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Seminar information archive
Seminar information archive ～07/26｜Today's seminar 07/27 | Future seminars 07/28～
2006/10/25
Number Theory Seminar
17:00-18:00 Room #117 (Graduate School of Math. Sci. Bldg.)
平之内 俊郎 (九州大学)
Extensions of truncated discrete valuation rings ( 田口雄一郎先生との共同研究 )
平之内 俊郎 (九州大学)
Extensions of truncated discrete valuation rings ( 田口雄一郎先生との共同研究 )
[ Abstract ]
局所体の拡大とその付値環の或る商である"truncated" dvrの拡大の圏を比較する. 不分岐拡大と剰余体の拡大が一対一対応するのと同じ様に, 分岐に関する条件を加えれば,局所体と "truncated" dvr の拡大の圏が同値になる (Deligne).
今回は, 古典的な(上付き)分岐群の代わりにAbbes-斎藤による分岐群を用いて分岐に関する条件を与える. そして,この分岐群の Rigid 幾何的解釈を踏襲する事でDeligneの定理の剰余体が非完全な場合への一般化が得られる事を述べる.
局所体の拡大とその付値環の或る商である"truncated" dvrの拡大の圏を比較する. 不分岐拡大と剰余体の拡大が一対一対応するのと同じ様に, 分岐に関する条件を加えれば,局所体と "truncated" dvr の拡大の圏が同値になる (Deligne).
今回は, 古典的な(上付き)分岐群の代わりにAbbes-斎藤による分岐群を用いて分岐に関する条件を与える. そして,この分岐群の Rigid 幾何的解釈を踏襲する事でDeligneの定理の剰余体が非完全な場合への一般化が得られる事を述べる.
Lectures
16:30-18:00 Room #122 (Graduate School of Math. Sci. Bldg.)
Heinz W. Engl (Industrial Mathematics Institute, Kepler University, Linz and Johann Radon Institute for Computational and Applied Mathematics, Austrian Academy of Sciences)
Regularization of nonlinear inverse problems: mathematics, industrial application fields, new challenges
Heinz W. Engl (Industrial Mathematics Institute, Kepler University, Linz and Johann Radon Institute for Computational and Applied Mathematics, Austrian Academy of Sciences)
Regularization of nonlinear inverse problems: mathematics, industrial application fields, new challenges
[ Abstract ]
Motivated by some of the industrial examples presented in the first talk, we outline the theory of regularization methods for the stable solution of nonlinear inverse problems. Then, we turn to some new problem fields of possible future industrial relevance in systems and molecular biology.
Motivated by some of the industrial examples presented in the first talk, we outline the theory of regularization methods for the stable solution of nonlinear inverse problems. Then, we turn to some new problem fields of possible future industrial relevance in systems and molecular biology.
2006/10/24
Tuesday Seminar on Topology
16:30-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)
Marco Zunino (JSPS, University of Tokyo)
A review of crossed G-structures
Marco Zunino (JSPS, University of Tokyo)
A review of crossed G-structures
[ Abstract ]
We present the definition of "crossed structures" as introduced by Turaev and others a few years ago. One of the original motivations in the introduction of these structures and of the related notion of a "Homotopy Quantum Field Theory" (HQFT) was the extension of Reshetikhin-Turaev invariants to the case of flat principal bundles on 3-manifolds. We resume both this aspect of the theory and other applications in both algebra and topology and we present our results on the algebraic structures involved.
We present the definition of "crossed structures" as introduced by Turaev and others a few years ago. One of the original motivations in the introduction of these structures and of the related notion of a "Homotopy Quantum Field Theory" (HQFT) was the extension of Reshetikhin-Turaev invariants to the case of flat principal bundles on 3-manifolds. We resume both this aspect of the theory and other applications in both algebra and topology and we present our results on the algebraic structures involved.
Tuesday Seminar of Algebraic Analysis
16:30-18:00 Room #052 (Graduate School of Math. Sci. Bldg.)
