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過去の記録
過去の記録 ～05/22｜本日 05/23 | 今後の予定 05/24～
東京無限可積分系セミナー
16:00-17:00 数理科学研究科棟(駒場) 002号室
Andrew Kels 氏 (東大総合文化)
Integrable quad equations derived from the quantum Yang-Baxter
equation. (ENGLISH)
Andrew Kels 氏 (東大総合文化)
Integrable quad equations derived from the quantum Yang-Baxter
equation. (ENGLISH)
[ 講演概要 ]
I will give an overview of an explicit correspondence that exists between
two different types of integrable equations; 1) the quantum Yang-Baxter
equation in its star-triangle relation (STR) form, and 2) the classical
3D-consistent quad equations in the Adler-Bobenko-Suris (ABS)
classification. The fundamental aspect of this correspondence is that the
equation of the critical point of a STR is equivalent to an ABS quad
equation. The STR's considered here are in fact equivalent to
hypergeometric integral transformation formulas. For example, a STR for
$H1_{(\varepsilon=0)}$ corresponds to the Euler Beta function, a STR for
$Q1_{(\delta=0)}$ corresponds to the $n=1$ Selberg integral, and STR's for
$H2_{\varepsilon=0,1}$, $H1_{(\varepsilon=1)}$, correspond to different
hypergeometric integral formulas of Barnes. I will discuss some of these
examples and some directions for future research.
I will give an overview of an explicit correspondence that exists between
two different types of integrable equations; 1) the quantum Yang-Baxter
equation in its star-triangle relation (STR) form, and 2) the classical
3D-consistent quad equations in the Adler-Bobenko-Suris (ABS)
classification. The fundamental aspect of this correspondence is that the
equation of the critical point of a STR is equivalent to an ABS quad
equation. The STR's considered here are in fact equivalent to
hypergeometric integral transformation formulas. For example, a STR for
$H1_{(\varepsilon=0)}$ corresponds to the Euler Beta function, a STR for
$Q1_{(\delta=0)}$ corresponds to the $n=1$ Selberg integral, and STR's for
$H2_{\varepsilon=0,1}$, $H1_{(\varepsilon=1)}$, correspond to different
hypergeometric integral formulas of Barnes. I will discuss some of these
examples and some directions for future research.
応用解析セミナー
16:00-17:30 数理科学研究科棟(駒場) 118号室
山本 宏子 氏 (東京大学)
いくつかの微分方程式に対する反応拡散近似 (Japanese)
山本 宏子 氏 (東京大学)
いくつかの微分方程式に対する反応拡散近似 (Japanese)
[ 講演概要 ]
本研究は，二宮広和氏（明治大学），田中吉太郎氏（はこだて未来大学）との共同研究に基づく結果を含んだものである．反応拡散系は連立の非線型放物型方程式で表され，化学反応系や燃焼系，生物系など，多くのモデル方程式に現れる．本研究では，反応拡散系の解の大域的挙動や方程式のクラスを調べることを目的として，反応拡散系により近似可能な方程式系を考察する．この近似は反応拡散近似と呼ばれる．例えばD. Hilhorst, R. van der Hout, L. A. Peletier(1996)により，単純な二成分の反応拡散系の解は，一相Stefan問題の近似解になることが示された．また非線型拡散問題に関しては，交差拡散系と呼ばれる準線型放物型方程式の解の近似を行った飯田-三村-二宮(2006)や，多孔性媒質方程式などの退化する非線型拡散問題の解析の難しさを解消した村川(2007)などの結果が知られている．本講演では，ある非局所発展方程式と半線形波動方程式の反応拡散近似に関する結果を報告する．
本研究は，二宮広和氏（明治大学），田中吉太郎氏（はこだて未来大学）との共同研究に基づく結果を含んだものである．反応拡散系は連立の非線型放物型方程式で表され，化学反応系や燃焼系，生物系など，多くのモデル方程式に現れる．本研究では，反応拡散系の解の大域的挙動や方程式のクラスを調べることを目的として，反応拡散系により近似可能な方程式系を考察する．この近似は反応拡散近似と呼ばれる．例えばD. Hilhorst, R. van der Hout, L. A. Peletier(1996)により，単純な二成分の反応拡散系の解は，一相Stefan問題の近似解になることが示された．また非線型拡散問題に関しては，交差拡散系と呼ばれる準線型放物型方程式の解の近似を行った飯田-三村-二宮(2006)や，多孔性媒質方程式などの退化する非線型拡散問題の解析の難しさを解消した村川(2007)などの結果が知られている．本講演では，ある非局所発展方程式と半線形波動方程式の反応拡散近似に関する結果を報告する．
2018年10月03日(水)
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
安藤浩志 氏 (千葉大)
Structure of bicentralizer algebras and inclusions of type III factors
安藤浩志 氏 (千葉大)
Structure of bicentralizer algebras and inclusions of type III factors
2018年10月02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
鮑 園園 氏 (東京大学大学院数理科学研究科)
An Alexander polynomial for MOY graphs (JAPANESE)
Tea: Common Room 16:30-17:00
鮑 園園 氏 (東京大学大学院数理科学研究科)
An Alexander polynomial for MOY graphs (JAPANESE)
[ 講演概要 ]
An MOY graph is a trivalent graph equipped with a balanced coloring. In this talk, we define a version of Alexander polynomial for an MOY graph. This polynomial is the Euler characteristic of the Heegaard Floer homology of an MOY graph. We give a characterization of the polynomial, which we call MOY-type relations, and show that it is equivalent to Viro’s gl(1 | 1)-Alexander polynomial of a graph. (A part of the talk is a joint work of Zhongtao Wu)
