授業の目的 【日本語】
Goals of the Course(JPN) | | Seminar on Convex Geometry in Complex Geometry and Diophantine Geometry.
(1) Geometry of Numbers.
(2) Alexandrov-Fenchel Inequality and Complex Geometry.
(3) Brunn-Minkowski Inequality in Geometry and Analysis |
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授業の目的 【英語】
Goals of the Course | | Seminar on Convex Geometry in Complex Geometry and Diophantine Geometry.
(1) Geometry of Numbers.
(2) Alexandrov-Fenchel Inequality and Complex Geometry.
(3) Brunn-Minkowski Inequality in Geometry and Analysis |
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到達目標 【日本語】
Objectives of the Course(JPN)) | | (1) Search for the relationship between Minkowski's Convex Body Theorem and the Diophantine analogue of Ahlfors' Lemma on Logarithmic Derivative for holomorphic curves into a projective variety proposed by Vojta.
(2) To understand the role of Measure Concentration Phenomenon in Diophantine Geometry.
(3) To understand the role of Convex Geometry in YDT Conjecture. |
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到達目標 【英語】
Objectives of the Course | | (1) Search for the relationship between Minkowski's Convex Body Theorem and the Diophantine analogue of Ahlfors' Lemma on Logarithmic Derivative for holomorphic curves into a projective variety proposed by Vojta.
(2) To understand the role of Measure Concentration Phenomenon in Diophantine Geometry.
(3) To understand the role of Convex Geometry in YDT Conjecture. |
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授業の内容や構成
Course Content / Plan | | セミナー形式で時代を画する論文を読む．
Reading epoc making papers. |
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履修条件
Course Prerequisites | | 学部の複素解析，幾何学，測度論を知っていると非有に良い．
しかしこれらをセミナーを通して学ぶことも可能である．
A good background from undergraduate complex analysis. geometry and measure theory.
However, students can learn these basics through the seminar. |
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関連する科目
Related Courses | | |
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成績評価の方法と基準
Course Evaluation Method and Criteria | | セミナーでの発表をもとに成績を評価する．
evaluation based on presentations at the seminar. |
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教科書・テキスト
Textbook | | Fukshansky, ``Geometry of Numbers''.
Bombieri-Gubler,``Heights in Diophantine Geometry''.
Ahlfors,``The theory of meromorphic curves''.
Meckes, ``Concentration of Measure and the Compact Classical Groups''.
Berndtsson,``An introduction to things d-bar''. |
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参考書
Reference Book | | GuedjーZeriahi,``Degenerate complex MongeーAmpere equations''.
Shoshichi Kobayashi, Hyperbolic Complex Spaces''. |
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課外学習等（授業時間外学習の指示）
Study Load(Self-directed Learning Outside Course Hours) | | | 数学をマスターするには時間を（日本的表現だが）湯水のように使わないとできないので，自主学習が何よりも重要である． |
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注意事項
Notice for Students | | | 基本的に対面で行うが，必要があれば遠隔実施もあり得る． |
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他学科聴講の可否
Propriety of Other department student's attendance | | |
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他学科聴講の条件
Conditions of Other department student's attendance | | |
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レベル
Level | | |
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キーワード
Keyword | | | Convex Geometry. Complex Geometry. Diophantine Geometry. |
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履修の際のアドバイス
Advice | | |
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授業開講形態等
Lecture format, etc. | | |
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遠隔授業（オンデマンド型）で行う場合の追加措置
Additional measures for remote class (on-demand class) | | |
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