn McKayが発見した有限群とディンキン図形の関係に基づく2次元のマッカイ対応について紹介し、その後、代数多様体の分類論や超弦理論と共に発展した3次元の特異点解消とマッカイ対応について解説したい。
本講演では、2次元有理二重点の特異点解消と1979年にJohn McKayが発見した有限群とディンキン図形の関係に基づく2次元のマッカイ対応について紹介し、その後、代数多様体の分類論や超弦理論と共に発展した3次元の特異点解消とマッカイ対応について解説したい。
2017年11月21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
境 圭一 氏 (信州大学)
The space of short ropes and the classifying space of the space of long knots (JAPANESE)
Tea: Common Room 16:30-17:00
境 圭一 氏 (信州大学)
The space of short ropes and the classifying space of the space of long knots (JAPANESE)
[ 講演概要 ]
We prove affirmatively the conjecture raised by J. Mostovoy; the space of short ropes is weakly homotopy equivalent to the classifying space of the topological monoid (or category) of long knots in R^3. We make use of techniques developed by S. Galatius and O. Randal-Williams to construct a manifold space model of the classifying space of the space of long knots, and we give an explicit map from the space of short ropes to the model in a geometric way. This is joint work with Syunji Moriya (Osaka Prefecture University).
We prove affirmatively the conjecture raised by J. Mostovoy; the space of short ropes is weakly homotopy equivalent to the classifying space of the topological monoid (or category) of long knots in R^3. We make use of techniques developed by S. Galatius and O. Randal-Williams to construct a manifold space model of the classifying space of the space of long knots, and we give an explicit map from the space of short ropes to the model in a geometric way. This is joint work with Syunji Moriya (Osaka Prefecture University).
PDE実解析研究会
10:30-11:30 数理科学研究科棟(駒場) 056号室
Felix Schulze 氏 (University College London)
Optimal isoperimetric inequalities for surfaces in any codimension
in Cartan-Hadamard manifolds (English)
Felix Schulze 氏 (University College London)
Optimal isoperimetric inequalities for surfaces in any codimension
in Cartan-Hadamard manifolds (English)
[ 講演概要 ]
Let $(M^n,g)$ be simply connected, complete, with non-positive sectional
curvatures, and $\Sigma$ a 2-dimensional surface in $M^n$. Let $S$ be an area
minimising 3-current such that $\partial S = \Sigma$. We use a weak mean
curvature flow, obtained via elliptic regularisation, starting from
$\Sigma$, to show that $S$ satisfies the optimal Euclidean isoperimetric
inequality: $|S| \leq 1/(6\sqrt{\pi}) |\Sigma|^{3/2}$. We also obtain the
optimal estimate in case the sectional curvatures of $M$ are bounded from
above by $\kappa < 0$ and characterise the case of equality. The proof
follows from an almost monotonicity of a suitable isoperimetric
difference along the approximating flows in one dimension higher.
Let $(M^n,g)$ be simply connected, complete, with non-positive sectional
curvatures, and $\Sigma$ a 2-dimensional surface in $M^n$. Let $S$ be an area
minimising 3-current such that $\partial S = \Sigma$. We use a weak mean
curvature flow, obtained via elliptic regularisation, starting from
$\Sigma$, to show that $S$ satisfies the optimal Euclidean isoperimetric
inequality: $|S| \leq 1/(6\sqrt{\pi}) |\Sigma|^{3/2}$. We also obtain the
optimal estimate in case the sectional curvatures of $M$ are bounded from
above by $\kappa < 0$ and characterise the case of equality. The proof
follows from an almost monotonicity of a suitable isoperimetric
difference along the approximating flows in one dimension higher.
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
Frédéric Campana 氏 (Université de Lorraine/KIAS)
Orbifold rational connectedness (English)
Frédéric Campana 氏 (Université de Lorraine/KIAS)
Orbifold rational connectedness (English)
[ 講演概要 ]
The first step in the decomposition by canonical fibrations with fibres of `signed' canonical bundle of an arbitrary complex projective manifolds $X$ is its `rational quotient' (also called `MRC' fibration): it has rationally connected fibres and non-uniruled base. In general, the further steps (such as the Moishezon-Iitaka fibration) of this decomposition will require the consideration of 'orbifold base' of fibrations in order to deal with the multiple fibres (as seen already for elliptic surfaces). One thus needs to work in the larger category of (smooth) `orbifold pairs' $(X,D)$ to achieve this decomposition. The aim of the talk is thus to introduce the notions of Rational Connectedness and 'rational quotient' in this context, by means of suitable equivalent notions of negativity for the orbifold cotangent bundle (suitably defined. When $D$ is reduced, this is just the usual Log-version). The expected equivalence with connecting families of `orbifold rational curves' remains however presently open.