吉野 邦生 (上智大理工)
Asymptotic expansions of solutions to heat equations with genelarized function initial value (岡康之氏との共同研究)
[ Reference URL ]
http://agusta.ms.u-tokyo.ac.jp/alganalysis.html
吉野 邦生 (上智大理工)
Asymptotic expansions of solutions to heat equations with genelarized function initial value (岡康之氏との共同研究)
[ Reference URL ]
http://agusta.ms.u-tokyo.ac.jp/alganalysis.html
2006/10/23
Geometry Seminar
14:40-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)
Naichung Conan Leung (Chinese University of Hong Kong) 14:40-16:10
Toric geometry and Mirror Symmetry
Balance point and stability of vector bundles over a projective manifold
Naichung Conan Leung (Chinese University of Hong Kong) 14:40-16:10
Toric geometry and Mirror Symmetry
[ Abstract ]
We first review the geometry of toric varieties. Then we will explain the SYZ mirror symmetry conjecture and how toric geometry plays an important role here.
Xiaowei Wang (Chinese University of Hong Kong) 16:30-18:00We first review the geometry of toric varieties. Then we will explain the SYZ mirror symmetry conjecture and how toric geometry plays an important role here.
Balance point and stability of vector bundles over a projective manifold
[ Abstract ]
In this talk, we will start with some basic theory of GIT and symplectic quotient, then introduce various kind of stability of a holomorphic vector bundle over a projective manifold. As an application of the general theory, we will answer a question raised by Donaldson by showing that GIT stable vector bundle produces a sequence of balanced embedding of the underlying projective manifold to the Grassmanian.
In this talk, we will start with some basic theory of GIT and symplectic quotient, then introduce various kind of stability of a holomorphic vector bundle over a projective manifold. As an application of the general theory, we will answer a question raised by Donaldson by showing that GIT stable vector bundle produces a sequence of balanced embedding of the underlying projective manifold to the Grassmanian.
Seminar on Geometric Complex Analysis
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
泊 昌孝 (日本大学文理学部)
Classification of hypersurface simple K3 singularities -- 95 and others
泊 昌孝 (日本大学文理学部)
Classification of hypersurface simple K3 singularities -- 95 and others
Lectures
16:30-18:00 Room #122 (Graduate School of Math. Sci. Bldg.)
Heinz W. Engl (Industrial Mathematics Institute, Kepler University, Linz and Johann Radon Institute for Computational and Applied Mathematics, Austrian Academy of Sciences )
Mathematical modelling and numerical simulation: from iron and steel making via inverse problems to finance
Heinz W. Engl (Industrial Mathematics Institute, Kepler University, Linz and Johann Radon Institute for Computational and Applied Mathematics, Austrian Academy of Sciences )
Mathematical modelling and numerical simulation: from iron and steel making via inverse problems to finance
[ Abstract ]
We first describe the industrial mathematics structure in linz, extending from basic research via graduate education to industrial collaboration. We then present a few projetcs from our experience, ranging from aspects of iron and steel processing via mathematical simulation and optimization in car industry to robust and fast pricing methods for financial derivates. Since some of the projects involve inverse problem, we give a first introduction into this field, which will be deepened in the second talk.
We first describe the industrial mathematics structure in linz, extending from basic research via graduate education to industrial collaboration. We then present a few projetcs from our experience, ranging from aspects of iron and steel processing via mathematical simulation and optimization in car industry to robust and fast pricing methods for financial derivates. Since some of the projects involve inverse problem, we give a first introduction into this field, which will be deepened in the second talk.
2006/10/21
Infinite Analysis Seminar Tokyo
13:30-14:30 Room #117 (Graduate School of Math. Sci. Bldg.)
国場敦夫 (東大総合文化)
組合せベーテ仮説とタウ関数
国場敦夫 (東大総合文化)
組合せベーテ仮説とタウ関数
[ Abstract ]
組合せベーテ仮説ではベーテ根とベーテベクトルの代わりにその組合せ論的類似物として rigged configuration と highest pathを対象物とする.
これらは Kerov-Kirillov-Reshetikhin (KKR)全単射により1対1対応する.
今回のお話では rigged configuration に付随した超離散タウ関数を導入し,以下の性質,結果について(時間の許すところまで)紹介します.
アフィン・クリスタルのエネルギー関数に一致する.
超離散双線形方程式をみたす.
KKR全単射の明示公式を与える.
箱玉系の角転送行列に相当し,一般Nソリトン解を与える
周期的 highest pathでは超離散リーマンテータ関数になる.
