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過去の記録
過去の記録 ～07/26｜本日 07/27 | 今後の予定 07/28～
応用解析セミナー
16:00-17:30 数理科学研究科棟(駒場) 002号室
Hatem Zaag 氏 (CNRS / パリ北大学)
A Liouville theorem for a semilinear heat equation with no gradient structure
Hatem Zaag 氏 (CNRS / パリ北大学)
A Liouville theorem for a semilinear heat equation with no gradient structure
[ 講演概要 ]
We prove a Liouville Theorem for entire solutions of a vector
valued semilinear heat equation with no gradient structure. Classical tools such as the maximum principle or energy techniques break down and have to be replaced by a new approach. These tools involve a very good understanding of the dynamical system formulation of the equation in the selfsimilar setting. Using the Liouville Theorem, we derive uniform estimates for blow-up solutions of the same equation.
We prove a Liouville Theorem for entire solutions of a vector
valued semilinear heat equation with no gradient structure. Classical tools such as the maximum principle or energy techniques break down and have to be replaced by a new approach. These tools involve a very good understanding of the dynamical system formulation of the equation in the selfsimilar setting. Using the Liouville Theorem, we derive uniform estimates for blow-up solutions of the same equation.
2009年12月16日(水)
統計数学セミナー
15:00-16:10 数理科学研究科棟(駒場) 128号室
Stefano Maria Iacus 氏 (Department of Economics, Business and Statistics, University of Milan, Italy)
ecent results on volatility change point analysis for discretely sampled stochastic differential equations
https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2009/12.html
Stefano Maria Iacus 氏 (Department of Economics, Business and Statistics, University of Milan, Italy)
ecent results on volatility change point analysis for discretely sampled stochastic differential equations
[ 講演概要 ]
In this seminar we review recent advances on change point analysis for the volatility component of stochastic differential equations under different discrete sampling schemes. We consider both ergodic and high frequency and non ergodic cases. Results have been obtained by means of least squares, CUSUM tests and quasi-maximum likelihood approach. We show an application to the recent financial crisis and finally present a Monte Carlo study to compare the three methods under different setups.
Join work with Prof. Nakahiro Yoshida.
[ 参考URL ]In this seminar we review recent advances on change point analysis for the volatility component of stochastic differential equations under different discrete sampling schemes. We consider both ergodic and high frequency and non ergodic cases. Results have been obtained by means of least squares, CUSUM tests and quasi-maximum likelihood approach. We show an application to the recent financial crisis and finally present a Monte Carlo study to compare the three methods under different setups.
Join work with Prof. Nakahiro Yoshida.
https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2009/12.html
2009年12月15日(火)
Lie群論・表現論セミナー
17:00-18:00 数理科学研究科棟(駒場) 056号室
トポロジー火曜セミナーと合同です。この週に砂田利一氏の集中講義が行われます
砂田利一氏 氏 (明治大学理工学部)
Open Problems in Discrete Geometric Analysis
https://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar2009.html#20091215sunada
トポロジー火曜セミナーと合同です。この週に砂田利一氏の集中講義が行われます
砂田利一氏 氏 (明治大学理工学部)
Open Problems in Discrete Geometric Analysis
[ 講演概要 ]
Discrete geometric analysis is a hybrid field of several traditional disciplines: graph theory, geometry, theory of discrete groups, and probability. This field concerns solely analysis on graphs, a synonym of "1-dimensional cell complex". In this talk, I shall discuss several open problems related to the discrete Laplacian, a "protagonist" in discrete geometric analysis. Topics dealt with are 1. Ramanujan graphs, 2. Spectra of covering graphs, 3. Zeta functions of finitely generated groups.
[ 参考URL ]Discrete geometric analysis is a hybrid field of several traditional disciplines: graph theory, geometry, theory of discrete groups, and probability. This field concerns solely analysis on graphs, a synonym of "1-dimensional cell complex". In this talk, I shall discuss several open problems related to the discrete Laplacian, a "protagonist" in discrete geometric analysis. Topics dealt with are 1. Ramanujan graphs, 2. Spectra of covering graphs, 3. Zeta functions of finitely generated groups.