The first step in the decomposition by canonical fibrations with fibres of `signed' canonical bundle of an arbitrary complex projective manifolds $X$ is its `rational quotient' (also called `MRC' fibration): it has rationally connected fibres and non-uniruled base. In general, the further steps (such as the Moishezon-Iitaka fibration) of this decomposition will require the consideration of 'orbifold base' of fibrations in order to deal with the multiple fibres (as seen already for elliptic surfaces). One thus needs to work in the larger category of (smooth) `orbifold pairs' $(X,D)$ to achieve this decomposition. The aim of the talk is thus to introduce the notions of Rational Connectedness and 'rational quotient' in this context, by means of suitable equivalent notions of negativity for the orbifold cotangent bundle (suitably defined. When $D$ is reduced, this is just the usual Log-version). The expected equivalence with connecting families of `orbifold rational curves' remains however presently open.
2017年11月20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
新田 泰文 氏 (東京工業大学)
Relative GIT stabilities of toric Fano manifolds in low dimensions
新田 泰文 氏 (東京工業大学)
Relative GIT stabilities of toric Fano manifolds in low dimensions
[ 講演概要 ]
In 2000, Mabuchi extended the notion of Kaehler-Einstein metrics to Fano manifolds with non-vanishing Futaki invariant. Such a metric is called generalized Kaehler-Einstein metric or Mabuchi metric in the literature. Recently this metrics were rediscovered by Yao in the story of Donaldson's infinite dimensional moment map picture. Moreover, he introduced (uniform) relative Ding stability for toric Fano manifolds and showed that the existence of generalized Kaehler-Einstein metrics is equivalent to its uniform relative Ding stability. This equivalence is in the context of the Yau-Tian-Donaldson conjecture. In this talk, we focus on uniform relative Ding stability of toric Fano manifolds. More precisely, we determine all the uniformly relatively Ding stable toric Fano 3- and 4-folds as well as unstable ones. This talk is based on a joint work with Shunsuke Saito and Naoto Yotsutani.
In 2000, Mabuchi extended the notion of Kaehler-Einstein metrics to Fano manifolds with non-vanishing Futaki invariant. Such a metric is called generalized Kaehler-Einstein metric or Mabuchi metric in the literature. Recently this metrics were rediscovered by Yao in the story of Donaldson's infinite dimensional moment map picture. Moreover, he introduced (uniform) relative Ding stability for toric Fano manifolds and showed that the existence of generalized Kaehler-Einstein metrics is equivalent to its uniform relative Ding stability. This equivalence is in the context of the Yau-Tian-Donaldson conjecture. In this talk, we focus on uniform relative Ding stability of toric Fano manifolds. More precisely, we determine all the uniformly relatively Ding stable toric Fano 3- and 4-folds as well as unstable ones. This talk is based on a joint work with Shunsuke Saito and Naoto Yotsutani.
