学部・大学院区分
Undergraduate / Graduate		多・博前
時間割コード
Registration Code		3211088
科目区分
Course Category		Ａ類Ⅱ（専門科目）
Category A-2
科目名　【日本語】
Course Title		数理科学特論Ⅱ
科目名　【英語】
Course Title		Topics in Mathematical ScienceⅡ
コースナンバリングコード
Course Numbering Code
担当教員　【日本語】
Instructor		HESSELHOLT LARS ○
担当教員　【英語】
Instructor		HESSELHOLT LARS ○
単位数
Credits		2
開講期・開講時間帯
Term / Day / Period		春 金曜日 １時限
Spring Fri 1
授業形態
Course style
学科・専攻
Department / Program
Graduate School of Mathematics
必修・選択
Required / Selected


授業の目的　【日本語】
Goals of the Course(JPN)
授業の目的　【英語】
Goals of the Course
The goal of the course is to present a proof of Poincare duality for algebraic de Rham cohomology due to Dustin Clausen. The proof uses a variety of modern tools, including infinity-categories, stacks, and deformation to the normal cone. The course will take a learning-by-doing approach to these tools.
到達目標　【日本語】
Objectives of the Course(JPN))
到達目標　【英語】
Objectives of the Course
The objective of the course is introduce participants to a variety of modern tools in algebraic geometry by applying these tools to a concrete and non-trivial problem.
授業の内容や構成
Course Content / Plan
The plan is to follow the course notes by Dustin Clausen available at https://sites.google.com/view/algebraicderham/home.
履修条件
Course Prerequisites
Some familiarity with scheme theory and with homological algebra will be helpful, but it is not necessarily essential.
関連する科目
Related Courses
成績評価の方法と基準
Course Evaluation Method and Criteria
The grade will be based on homework submissions.
教科書・テキスト
Textbook
We will use course notes by Dustin Clausen available at https://sites.google.com/view/algebraicderham/home, and I may occasionally write additional notes.
参考書
Reference Book
The material on infinity-categories that we will use can be found in Lurie's books Higher Topos Theory and Higher Algebra, which are available at https://www.math.ias.edu/~lurie. But you should consider these books as encyclopedias rather than books to be read from beginning to end.
課外学習等（授業時間外学習の指示）
Study Load(Self-directed Learning Outside Course Hours)
The course notes are well-written, but rather dense. It is important to invest time to understand the arguments therein.
注意事項
Notice for Students
他学科聴講の可否
Propriety of Other department student's attendance
他学科聴講の条件
Conditions of Other department student's attendance
レベル
Level
キーワード
Keyword
履修の際のアドバイス
Advice
授業開講形態等
Lecture format, etc.
Face-to-face.
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)