https://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar2009.html#20091215sunada
トポロジー火曜セミナー
17:00-18:00 数理科学研究科棟(駒場) 056号室
Tea: 16:40 - 17:00 コモンルーム
砂田 利一 氏 (明治大学)
Open Problems in Discrete Geometric Analysis
Tea: 16:40 - 17:00 コモンルーム
砂田 利一 氏 (明治大学)
Open Problems in Discrete Geometric Analysis
[ 講演概要 ]
Discrete geometric analysis is a hybrid field of several traditional disciplines: graph theory, geometry, theory of discrete groups, and probability. This field concerns solely analysis on graphs, a synonym of "1-dimensional cell complex". In this talk, I shall discuss several open problems related to the discrete Laplacian, a "protagonist" in discrete geometric analysis. Topics dealt with are 1. Ramanujan graphs, 2. Spectra of covering graphs, 3. Zeta functions of finitely generated groups.
Discrete geometric analysis is a hybrid field of several traditional disciplines: graph theory, geometry, theory of discrete groups, and probability. This field concerns solely analysis on graphs, a synonym of "1-dimensional cell complex". In this talk, I shall discuss several open problems related to the discrete Laplacian, a "protagonist" in discrete geometric analysis. Topics dealt with are 1. Ramanujan graphs, 2. Spectra of covering graphs, 3. Zeta functions of finitely generated groups.
2009年12月14日(月)
統計数学セミナー
14:00-15:10 数理科学研究科棟(駒場) 128号室
L. VOSTRIKOVA 氏 (LAREMA, Departement de Mathematiques, Universite d’Angers, FRANCE)
On the stability of contingent claimes in incomplet models under statistical estimations.
https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2009/11.html
L. VOSTRIKOVA 氏 (LAREMA, Departement de Mathematiques, Universite d’Angers, FRANCE)
On the stability of contingent claimes in incomplet models under statistical estimations.
[ 講演概要 ]
In exponential semi-martingale setting for risky asset we estimate the difference of prices of options when initial physical measure P and corresponding martingale measure Q change to tilde{P} and tilde{Q} respectively. Then, we estimate L1 distance of option’s prices for corresponding parametric models with known and estimated parameters. The results are applied to exponential Levy models with special choise of martingale measure as Esscher measure, minimal entropy measure and f^q -minimal martingale measure. We illustrate our results by considering GMY and CGMY models.
[ 参考URL ]In exponential semi-martingale setting for risky asset we estimate the difference of prices of options when initial physical measure P and corresponding martingale measure Q change to tilde{P} and tilde{Q} respectively. Then, we estimate L1 distance of option’s prices for corresponding parametric models with known and estimated parameters. The results are applied to exponential Levy models with special choise of martingale measure as Esscher measure, minimal entropy measure and f^q -minimal martingale measure. We illustrate our results by considering GMY and CGMY models.
https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2009/11.html
代数幾何学セミナー
14:40-16:10 数理科学研究科棟(駒場) 126号室
いつもと時間帯が異なります。ご注意ください。
Sergey Galkin 氏 (IPMU)
Invariants of Fano varieties via quantum D-module
いつもと時間帯が異なります。ご注意ください。
Sergey Galkin 氏 (IPMU)
Invariants of Fano varieties via quantum D-module
[ 講演概要 ]
We will introduce and compute Apery characteristic
class and Frobenius genera - invariants of Fano variety derived from
it's Gromov-Witten invariants. Then we will show how to compute them
and relate with other invariants.
We will introduce and compute Apery characteristic
class and Frobenius genera - invariants of Fano variety derived from
it's Gromov-Witten invariants. Then we will show how to compute them
and relate with other invariants.