2017年11月16日(木)
数理人口学・数理生物学セミナー
16:30-18:00 数理科学研究科棟(駒場) 123号室
中林潤 氏 (横浜市立大学 先端医科学研究センター )
Human Immunodeficiency Virus (HIV) の細胞内複製ダイナミクスと感染個体内における進化 (JAPANESE)
中林潤 氏 (横浜市立大学 先端医科学研究センター )
Human Immunodeficiency Virus (HIV) の細胞内複製ダイナミクスと感染個体内における進化 (JAPANESE)
[ 講演概要 ]
今回のセミナーではHuman Immunodeficiency Virus (HIV) の細胞内複製ダイナミクスと感染個体内における進化を取り扱った研究を紹介する。
HIVは+鎖RNAをゲノムとして持つレンチウイルス属に属するレトロウイルスである。RNAを鋳型として逆転写酵素によって産生されたウイルスDNAが、ホストのゲノムにintegrateされ、そこからウイルス遺伝子産物が産生され、最終的にウイルス粒子が複製される。HAART (Highly Active Antiretroviral Therapy) によってHIV感染患者の予後は劇的に改善されたが、いったんintegrateされたprovirusが休眠状態で残存し、何らかのきっかけで再びウイルスを産生することがあり、これがHIV治療の大きな妨げとなっている。Integration siteの決定機構を解明することは、HIVの治療戦略を検討するのに重要である。
HIVのintegration siteはホストのゲノム中に一様ではなく偏って分布していることが知られている。HIV細胞内複製を記述する数理モデルと、これを用いた進化シミュレーションを使って、HIV integration siteの選好性がどのように決定されるか検討した。またデータベースに登録されたHIV integration siteの情報と、ホストのepigenomeデータを統合して網羅的な解析を行い、integration site特異的な塩基配列について検討したので、これらの結果について紹介したい。
今回のセミナーではHuman Immunodeficiency Virus (HIV) の細胞内複製ダイナミクスと感染個体内における進化を取り扱った研究を紹介する。
HIVは+鎖RNAをゲノムとして持つレンチウイルス属に属するレトロウイルスである。RNAを鋳型として逆転写酵素によって産生されたウイルスDNAが、ホストのゲノムにintegrateされ、そこからウイルス遺伝子産物が産生され、最終的にウイルス粒子が複製される。HAART (Highly Active Antiretroviral Therapy) によってHIV感染患者の予後は劇的に改善されたが、いったんintegrateされたprovirusが休眠状態で残存し、何らかのきっかけで再びウイルスを産生することがあり、これがHIV治療の大きな妨げとなっている。Integration siteの決定機構を解明することは、HIVの治療戦略を検討するのに重要である。
HIVのintegration siteはホストのゲノム中に一様ではなく偏って分布していることが知られている。HIV細胞内複製を記述する数理モデルと、これを用いた進化シミュレーションを使って、HIV integration siteの選好性がどのように決定されるか検討した。またデータベースに登録されたHIV integration siteの情報と、ホストのepigenomeデータを統合して網羅的な解析を行い、integration site特異的な塩基配列について検討したので、これらの結果について紹介したい。
統計数学セミナー
13：00-16：00 数理科学研究科棟(駒場) 123号室
二宮嘉行 氏 (九州大学)
スパース推定法における自由度について
二宮嘉行 氏 (九州大学)
スパース推定法における自由度について
[ 講演概要 ]
スパース推定では、どれだけスパースに推定するかを決める、つまり罰則項の強弱を決めるチューニングパラメータの値を選択する必要がある。そして、その選択のための情報量規準で用いられる自由度が、主に正規線形回帰モデルの設定のもとで計算されている。本発表では、その自由度について紹介した後、それを形式上一般化線形モデルなどに拡張する情報量規準を導く。具体的には、古典的な統計的漸近理論に基づき、AIC型の情報量規準を導出する。
スパース推定では、どれだけスパースに推定するかを決める、つまり罰則項の強弱を決めるチューニングパラメータの値を選択する必要がある。そして、その選択のための情報量規準で用いられる自由度が、主に正規線形回帰モデルの設定のもとで計算されている。本発表では、その自由度について紹介した後、それを形式上一般化線形モデルなどに拡張する情報量規準を導く。具体的には、古典的な統計的漸近理論に基づき、AIC型の情報量規準を導出する。
2017年11月15日(水)
PDE実解析研究会
10:30-11:30 数理科学研究科棟(駒場) 056号室
※ 通常と曜日が異なります。
Kaj Nyström 氏 (Uppsala University)
Boundary value problems for parabolic equations with measurable coefficients (English)
※ 通常と曜日が異なります。
Kaj Nyström 氏 (Uppsala University)
Boundary value problems for parabolic equations with measurable coefficients (English)
[ 講演概要 ]
In recent joint works with P. Auscher and M. Egert we establish new results concerning boundary value problems in the upper half-space for second order parabolic equations (and systems) assuming only measurability and some transversal regularity in the coefficients of the elliptic part. To establish our results we introduce and develop a first order strategy by means of a parabolic Dirac operator at the boundary to obtain, in particular, Green's representation for solutions in natural classes involving square functions and non-tangential maximal functions, well-posedness results with data in $L^2$-Sobolev spaces together with invertibility of layer potentials, and perturbation results. In addition we solve the Kato square root problem for parabolic operators with coefficients of the elliptic part depending measurably on all variables. Using these results we are also able to solve the $L^p$-Dirichlet problem for parabolic equations with real, time-dependent, elliptic but non-symmetric coefficients. In this talk I will briefly describe some of these developments.