(坂本玲峰氏,山田泰彦氏との共同研究)
組合せベーテ仮説ではベーテ根とベーテベクトルの代わりにその組合せ論的類似物として rigged configuration と highest pathを対象物とする.
これらは Kerov-Kirillov-Reshetikhin (KKR)全単射により1対1対応する.
今回のお話では rigged configuration に付随した超離散タウ関数を導入し,以下の性質,結果について(時間の許すところまで)紹介します.
アフィン・クリスタルのエネルギー関数に一致する.
超離散双線形方程式をみたす.
KKR全単射の明示公式を与える.
箱玉系の角転送行列に相当し,一般Nソリトン解を与える
周期的 highest pathでは超離散リーマンテータ関数になる.
(坂本玲峰氏,山田泰彦氏との共同研究)
Infinite Analysis Seminar Tokyo
15:00-16:00 Room #117 (Graduate School of Math. Sci. Bldg.)
小森 靖 (名古屋大学) (名古屋大学多元数理)
ルート系に付随した多重ゼータ関数とベルヌーイ多項式
小森 靖 (名古屋大学) (名古屋大学多元数理)
ルート系に付随した多重ゼータ関数とベルヌーイ多項式
[ Abstract ]
ルート系に付随した多重ゼータ関数とは E. Witten によって導入された半単純リー代数の既約表現に関するゼータ関数を松本氏が多変数化したものである. この視点から見るとリーマンゼータ関数は A_1 型であり, Euler-Zagier 多重ゼータ関数は A_n 型で適当な変数を 0 にしたものであるといえる.
講演では, 特殊値とその間の関係式, 関数関係式, 母関数および付随するベルヌーイ多項式の性質を紹介する予定である.
(松本耕二氏, 津村博文氏との共同研究)
ルート系に付随した多重ゼータ関数とは E. Witten によって導入された半単純リー代数の既約表現に関するゼータ関数を松本氏が多変数化したものである. この視点から見るとリーマンゼータ関数は A_1 型であり, Euler-Zagier 多重ゼータ関数は A_n 型で適当な変数を 0 にしたものであるといえる.
講演では, 特殊値とその間の関係式, 関数関係式, 母関数および付随するベルヌーイ多項式の性質を紹介する予定である.
(松本耕二氏, 津村博文氏との共同研究)
2006/10/20
Colloquium
16:30-17:30 Room #123 (Graduate School of Math. Sci. Bldg.)
新井 仁之 (東大・数理)
視覚科学における数学的方法
http://faculty.ms.u-tokyo.ac.jp/~seminar/colloquium.html
新井 仁之 (東大・数理)
視覚科学における数学的方法
[ Abstract ]
眼球から入った視覚情報は,網膜から始まり LGN,そして脳内で処理が行われる.この講演で扱うのはこのうち網膜から主として大脳皮質の V1 野で加えられる視覚情報処理である.研究のキーワードは「錯視」.錯視は視覚の解明のための一つの重要な鍵と考えられており,100年以上前からさまざまな方法で研究されてきた.しかし未だ不明な点が多い.本講演では,視覚情報処理の離散ウェーブレットを用いた新しい非線形数理モデルを作り,それを用いて行った色や明暗の錯視発生のメカニズムに関する研究結果を述べる.
[ Reference URL ]眼球から入った視覚情報は,網膜から始まり LGN,そして脳内で処理が行われる.この講演で扱うのはこのうち網膜から主として大脳皮質の V1 野で加えられる視覚情報処理である.研究のキーワードは「錯視」.錯視は視覚の解明のための一つの重要な鍵と考えられており,100年以上前からさまざまな方法で研究されてきた.しかし未だ不明な点が多い.本講演では,視覚情報処理の離散ウェーブレットを用いた新しい非線形数理モデルを作り,それを用いて行った色や明暗の錯視発生のメカニズムに関する研究結果を述べる.
http://faculty.ms.u-tokyo.ac.jp/~seminar/colloquium.html
Infinite Analysis Seminar Tokyo
16:30-17:30 Room #118 (Graduate School of Math. Sci. Bldg.)
Petr Kulish (Steklov Math. Inst.)