An MOY graph is a trivalent graph equipped with a balanced coloring. In this talk, we define a version of Alexander polynomial for an MOY graph. This polynomial is the Euler characteristic of the Heegaard Floer homology of an MOY graph. We give a characterization of the polynomial, which we call MOY-type relations, and show that it is equivalent to Viro’s gl(1 | 1)-Alexander polynomial of a graph. (A part of the talk is a joint work of Zhongtao Wu)
2018年09月25日(火)
東京無限可積分系セミナー
16:00-17:00 数理科学研究科棟(駒場) 002号室
中園信孝 氏 (青山学院大学 理工学部物理・数理学科)
Classification of quad-equations on a cuboctahedron (JAPANESE)
中園信孝 氏 (青山学院大学 理工学部物理・数理学科)
Classification of quad-equations on a cuboctahedron (JAPANESE)
[ 講演概要 ]
Adelr-Bobenko-Suris(2003,2009)とBoll(2011)による立方体上のConsistencyを用いた4点の関係式(quad-equation)の分類が知られている．この立方体上のConsistencyにより可積分な2次元偏差分方程式(ABS方程式)が定義できる．ABS方程式の代表的なものとして，modified KdV equationの離散版であるlattice modified KdV equationなどがある．また，ABS方程式はその構成方法からラックス形式やベックルンド変換などの可積分な性質を持ち，さらに，相似簡約による離散および微分のパンルヴェ方程式への簡約があることも知られている．本講演では，立法八面体上のConsistencyによるquad-equationの分類およびそのConsistencyにより定義される偏差分方程式と離散パンルヴェ方程式の関係について説明する．本研究は，Nalini Joshi氏(シドニー大学)との共同研究である．
Adelr-Bobenko-Suris(2003,2009)とBoll(2011)による立方体上のConsistencyを用いた4点の関係式(quad-equation)の分類が知られている．この立方体上のConsistencyにより可積分な2次元偏差分方程式(ABS方程式)が定義できる．ABS方程式の代表的なものとして，modified KdV equationの離散版であるlattice modified KdV equationなどがある．また，ABS方程式はその構成方法からラックス形式やベックルンド変換などの可積分な性質を持ち，さらに，相似簡約による離散および微分のパンルヴェ方程式への簡約があることも知られている．本講演では，立法八面体上のConsistencyによるquad-equationの分類およびそのConsistencyにより定義される偏差分方程式と離散パンルヴェ方程式の関係について説明する．本研究は，Nalini Joshi氏(シドニー大学)との共同研究である．
2018年09月21日(金)
講演会
17:00-18:00 数理科学研究科棟(駒場) 056号室
Laurent Fargues 氏 (CNRS, Institut Mathématique de Jussieu)
On the geometry of some p-adic period domains (ENGLISH)
Laurent Fargues 氏 (CNRS, Institut Mathématique de Jussieu)
On the geometry of some p-adic period domains (ENGLISH)
[ 講演概要 ]
p-adic period spaces have been introduced by Rapoport and Zink as a generalization of Drinfeld upper half spaces and Lubin-Tate spaces. Those are open subsets of a rigid analytic p-adic flag manifold. An approximation of this open subset is the so called weakly admissible locus obtained by removing a profinite set of closed Schubert varieties. I will explain a recent theorem characterizing when the period space coincides with the weakly admissible locus. As an application we can compute the p-adic period space of K3 surfaces with supersingular reduction. The talk will be mainly introductory, presenting the objects showing up in this theorem. This is joint work with Miaofen Chen and Xu Shen.
p-adic period spaces have been introduced by Rapoport and Zink as a generalization of Drinfeld upper half spaces and Lubin-Tate spaces. Those are open subsets of a rigid analytic p-adic flag manifold. An approximation of this open subset is the so called weakly admissible locus obtained by removing a profinite set of closed Schubert varieties. I will explain a recent theorem characterizing when the period space coincides with the weakly admissible locus. As an application we can compute the p-adic period space of K3 surfaces with supersingular reduction. The talk will be mainly introductory, presenting the objects showing up in this theorem. This is joint work with Miaofen Chen and Xu Shen.
2018年09月18日(火)
講演会
17:00-18:00 数理科学研究科棟(駒場) 056号室
Alexander Beilinson 氏 (University of Chicago)
Topological epsilon-factors (ENGLISH)
Alexander Beilinson 氏 (University of Chicago)
Topological epsilon-factors (ENGLISH)
[ 講演概要 ]
I will explain (following mostly my old article arXiv:0610055) how the Kashiwara-Shapira Morse theory construction of the characteristic cycle of a constructible R-sheaf can be refined to yield the cycle with coefficients in the K-theory spectrum K(R). The construction can be viewed as a topological analog of the arithmetic theory of epsilon-factors.