In recent joint works with P. Auscher and M. Egert we establish new results concerning boundary value problems in the upper half-space for second order parabolic equations (and systems) assuming only measurability and some transversal regularity in the coefficients of the elliptic part. To establish our results we introduce and develop a first order strategy by means of a parabolic Dirac operator at the boundary to obtain, in particular, Green's representation for solutions in natural classes involving square functions and non-tangential maximal functions, well-posedness results with data in $L^2$-Sobolev spaces together with invertibility of layer potentials, and perturbation results. In addition we solve the Kato square root problem for parabolic operators with coefficients of the elliptic part depending measurably on all variables. Using these results we are also able to solve the $L^p$-Dirichlet problem for parabolic equations with real, time-dependent, elliptic but non-symmetric coefficients. In this talk I will briefly describe some of these developments.
2017年11月14日(火)
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
Meng Chen 氏 (Fudan )
A characterization of the birationality of 4-canonical maps of minimal 3-folds (English)
Meng Chen 氏 (Fudan )
A characterization of the birationality of 4-canonical maps of minimal 3-folds (English)
[ 講演概要 ]
We explain the following theorem: For any minimal 3-fold X of general type with p_g>4, the 4-canonical map is non-birational if and only if X is birationally fibred by a pencil of (1,2) surfaces. The statement fails in the case of p_g=4.
We explain the following theorem: For any minimal 3-fold X of general type with p_g>4, the 4-canonical map is non-birational if and only if X is birationally fibred by a pencil of (1,2) surfaces. The statement fails in the case of p_g=4.
数値解析セミナー
16:50-18:20 数理科学研究科棟(駒場) 002号室
石川歩惟 氏 (神戸大学大学院システム情報学研究科)
変分原理に基づくエネルギー保存数値解法と無制約最適化問題への応用 (Japanese)
石川歩惟 氏 (神戸大学大学院システム情報学研究科)
変分原理に基づくエネルギー保存数値解法と無制約最適化問題への応用 (Japanese)
[ 講演概要 ]
構造保存型数値解法は, 方程式のもつ力学的構造に着目し, その力学的性質を保つようにしてスキームを設計する数値計算法である. 特に, エネルギー保存則を厳密に保つような数値解法はエネルギー保存数値解法と呼ばれ, 離散勾配法などが知られている. 離散勾配法とは, 勾配の性質を引き継ぐよう定義された離散勾配と呼ばれるものをスキームに用いる方法で, この方法によるスキームは安定性に優れたものとなることが多い. その一方, 多くの場合に陰的になり, また, 解析力学における基本原理である変分原理との対応も明らかではない. また, 離散勾配自体の導出も, 容易でない場合もある.
そこで, 我々は, 離散勾配法の枠組みに変分原理を取り入れたエネルギー保存数値解法を提案してきた. 本講演では, この手法について紹介したのち, 変分原理を活かしたエネルギー散逸系に対する方法への拡張方法について述べる. また, これと離散勾配を自動的に導出する自動離散微分という方法を組み合わせ, 無制約最適化問題の近似解法を設計する. 最後に, 最近の話題として, Lie群上でのスキーム設計手法についても述べる.
構造保存型数値解法は, 方程式のもつ力学的構造に着目し, その力学的性質を保つようにしてスキームを設計する数値計算法である. 特に, エネルギー保存則を厳密に保つような数値解法はエネルギー保存数値解法と呼ばれ, 離散勾配法などが知られている. 離散勾配法とは, 勾配の性質を引き継ぐよう定義された離散勾配と呼ばれるものをスキームに用いる方法で, この方法によるスキームは安定性に優れたものとなることが多い. その一方, 多くの場合に陰的になり, また, 解析力学における基本原理である変分原理との対応も明らかではない. また, 離散勾配自体の導出も, 容易でない場合もある.