2009年12月11日(金)
GCOE社会数理講演シリーズ
16:20-17:50 数理科学研究科棟(駒場) 117号室
山下 浩 氏 (数理システム代表取締役 )
数理科学をビジネスに - 最適化とデータマイニングの周辺でⅠ
山下 浩 氏 (数理システム代表取締役 )
数理科学をビジネスに - 最適化とデータマイニングの周辺でⅠ
2009年12月10日(木)
講演会
10:40-12:10 数理科学研究科棟(駒場) 128号室
竹崎正道 氏 (UCLA)
冨田竹崎理論とその応用 (9)
竹崎正道 氏 (UCLA)
冨田竹崎理論とその応用 (9)
作用素環セミナー
16:30-18:00 数理科学研究科棟(駒場) 128号室
張欽 氏 (東大数理)
Symmetric norms and spaces of operators modelled on a semifinite von Neumann algebra
張欽 氏 (東大数理)
Symmetric norms and spaces of operators modelled on a semifinite von Neumann algebra
2009年12月09日(水)
講演会
14:40-16:10 数理科学研究科棟(駒場) 128号室
竹崎正道 氏 (UCLA)
冨田竹崎理論とその応用 (8)
竹崎正道 氏 (UCLA)
冨田竹崎理論とその応用 (8)
統計数学セミナー
15:00-16:10 数理科学研究科棟(駒場) 002号室
佐藤 整尚 氏 (統計数理研究所)
分離情報最尤法を使った高頻度金融データにおける実現分散、共分散の推定について
https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2009/10.html
佐藤 整尚 氏 (統計数理研究所)
分離情報最尤法を使った高頻度金融データにおける実現分散、共分散の推定について
[ 講演概要 ]
近年、金融データを使った分析の中で、高頻度データを用いるものが多くなってきている。 しかしながら、通常のヒストリカルな推定法で求めた分散、共分散ではバイアスが発生することが知られており、その一致推定量を求めることがこの分野で盛んに研究されてきている。 本報告では新たに開発された分離情報最尤法(SIML)を用いた推定法を紹介するとともにその性質に関して議論していきたい。さらに、非常に広範囲な応用可能性についても紹介する。
[ 参考URL ]近年、金融データを使った分析の中で、高頻度データを用いるものが多くなってきている。 しかしながら、通常のヒストリカルな推定法で求めた分散、共分散ではバイアスが発生することが知られており、その一致推定量を求めることがこの分野で盛んに研究されてきている。 本報告では新たに開発された分離情報最尤法(SIML)を用いた推定法を紹介するとともにその性質に関して議論していきたい。さらに、非常に広範囲な応用可能性についても紹介する。
https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2009/10.html
2009年12月08日(火)
講演会
14:40-16:10 数理科学研究科棟(駒場) 128号室
竹崎正道 氏 (UCLA)
冨田竹崎理論とその応用 (7)
竹崎正道 氏 (UCLA)
冨田竹崎理論とその応用 (7)
GCOEセミナー
17:30-19:00 数理科学研究科棟(駒場) 002号室
Giovanni Felder 氏 (ETH Zurich)
Gaudin subalgebras and stable rational curves. (ENGLISH)
Giovanni Felder 氏 (ETH Zurich)
Gaudin subalgebras and stable rational curves. (ENGLISH)
[ 講演概要 ]
We show that Abelian subalgebras of maximal dimensions spanned by generators of the n-th Kohno-Drinfeld Lie algebra are classified by the Grothendieck-Knudsen moduli space of stable rational curves with n+1 marked points. I will explain the relation with Gaudin integrable systems of statistical mechanics and the representation theory of the symmetric group in the formulation of Vershik and Okounkov. The talk is based on joint work with Leonardo Aguirre and Alexander Veselov.
We show that Abelian subalgebras of maximal dimensions spanned by generators of the n-th Kohno-Drinfeld Lie algebra are classified by the Grothendieck-Knudsen moduli space of stable rational curves with n+1 marked points. I will explain the relation with Gaudin integrable systems of statistical mechanics and the representation theory of the symmetric group in the formulation of Vershik and Okounkov. The talk is based on joint work with Leonardo Aguirre and Alexander Veselov.
2009年12月07日(月)
Kavli IPMU Komaba Seminar
17:30-19:00 数理科学研究科棟(駒場) 002号室
Weiping Zhang 氏 (Chern Institute of Mathematics, Nankai University)
Geometric quantization on noncompact manifolds
Weiping Zhang 氏 (Chern Institute of Mathematics, Nankai University)
Geometric quantization on noncompact manifolds
[ 講演概要 ]
We will describe our analytic approach with Youlinag Tian to the Guillemin-Sternberg geometric quantization conjecture which can be summarized as "quantization commutes with reduction". We will aslo describe a recent extension to the case of noncompact symplectic manifolds. This is a joint work with Xiaonan Ma in which we solve a conjecture of Vergne mentioned in her ICM2006 plenary lecture.
We will describe our analytic approach with Youlinag Tian to the Guillemin-Sternberg geometric quantization conjecture which can be summarized as "quantization commutes with reduction". We will aslo describe a recent extension to the case of noncompact symplectic manifolds. This is a joint work with Xiaonan Ma in which we solve a conjecture of Vergne mentioned in her ICM2006 plenary lecture.
