北京雁棲湖應用數學研究院和清華大學數學科學中心共同推出多門線上暑期課程，應用數學方向涵蓋計算共性幾何、密碼學、機器學習、人工智慧等課程；基礎數學方向涵蓋代數、拓撲、分析、等課程。課程面向校內外師生開放，歡迎參加！
本周（7.13～7.19）新開課程信息如下：
微分分次範疇及其應用
Differential Graded Categories
and Applications
Speaker: Bernhard Keller教授 巴黎大學（巴黎七大）
著名代數學家，在微分分次理論、cluster理論以及Hochschild同調理論中均做出了奠基性的學術成果。Keller教授是Sophie Germain獎得主，美國數學會會士，於2006年在國際數學家大會做邀請報告。
Date: July 17 (Fri.), July 22 (Wed.), July 29 (Wed.); Sep 2 (Wed.), Sep 9 (Wed.), Sep 16 (Wed.), Sep 23 (Wed.).
Time: Beijing time 8:00pm-9:40pm (2×45min+10min break) = Paris time 2:00pm-3:40pm
Online ID & password
7.17 Zoom ID: 665 2658 1476
Password: DG2020
7.17 Tencent Meeting ID: 202 617 298
Password: 202007
Course Description
his course is an introduction to differential graded (=dg) categories and their applications in representation theory and its links to algebraic geometry (commutative and non commutative).
Much of our motivation and inspiration comes from the (additive) categorification of Fomin-Zelevinsky cluster algebras (with coefficients). We will begin with the study of dg algebras, their derived categories, derived Morita equivalence and Koszul duality. We will then introduce dg categories, their quasi-equivalences and Morita equivalences and describe the corresponding model categories with their closed monoidal structure after Tabuada and Toen. The construction and characterization of dg localizations (e.g. Drinfeld quotients) and homotopy pushouts will be particularly important. We will then examine various important invariants associated with dg categories, notably K-theory, Hochschild and cyclic homology and Hochschild cohomology.
We will apply these in the construction of (relative) Calabi-Yau structures and Calabi-Yau completions following Ginzburg, Brav-Dyckerhoff and Yeung. The final part of the course will be an introduction to Bozec-Calaque-Scherotzke's recent work relating Calabi-Yau completions to shifted cotangent spaces.
Introduction to the Minimal Model Program
Speaker: 歐文浩, Associate Researcher, Chinese Academy of Sciences
Date：Every Thur. & Tue. July 16th ～ 30th
Time：Beijing time 13:30 ～ 15:00
Online ID & password
7.16 Tencent Meeting ID: 603 889 9103
密碼：195058
Course Description
The goal of this course is to give an introduction to the Minimal Model Program. We will start by reviewing some basic notion in birational geometry and the minimal model program for surfaces, which had already been established by the end of 19th century. Then we will proceed to the higher dimensional setting and introduce the cone theorem. We will also study MMP singularities in more details. In the end, we will try to describe the breakthrough in the last decade, especially the existence of minimal models of log general type (BCHM).
Prerequisite
The course tries to be as self-contained as possible. Nevertheless, some basic knowledge in algebraic geometry, such as the notion of varieties, sheaves, projective morphisms, would help a lot. All of these prerequisites can be found in Hartshorne’s Algebraic Geometry book.
Reference
Hartshornes, Algebraic Geometry
Iitaka, Algebraic Geometry
Kawamata and Matsuda and Matsuki, Introduction to the Minimal Model Program
Kollár and Mori, Birational Geometry of Algebraic Varieties
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清華大學丘成桐數學科學中心，是一所研究數學前沿問題、培養新一代數學人才及促進數學思想和成果交流的國際教學科研機構。