Spin systems related to Temperley - Lieb algebra
Petr Kulish (Steklov Math. Inst.)
Spin systems related to Temperley - Lieb algebra
2006/10/19
Operator Algebra Seminars
16:30-18:00 Room #126 (Graduate School of Math. Sci. Bldg.)
酒匂宏樹 (東大数理)
A unique decomposition result for HT factors with torsion free core (Popa の論文の紹介)
酒匂宏樹 (東大数理)
A unique decomposition result for HT factors with torsion free core (Popa の論文の紹介)
2006/10/18
Number Theory Seminar
16:30-18:45 Room #117 (Graduate School of Math. Sci. Bldg.)
Fabrice Orgogozo (東大数理・Ecole Polytechnique de Paris) 16:30-17:30
p-dimension of henselian fields: an application of Ofer Gabber's algebraization technique
Kim Minhyong (Purdue大学・京大数理研) 17:45-18:45
Fundamental groups and Diophantine geometry
Fabrice Orgogozo (東大数理・Ecole Polytechnique de Paris) 16:30-17:30
p-dimension of henselian fields: an application of Ofer Gabber's algebraization technique
Kim Minhyong (Purdue大学・京大数理研) 17:45-18:45
Fundamental groups and Diophantine geometry
Seminar on Probability and Statistics
16:20-17:30 Room #128 (Graduate School of Math. Sci. Bldg.)
松田 安昌 (東北大学大学院経済学研究科)
Fourier analysis of irregularly spaced data on R^d
https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2006/11.html
松田 安昌 (東北大学大学院経済学研究科)
Fourier analysis of irregularly spaced data on R^d
[ Abstract ]
1970年代にはじまった時系列解析の研究は、1変量時系列からはじまり、多変量時系列、空間系列、時空間系列へと対象が拡張されてきている。近年の空間系列、時空間系列の文献を調べてみれば、時系列と同じく等間隔に観測されたデータ(regularly spaced data) を前提としている場合が多い。しかし時系列とは異なり、空間系列ではランダムに散らばった地点で観測されたデータ (irregularly spaced data)を仮定する方が、応用範囲がひろい。そこで本発表では、irregularly spaced dataによる空間相関の推定問題を扱う。具体的にはデータを周波数領域に変換してスペクトルを推定する方法を提案し、推定量が一致性、漸近正規性を持つための条件を示す。本方法による東京地価データ分析例も紹介する。本研究は、矢島美寛教授(東京大学大学院経済学研究科)との共同研究です。
[ Reference URL ]1970年代にはじまった時系列解析の研究は、1変量時系列からはじまり、多変量時系列、空間系列、時空間系列へと対象が拡張されてきている。近年の空間系列、時空間系列の文献を調べてみれば、時系列と同じく等間隔に観測されたデータ(regularly spaced data) を前提としている場合が多い。しかし時系列とは異なり、空間系列ではランダムに散らばった地点で観測されたデータ (irregularly spaced data)を仮定する方が、応用範囲がひろい。そこで本発表では、irregularly spaced dataによる空間相関の推定問題を扱う。具体的にはデータを周波数領域に変換してスペクトルを推定する方法を提案し、推定量が一致性、漸近正規性を持つための条件を示す。本方法による東京地価データ分析例も紹介する。本研究は、矢島美寛教授(東京大学大学院経済学研究科)との共同研究です。
https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2006/11.html
Algebraic Geometry Seminar
16:00-18:15 Room #122 (Graduate School of Math. Sci. Bldg.)
E. Esteves (IMPA) 16:00-17:00
Jets of singular foliations and applications
to curves and their moduli spaces
F. Zak (Independent Univ. of Moscow) 17:15-18:15
Dual varieties, ramification, and Betti numbers
of projective varieties
E. Esteves (IMPA) 16:00-17:00
Jets of singular foliations and applications
to curves and their moduli spaces
F. Zak (Independent Univ. of Moscow) 17:15-18:15
Dual varieties, ramification, and Betti numbers
of projective varieties
2006/10/17
Tuesday Seminar on Topology
16:30-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)
Arnaud Deruelle (University of Tokyo)
Networking Seifert Fibered Surgeries on Knots (joint work with Katura Miyazaki and Kimihiko Motegi)
Arnaud Deruelle (University of Tokyo)
Networking Seifert Fibered Surgeries on Knots (joint work with Katura Miyazaki and Kimihiko Motegi)
[ Abstract ]
We define a Seifert Surgery Network which consists of integral Dehn surgeries on knots yielding Seifert fiber spaces;here we allow Seifert fiber space with a fiber of index zero as degenerate cases. Then we establish some fundamental properties of the network. Using the notion of the network, we will clarify relationships among known Seifert surgeries. In particular, we demonstrate that many Seifert surgeries are closely connected to those on torus knots in Seifert Surgery Network. Our study suggests that the network enables us to make a global picture of Seifert surgeries.