そこで, 我々は, 離散勾配法の枠組みに変分原理を取り入れたエネルギー保存数値解法を提案してきた. 本講演では, この手法について紹介したのち, 変分原理を活かしたエネルギー散逸系に対する方法への拡張方法について述べる. また, これと離散勾配を自動的に導出する自動離散微分という方法を組み合わせ, 無制約最適化問題の近似解法を設計する. 最後に, 最近の話題として, Lie群上でのスキーム設計手法についても述べる.
2017年11月13日(月)
東京確率論セミナー
16:00-17:30 数理科学研究科棟(駒場) 128号室
和田 正樹 氏 (福島大学 人間発達文化学類)
シュレディンガー形式における基本解の評価について (JAPANESE)
和田 正樹 氏 (福島大学 人間発達文化学類)
シュレディンガー形式における基本解の評価について (JAPANESE)
[ 講演概要 ]
シュレディンガー形式は、マルコフ過程に対応するディリクレ形式に摂動項を加えて得られる。本研究ではシュレディンガー形式における基本解を、元のマルコフ過程の推移確率密度関数(対応するディリクレ形式における基本解と同義)と比較することを目的としている。特に、摂動項が十分大きくなったとき（臨界的という）の基本解の挙動が、元のマルコフ過程の推移確率密度関数とどのように異なるのか、現時点で判明していることを紹介する。
シュレディンガー形式は、マルコフ過程に対応するディリクレ形式に摂動項を加えて得られる。本研究ではシュレディンガー形式における基本解を、元のマルコフ過程の推移確率密度関数(対応するディリクレ形式における基本解と同義)と比較することを目的としている。特に、摂動項が十分大きくなったとき（臨界的という）の基本解の挙動が、元のマルコフ過程の推移確率密度関数とどのように異なるのか、現時点で判明していることを紹介する。
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
Georg Schumacher 氏 (Philipps-Universität Marburg)
Relative Canonical Bundles for Families of Calabi-Yau Manifolds
Georg Schumacher 氏 (Philipps-Universität Marburg)
Relative Canonical Bundles for Families of Calabi-Yau Manifolds
[ 講演概要 ]
We consider holomorphic families of Calabi-Yau manifolds (here being defined by the vanishing of the first real Chern class). We study induced hermitian metrics on the relative canonical bundle, which are related to the Weil-Petersson form on the base. Under a certain condition the total space possesses a Kähler form, whose restriction to fibers are equal to the Ricci flat metrics. Furthermore we prove an extension theorem for the Weil-Petersson form and give applications.
We consider holomorphic families of Calabi-Yau manifolds (here being defined by the vanishing of the first real Chern class). We study induced hermitian metrics on the relative canonical bundle, which are related to the Weil-Petersson form on the base. Under a certain condition the total space possesses a Kähler form, whose restriction to fibers are equal to the Ricci flat metrics. Furthermore we prove an extension theorem for the Weil-Petersson form and give applications.
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
Juan Orendain 氏 (UNAM)
Globularily generated double categories: On the problem of existence of internalizations for decorated bicategories (English)
Juan Orendain 氏 (UNAM)
Globularily generated double categories: On the problem of existence of internalizations for decorated bicategories (English)
2017年11月10日(金)
東京無限可積分系セミナー
17:00-18:30 数理科学研究科棟(駒場) 122号室
Fabio Novaes 氏 (International Institute of Physics (UFRN))
Chern-Simons, gravity and integrable systems. (ENGLISH)
http://www.iip.ufrn.br/eventslecturer?inf==0EVRpXTR1TP
Fabio Novaes 氏 (International Institute of Physics (UFRN))
Chern-Simons, gravity and integrable systems. (ENGLISH)
[ 講演概要 ]
It is known since the 80's that pure three-dimensional gravity is classically equivalent to a Chern-Simons theory with gauge group SL(2,R) x SL(2,R). For a given set of boundary conditions, the asymptotic classical phase space has a central extension in terms of two copies of Virasoro algebra. In particular, this gives a conformal field theory representation of black hole solutions in 3d gravity, also known as BTZ black holes. The BTZ black hole entropy can then be recovered using CFT. In this talk, we review this story and discuss recent results on how to relax the BTZ boundary conditions to obtain the KdV hierarchy at the boundary. More generally, this shows that Chern-Simons theory can represent virtually any integrable system at the boundary, given some consistency conditions. We also briefly discuss how this formulation can be useful to describe non-relativistic systems.
