授業の目的 【日本語】
Goals of the Course(JPN) | | この講義は講師三人によるオムニバス形式の英語講義である.
内容は英文を参照すること.
See English text. |
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授業の目的 【英語】
Goals of the Course | | This course is an omnibus lecture given by 3 separate professors.
The subjects are as follows.
Part 1 (Takahashi): Introduction to tensor triangular geometry
Part 2 (Nayatani): A topic on geometric analysis
Part 3 (Garrigue): Type theory and the Curry-Howard isomorphism |
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到達目標 【日本語】
Objectives of the Course(JPN)) | | 各講師ごとに与えられたテーマに則した問題について考察し, レポートを作成, 提出することによってテーマの理解を深める. 各テーマの内容は英文を参照すること.
See English text. |
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到達目標 【英語】
Objectives of the Course | | Part 1: To master the Zariski topology and become familiar with basics in Balmer's tensor triangular geometry.
Part 2: To understand an aspect of geometric analysis through a specific variational problem.
Part 3: To master logical and type derivations, and become familiar with the basic lambda-calculi of the lambda-cube. |
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授業の内容や構成
Course Content / Plan | | Part 1 (Takahashi):
I will explain the Zariski topology of the prime ideal spectrum of a commutative ring, and the Balmer spectrum of a tensor triangulated category.
Part 2 (Nayatani):
I will discuss the problem of maximizing the first eigenvalue of the Laplacian over all Riemannian metics on a surface.
Part 3 (Garrigue):
The lecture will cover simply typed lambda-calculus, second-order lambda-calcus, their respective relations to propositional and second-order propositional intuitionistic logic, and dependent type system and their relation to predicate logic. |
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履修条件
Course Prerequisites | | Part 1: Undergraduate linear algebra, algebra, and general topology.
Part 2: Undergraduate calculus and linear algebra. Better be familiar with smooth surfaces or manifolds.
Part 3: No requirement, but a basic knowlege of logic is useful. |
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関連する科目
Related Courses | | Part 1: Undergraduate linear algebra, group theory, ring theory, general topology, and category theory.
Part 2: Undergraduate/graduate courses on geometry.
Part 3: Introduction to Computational Mathematics and Computer Science III/I
(Spring 2023). |
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成績評価の方法と基準
Course Evaluation Method and Criteria | | Grading is based on reports for the 3 parts.
The grade is based on the two best reports for each student. |
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教科書・テキスト
Textbook | | |
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参考書
Reference Book | | | Recommended books will be introduced in the lecture. |
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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) | | | Review of each lecture is highly recommended. |
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注意事項
Notice for Students | | |
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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 | | | Ask the instructors first. |
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レベル
Level | | |
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キーワード
Keyword | | Part 1: Commutative ring, ideal, tensor triangulated category, Zariski topology, Balmer spectrum, support, Thomason subset.
Part 2: Laplacian, eigenvalue and eigenfunction, minimal surface.
Part 3: Lambda calculus, type system, intuitionistic logic, proof theory. |
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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. | | | Face-to-face lecture (+ TACT when necessary) |
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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) | | | Access to TACT is needed. |
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