2009年12月03日(木)
作用素環セミナー
16:30-18:00 数理科学研究科棟(駒場) 128号室
見村万佐人 氏 (東大数理)
Vanishing of quasi-homomorphisms and the stable commutator
lengths on special linear groups over euclidean rings
見村万佐人 氏 (東大数理)
Vanishing of quasi-homomorphisms and the stable commutator
lengths on special linear groups over euclidean rings
2009年12月02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
北海道大学のHPには、第1回(2004年9月29日)～第38回(2008年10月15日)までの情報が掲載されております。
Juergen Saal 氏 (University of Konstanz)
A hyperbolic fluid model based on Cattaneo's law
北海道大学のHPには、第1回(2004年9月29日)～第38回(2008年10月15日)までの情報が掲載されております。
Juergen Saal 氏 (University of Konstanz)
A hyperbolic fluid model based on Cattaneo's law
[ 講演概要 ]
In various applications a delay of the propagation speed of a fluid (temperature, ...) has been observed. Such phenomena cannot be described by standard parabolic models, whose derivation relies on Fourier's law (Paradoxon of infinite propagation speed).
One way to give account to these observations and which was successfully applied to several models, is to replace Fourier's law by the law of Cattaneo. In the case of a fluid, this leads to a hyperbolicly perturbed quasilinear Navier-Stokes system for which existence and uniqueness results will be presented.
In various applications a delay of the propagation speed of a fluid (temperature, ...) has been observed. Such phenomena cannot be described by standard parabolic models, whose derivation relies on Fourier's law (Paradoxon of infinite propagation speed).
One way to give account to these observations and which was successfully applied to several models, is to replace Fourier's law by the law of Cattaneo. In the case of a fluid, this leads to a hyperbolicly perturbed quasilinear Navier-Stokes system for which existence and uniqueness results will be presented.
2009年12月01日(火)
トポロジー火曜セミナー
16:30-18:00 数理科学研究科棟(駒場) 056号室
Tea: 16:00 - 16:30 コモンルーム
Andrei Pajitnov 氏 (Univ. de Nantes)
Non-Abelian Novikov homology
Tea: 16:00 - 16:30 コモンルーム
Andrei Pajitnov 氏 (Univ. de Nantes)
Non-Abelian Novikov homology
[ 講演概要 ]
Classical construction of S.P. Novikov
associates to each circle-valued Morse map
a chain complex defined over a ring
of Laurent power series in one variable.
In this survey talk we shall explain several
results related to the construction and
properties of non-Abelian generalizations of the
Novikov complex.
Classical construction of S.P. Novikov
associates to each circle-valued Morse map
a chain complex defined over a ring
of Laurent power series in one variable.
In this survey talk we shall explain several
results related to the construction and
properties of non-Abelian generalizations of the
Novikov complex.
2009年11月30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
奥山裕介 氏 (京都工芸繊維大学)
Equidistribution and Nevanlinna theory
奥山裕介 氏 (京都工芸繊維大学)
Equidistribution and Nevanlinna theory
Kavli IPMU Komaba Seminar
16:30-18:00 数理科学研究科棟(駒場) 002号室
Junya Yagi 氏 (Rutgers University)
Chiral Algebras of (0,2) Models: Beyond Perturbation Theory
Junya Yagi 氏 (Rutgers University)
Chiral Algebras of (0,2) Models: Beyond Perturbation Theory
[ 講演概要 ]
The chiral algebras of two-dimensional sigma models with (0,2)
supersymmetry are infinite-dimensional generalizations of the chiral
rings of (2,2) models. Perturbatively, they enjoy rich mathematical
structures described by sheaves of chiral differential operators.
Nonperturbatively, however, they vanish completely for certain (0,2)
models with no left-moving fermions. In this talk, I will explain how
this vanishing phenomenon takes places. The vanishing of the chiral
algebra of a (0, 2) model implies that supersymmetry is spontaneously
broken in the model, which in turn suggests that no harmonic spinors
exist on the loop space of the target space. In particular, the
elliptic genus of the model vanishes, thereby providing a physics
proof of a special case of the Hoelhn-Stolz conjecture.
The chiral algebras of two-dimensional sigma models with (0,2)
supersymmetry are infinite-dimensional generalizations of the chiral
rings of (2,2) models. Perturbatively, they enjoy rich mathematical
structures described by sheaves of chiral differential operators.