We define a Seifert Surgery Network which consists of integral Dehn surgeries on knots yielding Seifert fiber spaces;here we allow Seifert fiber space with a fiber of index zero as degenerate cases. Then we establish some fundamental properties of the network. Using the notion of the network, we will clarify relationships among known Seifert surgeries. In particular, we demonstrate that many Seifert surgeries are closely connected to those on torus knots in Seifert Surgery Network. Our study suggests that the network enables us to make a global picture of Seifert surgeries.
2006/10/16
Seminar on Geometric Complex Analysis
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Sebastien Boucksom (東大数理 JSPS研究員)
Differentiability of the volume of divisors and Khovanskii-Teissier inequalities
Sebastien Boucksom (東大数理 JSPS研究員)
Differentiability of the volume of divisors and Khovanskii-Teissier inequalities
2006/10/12
Operator Algebra Seminars
16:30-18:00 Room #126 (Graduate School of Math. Sci. Bldg.)
酒匂宏樹 (東大数理)
保測同値関係の Haagerup property
酒匂宏樹 (東大数理)
保測同値関係の Haagerup property
2006/10/11
Seminar on Probability and Statistics
16:20-17:30 Room #128 (Graduate School of Math. Sci. Bldg.)
石川保志 (愛媛大学)
Optimal stopping problem associated with jump-diffusion processes
石川保志 (愛媛大学)
Optimal stopping problem associated with jump-diffusion processes
[ Abstract ]
We study an optimal stopping problem of some performance function with respect to a jump-diffusion process.
We study an optimal stopping problem of some performance function with respect to a jump-diffusion process.
2006/10/10
Tuesday Seminar on Topology
16:30-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)
Elmar Vogt (Frie Universitat Berlin)
Estimating Lusternik-Schnirelmann Category for Foliations:A Survey of Available Techniques
Elmar Vogt (Frie Universitat Berlin)
Estimating Lusternik-Schnirelmann Category for Foliations:A Survey of Available Techniques
[ Abstract ]
The Lusternik-Schnirelmann category of a space $X$ is the smallest number $r$ such that $X$ can be covered by $r + 1$ open sets which are contractible in $X$.For foliated manifolds there are several notions generalizing this concept, all of them due
to Helen Colman. We are mostly concerned with the concept of tangential Lusternik-Schnirelmann category (tangential LS-category). Here one requires a covering by open sets $U$ with the following property. There is a leafwise homotopy starting with the inclusion of $U$ and ending in a map that throws for each leaf $F$ of the foliation each component of $U \\cap F$ onto a single point. A leafwise homotopy is a homotopy moving points only inside leaves. Rather than presenting the still very few results obtained about the LS category of foliations, we survey techniques, mostly quite elementary, to estimate the tangential LS-category from below and above.
The Lusternik-Schnirelmann category of a space $X$ is the smallest number $r$ such that $X$ can be covered by $r + 1$ open sets which are contractible in $X$.For foliated manifolds there are several notions generalizing this concept, all of them due
to Helen Colman. We are mostly concerned with the concept of tangential Lusternik-Schnirelmann category (tangential LS-category). Here one requires a covering by open sets $U$ with the following property. There is a leafwise homotopy starting with the inclusion of $U$ and ending in a map that throws for each leaf $F$ of the foliation each component of $U \\cap F$ onto a single point. A leafwise homotopy is a homotopy moving points only inside leaves. Rather than presenting the still very few results obtained about the LS category of foliations, we survey techniques, mostly quite elementary, to estimate the tangential LS-category from below and above.
