Seminar| Institute of Mathematical Sciences
Speaker: Yu Zhao, The University of Tokyo
Organizer: Zhiyuan Ding
Abstract: 导出射影化理论和导出blow-up理论是由姜清元和Jeroen Hekking正在发展的新理论，其可以看做是经典的Grothendieck射影化和blow-up理论在导出代数几何架构上的自然延伸。在本次mini-course中，我将借助以上理论，提出一种拟光滑概型上的相对的广义消没理论。在时间允许的情况下，我会进一步讨论该理论在中岛箙多样体和量子圈群的Drinfeld表现中的应用。
The theories of derived projectivization and derived blow-ups are being developed by Qingyuan Jiang and Jeroen Hekking at the moment. They can be viewed as natural generalizations of the classical Grothendieck projectivization and blow-ups in the framework of derived algebraic geometry. In this mini-course, with the help of these theories, I will propose a generalized relative vanishing theory on quasi-smooth schemes. If time permits, I will discuss its applications to Nakajima quiver varieties and Drinfeld presentations of quantum loop groups.
Schedule
July 5th, 10:00-11:00
引子: 从Calaque-Caldararu-Tu的导出自相交定理到导出Rees代数。
Introduction: From the Calaque-Caldararu-Tu derived self-intersection theorem to derived Rees algebras.
July 7th, 10:00-11:00
导出射影化理论和导出blow-up理论概述。（不同于一般的课程，本mini-course将更偏向具体的例子而非抽象理论。）
Derived projectivization and derived blow-ups, with emphases on concrete examples instead of abstract theories.
July 9th, 10:00-11:00
广义消没定理
Generalized vanishing theorem.
July 11st, 10:00-11:00
神保-Drinfeld量子群与中岛箙多样体。
Jimbo-Drinfeld quantum groups and Nakajima quiver varieties