Introduction to Derived Geometry

Time: 2021-06-21 Published By: Meng Yu

Speaker(s): Tony Yue Yu (CNRS & Université Paris-Saclay)

Time: March 12 - June 18, 2021

Venue: Room 82J13, Jingchunyuan 82, BICMR & Online

TIME

Fridays 15:10 - 17:00, from March 12 to June 18

ABSTRACT

This course is an introduction to the basic ideas in derived geometry. Derived geometry is a theory for working with non-transverse situations in geometry, which are abundant in intersection theory, enumerative geometry, symplectic geometry, representation theory, etc. Although the ideas of derived geometry are natural and beautiful, the underlying machinery is quite demanding. So I will mainly focus on motivations and geometric ideas. I will explain higher stacks, Lurie’s theory of structured spaces, Lurie’s representability theorem, formal moduli problems, shifted symplectic structures, and applications to virtual fundamental classes. If time permits, I will mention my works with M. Porta on derived analytic geometry. Knowledge of undergraduate algebraic geometry is sufficient to follow the course.

摘要

本课程旨在介绍导出几何的一些基本概念。导出几何是一个用于处理几何中非横截情形的理论。非横截情形在相交理论、计数几何、辛几何、表示论中大量出现。虽然导出几何的想法很自然和漂亮，它背后的技术却很苛求。所以我会侧重于介绍动机和概念。我会解释高阶栈、Lurie结构空间理论、Lurie表示定理、形式模问题、转移辛结构、以及对于虚拟基本类的应用。如果时间允许，我会提及我和M. Porta在导出解析几何中的工作。本科代数几何的知识足够跟上本课程。

ZOOM INFO

ID: 829 3178 8351

Password: 362374

Join Zoom Meeting

https://zoom.com.cn/j/82931788351?pwd=QjhQRDF2L2JUT1Byam5tVDlHU05VZz09

NOTES

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