2006/10/06
Mathematical Biology Seminar
16:30-17:30 Room #123 (Graduate School of Math. Sci. Bldg.)
石井 太 (国立社会保障・人口問題研究所)
人口指標の精度について
石井 太 (国立社会保障・人口問題研究所)
人口指標の精度について
[ Abstract ]
近年の急速な少子化の進行に伴い、出生率の動向への関心が高まっている。しかしながら、その指標が注目され、様々に論じられる中に、指標の持つ精度を度外視した議論なども見受けられる。人口統計は人口分析の中心となるデータソースであり、人口指標の精度は重要な問題であるが、わが国においてはこれまで比較的精度の高い人口統計が取得されてきたこともあり、それほど重視せず、確定的なものと捉えがちな傾向があったように思われる。一方では、近年、統計調査環境の悪化などもあり、各々の人口指標についてどこまで詳細な議論が可能なのか、指標の精度について理論的・実務的な観点からより深い認識を持つことが必要となってきている。
本報告では、出生率での具体例を中心に、さまざまな誤差の発生要因に応じた人口指標の評価について提示することとしたい。
近年の急速な少子化の進行に伴い、出生率の動向への関心が高まっている。しかしながら、その指標が注目され、様々に論じられる中に、指標の持つ精度を度外視した議論なども見受けられる。人口統計は人口分析の中心となるデータソースであり、人口指標の精度は重要な問題であるが、わが国においてはこれまで比較的精度の高い人口統計が取得されてきたこともあり、それほど重視せず、確定的なものと捉えがちな傾向があったように思われる。一方では、近年、統計調査環境の悪化などもあり、各々の人口指標についてどこまで詳細な議論が可能なのか、指標の精度について理論的・実務的な観点からより深い認識を持つことが必要となってきている。
本報告では、出生率での具体例を中心に、さまざまな誤差の発生要因に応じた人口指標の評価について提示することとしたい。
2006/10/05
Seminar on Mathematics for various disciplines
16:30-17:30 Room #123 (Graduate School of Math. Sci. Bldg.)
成田誠 (Department of Mathematics, National Taiwan University)
Global existence and asymptotic behavior of Gowdy symmetric spacetimes with nonlinear scalar field
http://coe.math.sci.hokudai.ac.jp/sympo/various/index.html
成田誠 (Department of Mathematics, National Taiwan University)
Global existence and asymptotic behavior of Gowdy symmetric spacetimes with nonlinear scalar field
[ Abstract ]
We study global properties of Gowdy symmetric (the existence of a symmetry group with two-dimensional spacelike orbits) spacetimes with nonlinear scalar field, which naturally arises in modern cosmology based on superstring theory.
The system of the Einstein and scalar field equations becomes a system consisting of wave map and nonlinear wave equations in one space dimension. We prove a global existence theorem for this system. Also, asymptotic energy decay will be discussed.
[ Reference URL ]We study global properties of Gowdy symmetric (the existence of a symmetry group with two-dimensional spacelike orbits) spacetimes with nonlinear scalar field, which naturally arises in modern cosmology based on superstring theory.
The system of the Einstein and scalar field equations becomes a system consisting of wave map and nonlinear wave equations in one space dimension. We prove a global existence theorem for this system. Also, asymptotic energy decay will be discussed.
http://coe.math.sci.hokudai.ac.jp/sympo/various/index.html
2006/09/27
PDE Real Analysis Seminar
10:30-11:30 Room #056 (Graduate School of Math. Sci. Bldg.)
Professor Vakhtang Kokilashvili (A. Razmadze Mathematical Institute, Georgian Academy of Science)
Integral operators in the weighted Lebesgue spaces with a variable exponent
http://coe.math.sci.hokudai.ac.jp/sympo/pde_ra/index.html
Professor Vakhtang Kokilashvili (A. Razmadze Mathematical Institute, Georgian Academy of Science)
Integral operators in the weighted Lebesgue spaces with a variable exponent
[ Abstract ]
We present a boundedness criteria of the maximal functions and the singular integral operators defined on Carleson curves in the weighted Lebesgue spaces with a variable exponent. There are also given the weighted estimates for the generalized singular integrals raised in the theory of generalized analytic functions of I.N.Vekua and the weighted Sobolev theorems for potentials on Carleson curves. The weight functions may be of power function type as well as oscillating type. The certain version of a Muckenhoupt-type condition for a variable exponent will be considered.