I will explain (following mostly my old article arXiv:0610055) how the Kashiwara-Shapira Morse theory construction of the characteristic cycle of a constructible R-sheaf can be refined to yield the cycle with coefficients in the K-theory spectrum K(R). The construction can be viewed as a topological analog of the arithmetic theory of epsilon-factors.
2018年08月24日(金)
博士論文発表会
13:30-14:45 数理科学研究科棟(駒場) 128号室
佐藤 謙太 氏 (東京大学大学院数理科学研究科)
Studies on the ascending chain condition for F-pure thresholds
(F純閾値の昇鎖条件に関する研究）
(JAPANESE)
佐藤 謙太 氏 (東京大学大学院数理科学研究科)
Studies on the ascending chain condition for F-pure thresholds
(F純閾値の昇鎖条件に関する研究）
(JAPANESE)
作用素環セミナー
16:45-18:15 数理科学研究科棟(駒場) 002号室
Lucas Teyssier 氏 (Ecole Normale Superieure)
Limit profile for the card shuffle by random transpositions
Lucas Teyssier 氏 (Ecole Normale Superieure)
Limit profile for the card shuffle by random transpositions
2018年08月08日(水)
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
Srinivasan Raman 氏 (Chennai Mathematical Institute)
$E_0$-semigroups on factors
Srinivasan Raman 氏 (Chennai Mathematical Institute)
$E_0$-semigroups on factors
2018年07月31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 (京都大学)
長距離型N体問題における散乱行列、一般化フーリエ変換及び伝播評価 (日本語)
蘆田聡平 氏 (京都大学)
長距離型N体問題における散乱行列、一般化フーリエ変換及び伝播評価 (日本語)
[ 講演概要 ]
本講演では長距離型ポテンシャルによるN体問題における散乱行列の一般化固有関数の遠方での漸近挙動に基いた定義を与え、そのようにして得られた散乱行列が波動作用素によって得られる散乱行列と等価であることを示す。また、一般化フーリエ変換を非斉次方程式の外向き進行波解の遠方での漸近挙動よって定義し、その共役作用素がポアソン作用素により与えられることを示す。さらに、クラスターが２つである散乱チャネルに対する新しい改良された伝播評価を散乱チャネルに近い概不変部分空間への正射影作用素を用いて与える。
本講演では長距離型ポテンシャルによるN体問題における散乱行列の一般化固有関数の遠方での漸近挙動に基いた定義を与え、そのようにして得られた散乱行列が波動作用素によって得られる散乱行列と等価であることを示す。また、一般化フーリエ変換を非斉次方程式の外向き進行波解の遠方での漸近挙動よって定義し、その共役作用素がポアソン作用素により与えられることを示す。さらに、クラスターが２つである散乱チャネルに対する新しい改良された伝播評価を散乱チャネルに近い概不変部分空間への正射影作用素を用いて与える。
数値解析セミナー
14:00-15:00 数理科学研究科棟(駒場) 056号室
Jichun Li 氏 (University of Nevada Las Vegas)
Recent advances on numerical analysis and simulation of invisibility cloaks with metamaterials (English)
Jichun Li 氏 (University of Nevada Las Vegas)
Recent advances on numerical analysis and simulation of invisibility cloaks with metamaterials (English)
[ 講演概要 ]
In the June 23, 2006's issue of Science magazine, Pendry et al. and Leonhardt independently published their seminar papers on electromagnetic cloaking. Since then, there is a growing interest in using metamaterials to design invisibility cloaks. In this talk, I will first give a brief introduction to invisibility cloaks with metamaterials, then I will focus on some time-domain cloaking models we studied in the last few years. Well-posedness study and time-domain finite element method for these models will be presented. I will conclude the talk with some open issues.
In the June 23, 2006's issue of Science magazine, Pendry et al. and Leonhardt independently published their seminar papers on electromagnetic cloaking. Since then, there is a growing interest in using metamaterials to design invisibility cloaks. In this talk, I will first give a brief introduction to invisibility cloaks with metamaterials, then I will focus on some time-domain cloaking models we studied in the last few years. Well-posedness study and time-domain finite element method for these models will be presented. I will conclude the talk with some open issues.
2018年07月30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) 126号室
早瀬 友裕 氏 (東京大学大学院数理科学研究科)
自由確率論によるランダム行列モデルのパラメータ推定 (JAPANESE)
https://www.ms.u-tokyo.ac.jp/~hayase/
早瀬 友裕 氏 (東京大学大学院数理科学研究科)
自由確率論によるランダム行列モデルのパラメータ推定 (JAPANESE)
[ 講演概要 ]
ランダム行列モデルにおいて, サンプル行列がひとつしかなければ, 経験尤度関数に基づいたパラメータ推定は様々な（現実的でない）仮定が必要です. 今回, 経験尤度ではなく経験固有値分布に基づいた,そのような仮定を必要としない手法を紹介します. ひとつのポイントは, 経験固有値分布をCauchy noiseで摂動させた分布を使うことです. この摂動された分布を使うのは, (自由確率論のFree Deterministic Equivalentという良い道具に基づき）, それがなめらかでアクセス可能な密度を持つ分布でfittingされるからです.
