学部・大学院区分
Undergraduate / Graduate
多・博前
時間割コード
Registration Code
3211002
科目区分
Course Category
A類Ⅰ(基礎科目)
Category A-1
科目名 【日本語】
Course Title
数理科学展望Ⅱ
科目名 【英語】
Course Title
Perspectives in Mathematical Science II
コースナンバリングコード
Course Numbering Code
担当教員 【日本語】
Instructor
GARRIGUE JACQUES ○ 納谷 信 髙橋 亮
担当教員 【英語】
Instructor
GARRIGUE JACQUES ○ NAYATANI Shin TAKAHASHI Ryo
単位数
Credits
2
開講期・開講時間帯
Term / Day / Period
秋 火曜日 3時限
Fall Tue 3
授業形態
Course style

学科・専攻
Department / Program
多元数理科学研究科
必修・選択
Required / Selected
選択


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.
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
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.
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.
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.
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.
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).
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.
教科書・テキスト
Textbook
No textbook is used.
参考書
Reference Book
Recommended books will be introduced in the lecture.
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.
注意事項
Notice for Students
-
他学科聴講の可否
Propriety of Other department student's attendance
Possible
他学科聴講の条件
Conditions of Other department student's attendance
Ask the instructors first.
レベル
Level
2
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.
履修の際のアドバイス
Advice
-
授業開講形態等
Lecture format, etc.
Face-to-face lecture (+ TACT when necessary)
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.