Nonperturbatively, however, they vanish completely for certain (0,2)
models with no left-moving fermions. In this talk, I will explain how
this vanishing phenomenon takes places. The vanishing of the chiral
algebra of a (0, 2) model implies that supersymmetry is spontaneously
broken in the model, which in turn suggests that no harmonic spinors
exist on the loop space of the target space. In particular, the
elliptic genus of the model vanishes, thereby providing a physics
proof of a special case of the Hoelhn-Stolz conjecture.
2009年11月27日(金)
GCOE社会数理講演シリーズ
16:20-17:50 数理科学研究科棟(駒場) 117号室
池森俊文氏(高野 康 氏) 氏 (みずほ第一フィナンシャルテクノロジー(株))
金融リスク管理と数理(実践)
池森俊文氏(高野 康 氏) 氏 (みずほ第一フィナンシャルテクノロジー(株))
金融リスク管理と数理(実践)
統計数学セミナー
13:40-14:50 数理科学研究科棟(駒場) 128号室
加藤 賢悟 氏 (広島大学大学院理学研究科数学専攻)
非線形時系列モデルのイノベーション密度の推定
https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2009/09.html
加藤 賢悟 氏 (広島大学大学院理学研究科数学専攻)
非線形時系列モデルのイノベーション密度の推定
[ 講演概要 ]
In this talk, we consider the problem of estimating the innovation density in nonlinear autoregressive models. Specifically, we establish the convergence rate of the supremum distance between the residual-based kernel density estimator and the kernel density estimator using the unobservable actual innovation variables. The proof of the main theorem relies on empirical process theory instead of the conventional Taylor expansion approach. As applications, we obtain the exact rate of weak uniform consistency on the whole line, pointwise asymptotic normality of the residual-based kernel density estimator and the asymptotic distribution of a Bickel-Rosenblatt type global measure statistic related to it. We also examine the conditions of the main theorem for some specic time series model.
[ 参考URL ]In this talk, we consider the problem of estimating the innovation density in nonlinear autoregressive models. Specifically, we establish the convergence rate of the supremum distance between the residual-based kernel density estimator and the kernel density estimator using the unobservable actual innovation variables. The proof of the main theorem relies on empirical process theory instead of the conventional Taylor expansion approach. As applications, we obtain the exact rate of weak uniform consistency on the whole line, pointwise asymptotic normality of the residual-based kernel density estimator and the asymptotic distribution of a Bickel-Rosenblatt type global measure statistic related to it. We also examine the conditions of the main theorem for some specic time series model.
https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2009/09.html
2009年11月26日(木)
応用解析セミナー
16:00-17:30 数理科学研究科棟(駒場) 002号室
小池 茂昭 氏 (埼玉大学・理学部数学科)
L^p 粘性解の弱ハルナック不等式の最近の進展
小池 茂昭 氏 (埼玉大学・理学部数学科)
L^p 粘性解の弱ハルナック不等式の最近の進展
[ 講演概要 ]
Caffarelli による粘性解の regularity 研究 (1989 年) を基に, 1996 年に Caffarelli- Crandall-Kocan-Swiech によって L^p 粘性解の概念が導入された. L^p 粘性解とは, 通 常の粘性解理論では扱えなかった, 非有界非斉次項を持つ (非発散型) 偏微分方程 式にも適用可能な弱解である.
しかしながら, 係数に関しては有界係数しか研究されていなかった. その後, Swiech との共同研究により, 係数が非有界だが適当なべき乗可積分性を仮定して Aleksandrov-Bakelman-Pucci 型の最大値原理を導くことが可能になった.
本講演では, 非有界係数・非斉事項を持った, 完全非線形 2 階一様楕円型方程式 の L^p 粘性解の弱ハルナック不等式に関する最近のSwiech との共同研究の結果を紹 介する.
Caffarelli による粘性解の regularity 研究 (1989 年) を基に, 1996 年に Caffarelli- Crandall-Kocan-Swiech によって L^p 粘性解の概念が導入された. L^p 粘性解とは, 通 常の粘性解理論では扱えなかった, 非有界非斉次項を持つ (非発散型) 偏微分方程 式にも適用可能な弱解である.
しかしながら, 係数に関しては有界係数しか研究されていなかった. その後, Swiech との共同研究により, 係数が非有界だが適当なべき乗可積分性を仮定して Aleksandrov-Bakelman-Pucci 型の最大値原理を導くことが可能になった.