加えて, 確率的主成分分析などに現れるランダム行列モデルのパラメータ推定, ランク推定に有効であること, 真の信号が極端に低ランクでなくても, 当手法が真のランクを推定することを紹介します.
[ 参考URL ]ランダム行列モデルにおいて, サンプル行列がひとつしかなければ, 経験尤度関数に基づいたパラメータ推定は様々な（現実的でない）仮定が必要です. 今回, 経験尤度ではなく経験固有値分布に基づいた,そのような仮定を必要としない手法を紹介します. ひとつのポイントは, 経験固有値分布をCauchy noiseで摂動させた分布を使うことです. この摂動された分布を使うのは, (自由確率論のFree Deterministic Equivalentという良い道具に基づき）, それがなめらかでアクセス可能な密度を持つ分布でfittingされるからです.
加えて, 確率的主成分分析などに現れるランダム行列モデルのパラメータ推定, ランク推定に有効であること, 真の信号が極端に低ランクでなくても, 当手法が真のランクを推定することを紹介します.
https://www.ms.u-tokyo.ac.jp/~hayase/
2018年07月27日(金)
数理人口学・数理生物学セミナー
15:00-16:00 数理科学研究科棟(駒場) 118号室
Somdatta Sinha 氏 (Department of Biological Sciences, Indian Institute of Science Education and Research (IISER) Mohali INDIA)
Modelling Malaria in India: Statistical, Mathematical and Graphical Approaches
Somdatta Sinha 氏 (Department of Biological Sciences, Indian Institute of Science Education and Research (IISER) Mohali INDIA)
Modelling Malaria in India: Statistical, Mathematical and Graphical Approaches
[ 講演概要 ]
Malaria has existed in India since antiquity. Different periods of
elimination and control policies have been adopted by the government for
tackling the disease. Malaria parasite was dissevered in India by Sir
Ronald Ross who also developed the simplest mathematical model in early
1900. Malaria modelling has since come through many variations that
incorporated various intrinsic and extrinsic/environmental factors to
describe the disease progression in population. Collection of disease
incidence and prevalence data, however, has been quite variable with both
governmental and non-governmental agencies independently collecting data at
different space and time scales. In this talk I will describe our work on
modelling malaria prevalence using three different approaches. For monthly
prevalence data, I will discuss (i) a regression-based statistical model
based on a specific data-set, and (ii) a general mathematical model that
fits the same data. For more coarse-grained temporal (yearly) data, I will
show graphical analysis that uncovers some useful information from the mass
of data tables. This presentation aims to highlight the suitability of
multiple modelling methods for disease prevalence from variable quality data.
Malaria has existed in India since antiquity. Different periods of
elimination and control policies have been adopted by the government for
tackling the disease. Malaria parasite was dissevered in India by Sir
Ronald Ross who also developed the simplest mathematical model in early
1900. Malaria modelling has since come through many variations that
incorporated various intrinsic and extrinsic/environmental factors to
describe the disease progression in population. Collection of disease
incidence and prevalence data, however, has been quite variable with both
governmental and non-governmental agencies independently collecting data at
different space and time scales. In this talk I will describe our work on
modelling malaria prevalence using three different approaches. For monthly
prevalence data, I will discuss (i) a regression-based statistical model
based on a specific data-set, and (ii) a general mathematical model that
fits the same data. For more coarse-grained temporal (yearly) data, I will
show graphical analysis that uncovers some useful information from the mass
of data tables. This presentation aims to highlight the suitability of
multiple modelling methods for disease prevalence from variable quality data.