We also expect to treat two-weight problems for the classical integral operators in the variable Lebesgue spaces and to give some applications of the obtained results to the summability problems of Fourier series in two-weighted setting.
[ Reference URL ]We present a boundedness criteria of the maximal functions and the singular integral operators defined on Carleson curves in the weighted Lebesgue spaces with a variable exponent. There are also given the weighted estimates for the generalized singular integrals raised in the theory of generalized analytic functions of I.N.Vekua and the weighted Sobolev theorems for potentials on Carleson curves. The weight functions may be of power function type as well as oscillating type. The certain version of a Muckenhoupt-type condition for a variable exponent will be considered.
We also expect to treat two-weight problems for the classical integral operators in the variable Lebesgue spaces and to give some applications of the obtained results to the summability problems of Fourier series in two-weighted setting.
http://coe.math.sci.hokudai.ac.jp/sympo/pde_ra/index.html
Mathematical Biology Seminar
16:30-17:30 Room #123 (Graduate School of Math. Sci. Bldg.)
中丸麻由子 (東京工業大学)
The coevolution of altruism and punishment:role of the selfish punisher
中丸麻由子 (東京工業大学)
The coevolution of altruism and punishment:role of the selfish punisher
[ Abstract ]
Punishment is an important mechanism promoting the evolution of altruism among nonrelatives. We investigate the coevolution of altruism and punitive behavior, considering four strategies: a cooperator who punishes defectors (AP), a pure cooperator (AN), a defector who punishes defectors (selfish punisher or SP), and a pure defector (SN). We especially focus on the effects of SP on the coevolution of altruism and punishment, studying both the score-dependent viability model (whereby the game's score affects survivorship only) and the score-dependent fertility model (whereby the score affects fertility only). In the viability model of a completely mixed population, SP helps cooperators to evolve, but SP does not in the fertility model. In both models of a lattice-structured population, SP promotes the spread of AP, but AN discourages it. These results indicate that punishment is a form of spite behavior and that different models give different magnitude of advantage to spite behavior.
Punishment is an important mechanism promoting the evolution of altruism among nonrelatives. We investigate the coevolution of altruism and punitive behavior, considering four strategies: a cooperator who punishes defectors (AP), a pure cooperator (AN), a defector who punishes defectors (selfish punisher or SP), and a pure defector (SN). We especially focus on the effects of SP on the coevolution of altruism and punishment, studying both the score-dependent viability model (whereby the game's score affects survivorship only) and the score-dependent fertility model (whereby the score affects fertility only). In the viability model of a completely mixed population, SP helps cooperators to evolve, but SP does not in the fertility model. In both models of a lattice-structured population, SP promotes the spread of AP, but AN discourages it. These results indicate that punishment is a form of spite behavior and that different models give different magnitude of advantage to spite behavior.
2006/09/25
Seminar on Probability and Statistics
13:00-14:10 Room #128 (Graduate School of Math. Sci. Bldg.)
西山 陽一 (統計数理研究所)
Nonparametric testing time-homogeneity for L'evy processes
https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2006/09.html
西山 陽一 (統計数理研究所)
Nonparametric testing time-homogeneity for L'evy processes
[ Abstract ]
First, a review about uniform central limit theorems for martingales is given. The main part of the talk is concerned with a change point problem for L'evy processes. The null hypothesis is that the L'evy process is time-homogeneous, and the alternative is that the L'evy measure changes at a certain time point of the observation period. We propose an empirical process type statistics, and derive its asymptotic behaviour under the null and the alternative hypotheses. The limiting distribution under the null hypothesis is a functional of the standard Brownian motion.
[ Reference URL ]First, a review about uniform central limit theorems for martingales is given. The main part of the talk is concerned with a change point problem for L'evy processes. The null hypothesis is that the L'evy process is time-homogeneous, and the alternative is that the L'evy measure changes at a certain time point of the observation period. We propose an empirical process type statistics, and derive its asymptotic behaviour under the null and the alternative hypotheses. The limiting distribution under the null hypothesis is a functional of the standard Brownian motion.
https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2006/09.html
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