[ 参考URL ]It is known since the 80's that pure three-dimensional gravity is classically equivalent to a Chern-Simons theory with gauge group SL(2,R) x SL(2,R). For a given set of boundary conditions, the asymptotic classical phase space has a central extension in terms of two copies of Virasoro algebra. In particular, this gives a conformal field theory representation of black hole solutions in 3d gravity, also known as BTZ black holes. The BTZ black hole entropy can then be recovered using CFT. In this talk, we review this story and discuss recent results on how to relax the BTZ boundary conditions to obtain the KdV hierarchy at the boundary. More generally, this shows that Chern-Simons theory can represent virtually any integrable system at the boundary, given some consistency conditions. We also briefly discuss how this formulation can be useful to describe non-relativistic systems.
http://www.iip.ufrn.br/eventslecturer?inf==0EVRpXTR1TP
2017年11月09日(木)
Kavli IPMU Komaba Seminar
13:30-14:30 数理科学研究科棟(駒場) 056号室
Edouard Brezin 氏 (lpt ens, Paris)
Various applications of supersymmetry in statistical physics (English)
Edouard Brezin 氏 (lpt ens, Paris)
Various applications of supersymmetry in statistical physics (English)
[ 講演概要 ]
Supersymmetry is a fundamental concept in particle physics (although it has not been seen experimentally so far). But it is although a powerful tool in a number of problems arising in quantum mechanics and statistical physics. It has been widely used in the theory of disordered systems (Efetov et al.), it led to dimensional reduction for branched polymers (Parisi-Sourlas), for the susy classical gas (Brydges and Imbrie), for Landau levels with impurities. If has also many powerful applications in the theory of random matrices. I will briefly review some of these topics.
Supersymmetry is a fundamental concept in particle physics (although it has not been seen experimentally so far). But it is although a powerful tool in a number of problems arising in quantum mechanics and statistical physics. It has been widely used in the theory of disordered systems (Efetov et al.), it led to dimensional reduction for branched polymers (Parisi-Sourlas), for the susy classical gas (Brydges and Imbrie), for Landau levels with impurities. If has also many powerful applications in the theory of random matrices. I will briefly review some of these topics.
2017年11月08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
Xin Wan 氏 (Morningside Center for Mathematics)
Iwasawa theory and Bloch-Kato conjecture for modular forms (ENGLISH)
Xin Wan 氏 (Morningside Center for Mathematics)
Iwasawa theory and Bloch-Kato conjecture for modular forms (ENGLISH)
[ 講演概要 ]
Bloch and Kato formulated conjectures relating sizes of p-adic Selmer groups with special values of L-functions. Iwasawa theory is a useful tool for studying these conjectures and BSD conjecture for elliptic curves. For example the Iwasawa main conjecture for modular forms formulated by Kato implies the Tamagawa number formula for modular forms of analytic rank 0.
In this talk I'll first briefly review the above theory. Then we will focus on a different Iwasawa theory approach for this problem. The starting point is a recent joint work with Jetchev and Skinner proving the BSD formula for elliptic curves of analytic rank 1. We will discuss how such results are generalized to modular forms. If time allowed we may also explain the possibility to use it to deduce Bloch-Kato conjectures in both analytic rank 0 and 1 cases. In certain aspects such approach should be more powerful than classical Iwasawa theory, and has some potential to attack cases with bad ramification at p.
（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．今回は北京からの中継です．）
Bloch and Kato formulated conjectures relating sizes of p-adic Selmer groups with special values of L-functions. Iwasawa theory is a useful tool for studying these conjectures and BSD conjecture for elliptic curves. For example the Iwasawa main conjecture for modular forms formulated by Kato implies the Tamagawa number formula for modular forms of analytic rank 0.
In this talk I'll first briefly review the above theory. Then we will focus on a different Iwasawa theory approach for this problem. The starting point is a recent joint work with Jetchev and Skinner proving the BSD formula for elliptic curves of analytic rank 1. We will discuss how such results are generalized to modular forms. If time allowed we may also explain the possibility to use it to deduce Bloch-Kato conjectures in both analytic rank 0 and 1 cases. In certain aspects such approach should be more powerful than classical Iwasawa theory, and has some potential to attack cases with bad ramification at p.
（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．今回は北京からの中継です．）
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