2018年07月26日(木)
数値解析セミナー
16:00-17:30 数理科学研究科棟(駒場) 056号室
柏原崇人 氏 (東京大学大学院数理科学研究科)
滑らかな領域における楕円型・放物型ノイマン境界値問題に対する有限要素法の$L^\infty$誤差評価について (日本語)
柏原崇人 氏 (東京大学大学院数理科学研究科)
滑らかな領域における楕円型・放物型ノイマン境界値問題に対する有限要素法の$L^\infty$誤差評価について (日本語)
[ 講演概要 ]
楕円型および放物型問題に対する$L^\infty$ノルム（最大値ノルム）による汎用的な誤差評価手法の開発については，1970年代のJ.A. Nitsche, A.H. Schatz, L.B. Wahlbinを含む先駆者の研究以来，多くの貢献がなされ，現在では標準的な証明法が確立されたと言える状況にある．一方で，有限要素法で滑らかな領域（曲がった境界を持つ領域）を扱う際は，多角形や多面体領域で近似した上で三角形分割・有限要素空間の導入・定式化を行うのが最も基本的であるが，そのような領域近似（領域摂動）に伴う誤差を考慮した厳密な$L^\infty$誤差解析は，斉次ディリクレ境界条件の場合しか知られていないと思われる．本講演では，ポアソン方程式と熱方程式の非斉次ノイマン問題に対して，領域摂動誤差を考慮した$L^\infty$誤差評価を考察し，$O(h^2 |\log h|)$すなわち領域摂動なしのP1要素の場合と同等の評価が得られたことを報告する．証明の鍵は，汎用的な誤差評価手法において複数回用いられるガラーキン直交性が厳密には成立しなくなるものの，メッシュサイズが0になる極限のもとで漸近的に成り立つことを領域摂動評価を用いて示す点にある．
楕円型および放物型問題に対する$L^\infty$ノルム（最大値ノルム）による汎用的な誤差評価手法の開発については，1970年代のJ.A. Nitsche, A.H. Schatz, L.B. Wahlbinを含む先駆者の研究以来，多くの貢献がなされ，現在では標準的な証明法が確立されたと言える状況にある．一方で，有限要素法で滑らかな領域（曲がった境界を持つ領域）を扱う際は，多角形や多面体領域で近似した上で三角形分割・有限要素空間の導入・定式化を行うのが最も基本的であるが，そのような領域近似（領域摂動）に伴う誤差を考慮した厳密な$L^\infty$誤差解析は，斉次ディリクレ境界条件の場合しか知られていないと思われる．本講演では，ポアソン方程式と熱方程式の非斉次ノイマン問題に対して，領域摂動誤差を考慮した$L^\infty$誤差評価を考察し，$O(h^2 |\log h|)$すなわち領域摂動なしのP1要素の場合と同等の評価が得られたことを報告する．証明の鍵は，汎用的な誤差評価手法において複数回用いられるガラーキン直交性が厳密には成立しなくなるものの，メッシュサイズが0になる極限のもとで漸近的に成り立つことを領域摂動評価を用いて示す点にある．
博士論文発表会
13:00-14:15 数理科学研究科棟(駒場) 128号室
吉田 純 氏 (東京大学大学院数理科学研究科)
Categories of operators for multicategories with various symmetries
(多彩な対称性を持つマルチ圏のオペレーターの圏)
(JAPANESE)
吉田 純 氏 (東京大学大学院数理科学研究科)
Categories of operators for multicategories with various symmetries
(多彩な対称性を持つマルチ圏のオペレーターの圏)
(JAPANESE)
2018年07月25日(水)
FMSPレクチャーズ
10:15-12:15 数理科学研究科棟(駒場) 118号室
集中講義901-118「数物先端科学X」として行われます（7/18,20,23,24,25の全5回）。
Christian Schnell 氏 (Stony Book University)
Singular hermitian metrics and morphisms to abelian varieties (ENGLISH)
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Schnell.pdf
集中講義901-118「数物先端科学X」として行われます（7/18,20,23,24,25の全5回）。
Christian Schnell 氏 (Stony Book University)
Singular hermitian metrics and morphisms to abelian varieties (ENGLISH)
[ 講演概要 ]
Consider a morphism from a smooth projective variety to an abelian variety (over the field of complex numbers). After reviewing what is known about the pushforward of the canonical bundle under such a morphism, we will try to extend these results to the case of pluricanonical bundles (= the tensor powers of the canonical bundle). Along the way, we will learn about three important tools: generic vanishing theory; Viehweg's cyclic covering trick; and some new results from complex analysis about metrics with singularities. As an application, we will discuss the proof of Iitaka's conjecture (about the subadditivity of the Kodaira dimension in algebraic fiber spaces) over abelian varieties, following Cao and Paun.
[ 参考URL ]Consider a morphism from a smooth projective variety to an abelian variety (over the field of complex numbers). After reviewing what is known about the pushforward of the canonical bundle under such a morphism, we will try to extend these results to the case of pluricanonical bundles (= the tensor powers of the canonical bundle). Along the way, we will learn about three important tools: generic vanishing theory; Viehweg's cyclic covering trick; and some new results from complex analysis about metrics with singularities. As an application, we will discuss the proof of Iitaka's conjecture (about the subadditivity of the Kodaira dimension in algebraic fiber spaces) over abelian varieties, following Cao and Paun.
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Schnell.pdf
2018年07月24日(火)
FMSPレクチャーズ
10:15-12:15 数理科学研究科棟(駒場) 118号室
集中講義901-118「数物先端科学X」として行われます（7/18,20,23,24,25の全5回）。
Christian Schnell 氏 (Stony Book University)
Singular hermitian metrics and morphisms to abelian varieties (ENGLISH)
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Schnell.pdf
集中講義901-118「数物先端科学X」として行われます（7/18,20,23,24,25の全5回）。
Christian Schnell 氏 (Stony Book University)
Singular hermitian metrics and morphisms to abelian varieties (ENGLISH)
[ 講演概要 ]
Consider a morphism from a smooth projective variety to an abelian variety (over the field of complex numbers). After reviewing what is known about the pushforward of the canonical bundle under such a morphism, we will try to extend these results to the case of pluricanonical bundles (= the tensor powers of the canonical bundle). Along the way, we will learn about three important tools: generic vanishing theory; Viehweg's cyclic covering trick; and some new results from complex analysis about metrics with singularities. As an application, we will discuss the proof of Iitaka's conjecture (about the subadditivity of the Kodaira dimension in algebraic fiber spaces) over abelian varieties, following Cao and Paun.