本講演では, 非有界係数・非斉事項を持った, 完全非線形 2 階一様楕円型方程式 の L^p 粘性解の弱ハルナック不等式に関する最近のSwiech との共同研究の結果を紹 介する.
2009年11月25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
北海道大学のHPには、第1回(2004年9月29日)～第38回(2008年10月15日)までの情報が掲載されております。
Hermann Sohr 氏 (University Paderborn)
Recent results on weak and strong solutions of the Navier-Stokes equations
北海道大学のHPには、第1回(2004年9月29日)～第38回(2008年10月15日)までの情報が掲載されております。
Hermann Sohr 氏 (University Paderborn)
Recent results on weak and strong solutions of the Navier-Stokes equations
[ 講演概要 ]
Our purpose is to develop the optimal initial value condition for the existence of a unique local strong solution of the Navier-Stokes equations in a smooth bounded domain.
This condition is not only sufficient
- there are several well-known sufficient conditions in this context
- but also necessary, and yields therefore the largest possible class of such strong solutions.
As an application we obtain several extensions of Serrin's regularity condition. A restricted result also holds for completely general domains. Furthermore we extend the well-known class of Leray-Hopf weak solutions with zero boundary conditions and zero divergence to a larger class with corresponding nonzero conditions.
Our purpose is to develop the optimal initial value condition for the existence of a unique local strong solution of the Navier-Stokes equations in a smooth bounded domain.
This condition is not only sufficient
- there are several well-known sufficient conditions in this context
- but also necessary, and yields therefore the largest possible class of such strong solutions.
As an application we obtain several extensions of Serrin's regularity condition. A restricted result also holds for completely general domains. Furthermore we extend the well-known class of Leray-Hopf weak solutions with zero boundary conditions and zero divergence to a larger class with corresponding nonzero conditions.
2009年11月24日(火)
解析学火曜セミナー
16:30-18:00 数理科学研究科棟(駒場) 128号室
吉野 邦生 氏 (東京都市大学)
Analytic Properties of Eigen Values of Daubechies Localization Operator
吉野 邦生 氏 (東京都市大学)
Analytic Properties of Eigen Values of Daubechies Localization Operator
[ 講演概要 ]
1)ドーベシー局在化作用素の固有値の解析的性質、積分表示式、
(2)ドーベシー局在化作用素のシンボルの再現公式、
(3)ドーベシー局在化作用素のバーグマンーフォック空間での表示
等について述べる。
1)ドーベシー局在化作用素の固有値の解析的性質、積分表示式、
(2)ドーベシー局在化作用素のシンボルの再現公式、
(3)ドーベシー局在化作用素のバーグマンーフォック空間での表示
等について述べる。
トポロジー火曜セミナー
16:30-18:00 数理科学研究科棟(駒場) 056号室
Tea: 16:00 - 16:30 コモンルーム
Adam Clay 氏 (University of British Columbia)
A topological approach to left orderable groups
Tea: 16:00 - 16:30 コモンルーム
Adam Clay 氏 (University of British Columbia)
A topological approach to left orderable groups
[ 講演概要 ]
A group G is said to be left orderable if there is a strict
total ordering of its elements such that g
space. In general, the structure of the space LO(G) is not well understood, although there are surprising results in a few special cases.
For example, the space of left orderings of the braid group B_n for n>2
contains isolated points (yet it is uncountable), while the space of left
orderings of the fundamental group of the Klein bottle is finite.
Twice in recent years, the space of left orderings has been used very
successfully to solve difficult open problems from the field of left
orderable groups, even though the connection between the topology of LO(G) and the algebraic properties of G was still unclear. I will explain the
newest understanding of this connection, and highlight some potential
applications of further advances.
A group G is said to be left orderable if there is a strict
total ordering of its elements such that g
space. In general, the structure of the space LO(G) is not well understood, although there are surprising results in a few special cases.
For example, the space of left orderings of the braid group B_n for n>2
contains isolated points (yet it is uncountable), while the space of left
orderings of the fundamental group of the Klein bottle is finite.
Twice in recent years, the space of left orderings has been used very
successfully to solve difficult open problems from the field of left
orderable groups, even though the connection between the topology of LO(G) and the algebraic properties of G was still unclear. I will explain the
newest understanding of this connection, and highlight some potential
applications of further advances.
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