[ 参考URL ]Consider a morphism from a smooth projective variety to an abelian variety (over the field of complex numbers). After reviewing what is known about the pushforward of the canonical bundle under such a morphism, we will try to extend these results to the case of pluricanonical bundles (= the tensor powers of the canonical bundle). Along the way, we will learn about three important tools: generic vanishing theory; Viehweg's cyclic covering trick; and some new results from complex analysis about metrics with singularities. As an application, we will discuss the proof of Iitaka's conjecture (about the subadditivity of the Kodaira dimension in algebraic fiber spaces) over abelian varieties, following Cao and Paun.
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Schnell.pdf
2018年07月23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
Filippo Bracci 氏 (University of Rome Tor Vergata)
Strange Fatou components of automorphisms of $\mathbb{C}^2$ and Runge embedding of $\mathbb{C} \times \mathbb{C}^*$ into $\mathbb{C}^2$. (ENGLISH)
Filippo Bracci 氏 (University of Rome Tor Vergata)
Strange Fatou components of automorphisms of $\mathbb{C}^2$ and Runge embedding of $\mathbb{C} \times \mathbb{C}^*$ into $\mathbb{C}^2$. (ENGLISH)
[ 講演概要 ]
The classification of Fatou components for automorphisms of the complex space of dimension greater than $1$ is an interesting and difficult task. Recent deep results prove that the one-dimensional setting is deeply different from the higher dimensional one. Given an automorphism F of $\mathbb{C}^k$, the first bricks in the theory that one would like to understand are invariant Fatou components, namely, those connected open sets $U$, completely invariant under $F$, where the dynamics of $F$ is not chaotic. Among those, we consider “attracting” Fatou components, that is, those components on which the iterates of $F$ converge to a single point. Attracting Fatou components can be recurrent, if the limit point is inside the component or non-recurrent. Recurrent attracting Fatou components are always biholomorphic to $\mathbb{C}^k$, since it was proved by H. Peters, L. Vivas and E. F. Wold that in such a case the point is an attracting (hyperbolic) fixed point, and the Fatou component coincides with the global basin of attraction. Also, as a consequence of works of Ueda and Peters-Lyubich, it is know that all attracting non-recurrent Fatou components of polynomial automorphisms of $\mathbb{C}^2$ are biholomorphic to $\mathbb{C}^2$. One can quite easily find non-simply connected non-recurrent attracting Fatou components in $\mathbb{C}^3$ (mixing a two- dimensional dynamics with a dynamics with non-isolated fixed points in one- variable). In this talk I will explain how to construct a non-recurrent attracting Fatou component in $\mathbb{C}^2$ which is biholomorphic to $\mathbb{C}\times\mathbb{C}^*$. This“fantastic beast” is obtained by globalizing, using a result of F. Forstneric, a local construction due to the speaker and Zaitsev, which allows to create a global basin of attraction for an automorphism, and a Fatou coordinate on it. The Fatou coordinate turns out to be a fiber bundle map on $\mathbb{C}$, whose fiber is $\mathbb{C}^*$, then the global basin is biholomorphic to $\mathbb{C}\times\mathbb{C}^*$. The most subtle point is to show that such a basin is indeed a Fatou component. This is done exploiting Poschel's results about existence of local Siegel discs and suitable estimates for the Kobayashi distance.
Since attracting Fatou components are Runge, it turns out that this construction gives also an example of a Runge embedding of $\mathbb{C}\times\mathbb{C}^*$ into $\mathbb{C}^2$. Moreover, this example shows an automorphism of $\mathbb{C}^2$ leaving invariant two analytic discs intersecting transversally at the origin.
The talk is based on a joint work with J. Raissy and B. Stensones.
The classification of Fatou components for automorphisms of the complex space of dimension greater than $1$ is an interesting and difficult task. Recent deep results prove that the one-dimensional setting is deeply different from the higher dimensional one. Given an automorphism F of $\mathbb{C}^k$, the first bricks in the theory that one would like to understand are invariant Fatou components, namely, those connected open sets $U$, completely invariant under $F$, where the dynamics of $F$ is not chaotic. Among those, we consider “attracting” Fatou components, that is, those components on which the iterates of $F$ converge to a single point. Attracting Fatou components can be recurrent, if the limit point is inside the component or non-recurrent. Recurrent attracting Fatou components are always biholomorphic to $\mathbb{C}^k$, since it was proved by H. Peters, L. Vivas and E. F. Wold that in such a case the point is an attracting (hyperbolic) fixed point, and the Fatou component coincides with the global basin of attraction. Also, as a consequence of works of Ueda and Peters-Lyubich, it is know that all attracting non-recurrent Fatou components of polynomial automorphisms of $\mathbb{C}^2$ are biholomorphic to $\mathbb{C}^2$. One can quite easily find non-simply connected non-recurrent attracting Fatou components in $\mathbb{C}^3$ (mixing a two- dimensional dynamics with a dynamics with non-isolated fixed points in one- variable). In this talk I will explain how to construct a non-recurrent attracting Fatou component in $\mathbb{C}^2$ which is biholomorphic to $\mathbb{C}\times\mathbb{C}^*$. This“fantastic beast” is obtained by globalizing, using a result of F. Forstneric, a local construction due to the speaker and Zaitsev, which allows to create a global basin of attraction for an automorphism, and a Fatou coordinate on it. The Fatou coordinate turns out to be a fiber bundle map on $\mathbb{C}$, whose fiber is $\mathbb{C}^*$, then the global basin is biholomorphic to $\mathbb{C}\times\mathbb{C}^*$. The most subtle point is to show that such a basin is indeed a Fatou component. This is done exploiting Poschel's results about existence of local Siegel discs and suitable estimates for the Kobayashi distance.
Since attracting Fatou components are Runge, it turns out that this construction gives also an example of a Runge embedding of $\mathbb{C}\times\mathbb{C}^*$ into $\mathbb{C}^2$. Moreover, this example shows an automorphism of $\mathbb{C}^2$ leaving invariant two analytic discs intersecting transversally at the origin.
The talk is based on a joint work with J. Raissy and B. Stensones.
FMSPレクチャーズ
10:15-12:15 数理科学研究科棟(駒場) 118号室
集中講義901-118「数物先端科学X」として行われます（7/18,20,23,24,25の全5回）。
Christian Schnell 氏 (Stony Book University)
Singular hermitian metrics and morphisms to abelian varieties (ENGLISH)
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Schnell.pdf
集中講義901-118「数物先端科学X」として行われます（7/18,20,23,24,25の全5回）。
Christian Schnell 氏 (Stony Book University)
Singular hermitian metrics and morphisms to abelian varieties (ENGLISH)
[ 講演概要 ]
Consider a morphism from a smooth projective variety to an abelian variety (over the field of complex numbers). After reviewing what is known about the pushforward of the canonical bundle under such a morphism, we will try to extend these results to the case of pluricanonical bundles (= the tensor powers of the canonical bundle). Along the way, we will learn about three important tools: generic vanishing theory; Viehweg's cyclic covering trick; and some new results from complex analysis about metrics with singularities. As an application, we will discuss the proof of Iitaka's conjecture (about the subadditivity of the Kodaira dimension in algebraic fiber spaces) over abelian varieties, following Cao and Paun.
[ 参考URL ]Consider a morphism from a smooth projective variety to an abelian variety (over the field of complex numbers). After reviewing what is known about the pushforward of the canonical bundle under such a morphism, we will try to extend these results to the case of pluricanonical bundles (= the tensor powers of the canonical bundle). Along the way, we will learn about three important tools: generic vanishing theory; Viehweg's cyclic covering trick; and some new results from complex analysis about metrics with singularities. As an application, we will discuss the proof of Iitaka's conjecture (about the subadditivity of the Kodaira dimension in algebraic fiber spaces) over abelian varieties, following Cao and Paun.
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Schnell.pdf
2018年07月20日(金)
FMSPレクチャーズ
10:15-12:15 数理科学研究科棟(駒場) 118号室
集中講義901-118「数物先端科学X」として行われます（7/18,20,23,24,25の全5回）。
Christian Schnell 氏 (Stony Book University)
Singular hermitian metrics and morphisms to abelian varieties (ENGLISH)
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Schnell.pdf
集中講義901-118「数物先端科学X」として行われます（7/18,20,23,24,25の全5回）。
Christian Schnell 氏 (Stony Book University)
Singular hermitian metrics and morphisms to abelian varieties (ENGLISH)
[ 講演概要 ]
Consider a morphism from a smooth projective variety to an abelian variety (over the field of complex numbers). After reviewing what is known about the pushforward of the canonical bundle under such a morphism, we will try to extend these results to the case of pluricanonical bundles (= the tensor powers of the canonical bundle). Along the way, we will learn about three important tools: generic vanishing theory; Viehweg's cyclic covering trick; and some new results from complex analysis about metrics with singularities. As an application, we will discuss the proof of Iitaka's conjecture (about the subadditivity of the Kodaira dimension in algebraic fiber spaces) over abelian varieties, following Cao and Paun.
[ 参考URL ]Consider a morphism from a smooth projective variety to an abelian variety (over the field of complex numbers). After reviewing what is known about the pushforward of the canonical bundle under such a morphism, we will try to extend these results to the case of pluricanonical bundles (= the tensor powers of the canonical bundle). Along the way, we will learn about three important tools: generic vanishing theory; Viehweg's cyclic covering trick; and some new results from complex analysis about metrics with singularities. As an application, we will discuss the proof of Iitaka's conjecture (about the subadditivity of the Kodaira dimension in algebraic fiber spaces) over abelian varieties, following Cao and Paun.
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Schnell.pdf
2018年07月19日(木)
応用解析セミナー
16:00-17:30 数理科学研究科棟(駒場) 118号室
生駒 典久 氏 (慶應義塾大学)
Uniqueness and nondegeneracy of ground states to scalar field equation involving critical Sobolev exponent
(Japanese)
生駒 典久 氏 (慶應義塾大学)
Uniqueness and nondegeneracy of ground states to scalar field equation involving critical Sobolev exponent
(Japanese)
[ 講演概要 ]
This talk is devoted to studying the uniqueness and nondegeneracy of ground states to a nonlinear scalar field equation on the whole space. The nonlinearity consists of two power functions, and their growths are subcritical and critical in the Sobolev sense respectively. Under some assumptions, it is known that the equation admits a positive radial ground state and other ground states are made from the positive radial one. We show that if the dimensions are greater than or equal to 5 and the frequency is sufficiently large, then the positive radial ground state is unique and nondegenerate. This is based on joint work with Takafumi Akahori (Shizuoka Univ.), Slim Ibrahim (Univ. of Victoria), Hiroaki Kikuchi (Tsuda Univ.) and Hayato Nawa (Meiji Univ.).
This talk is devoted to studying the uniqueness and nondegeneracy of ground states to a nonlinear scalar field equation on the whole space. The nonlinearity consists of two power functions, and their growths are subcritical and critical in the Sobolev sense respectively. Under some assumptions, it is known that the equation admits a positive radial ground state and other ground states are made from the positive radial one. We show that if the dimensions are greater than or equal to 5 and the frequency is sufficiently large, then the positive radial ground state is unique and nondegenerate. This is based on joint work with Takafumi Akahori (Shizuoka Univ.), Slim Ibrahim (Univ. of Victoria), Hiroaki Kikuchi (Tsuda Univ.) and Hayato Nawa (Meiji Univ.).
2018年07月18日(水)
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
普段と違う水曜日にセミナーを行います。The seminar will be held on Wednesday. This is a different day from usual.
Jun-Muk Hwang 氏 (KIAS)
Normal Legendrian singularities (English)
普段と違う水曜日にセミナーを行います。The seminar will be held on Wednesday. This is a different day from usual.
Jun-Muk Hwang 氏 (KIAS)
Normal Legendrian singularities (English)
[ 講演概要 ]
A germ of a Legendrian subvariety in a holomorphic contact manifold
is called a Legendrian singularity. Legendrian singularities are usually not normal.
We look at some examples of normal Legendrian singularities and discuss their rigidity under deformation.
A germ of a Legendrian subvariety in a holomorphic contact manifold
is called a Legendrian singularity. Legendrian singularities are usually not normal.
We look at some examples of normal Legendrian singularities and discuss their rigidity under deformation.
数理人口学・数理生物学セミナー
15:00-16:00 数理科学研究科棟(駒場) 118号室
Malay Banerjee 氏 (Department of Mathematics & Statistics, IIT Kanpur)
Effect of demographic stochasticity on large amplitude oscillation
Malay Banerjee 氏 (Department of Mathematics & Statistics, IIT Kanpur)
Effect of demographic stochasticity on large amplitude oscillation
[ 講演概要 ]
Classical Rosenzweig-MacArthur model exhibits two types of stable coexistence, steady-state and oscillatory coexistence. The oscillatory coexistence is the result of super-critical Hopf-bifurcation and the Hopf-bifurcating limit cycle remains stable for parameter values beyond the bifurcation threshold. The size of the limit cycle grows with the increase in carrying capacity of prey and finally both the populations show high amplitude oscillations. Time evolution of prey and predator population densities exhibit large amplitude peaks separated by low density lengthy valleys. Persistence of both the populations at low population density over a longer time period is more prominent in case of fast growth of prey and comparatively slow growth of predator species due to slow-fast dynamics. In this situation, small amount of demographic stochasticity can cause the extinction of one or both the species. Main aim of this talk is to explain the effect of demographic stochasticity on the high amplitude oscillations produced by two and higher dimensional interacting population models.
Classical Rosenzweig-MacArthur model exhibits two types of stable coexistence, steady-state and oscillatory coexistence. The oscillatory coexistence is the result of super-critical Hopf-bifurcation and the Hopf-bifurcating limit cycle remains stable for parameter values beyond the bifurcation threshold. The size of the limit cycle grows with the increase in carrying capacity of prey and finally both the populations show high amplitude oscillations. Time evolution of prey and predator population densities exhibit large amplitude peaks separated by low density lengthy valleys. Persistence of both the populations at low population density over a longer time period is more prominent in case of fast growth of prey and comparatively slow growth of predator species due to slow-fast dynamics. In this situation, small amount of demographic stochasticity can cause the extinction of one or both the species. Main aim of this talk is to explain the effect of demographic stochasticity on the high amplitude oscillations produced by two and higher dimensional interacting population models.
博士論文発表会
15:30-16:45 数理科学研究科棟(駒場) 128号室
張 龍傑 氏 (東京大学大学院数理科学研究科)
Mean curvature flow with driving force
(駆動力付きの平均曲率流方程式)
(JAPANESE)
張 龍傑 氏 (東京大学大学院数理科学研究科)
Mean curvature flow with driving force
(駆動力付きの平均曲率流方程式)
(JAPANESE)
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