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[Lecture] Introduction to Derived Geometry

MAR . 12 2021
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.

BIOGRAPHY

Tony Yue Yu studied at Peking University from 2007 to 2010, and received his PhD in 2016 from Université Paris Diderot under the supervision of Maxim Kontsevich and Antoine Chambert-Loir. He is currently a researcher at CNRS and Université Paris-Saclay. He works on mirror symmetry, non-archimedean geometry, tropical geometry and derived geometry. He aims to build a theory of enumerative geometry in the setting of Berkovich spaces. Such a theory will give us a new understanding of the enumerative geometry of Calabi-Yau manifolds, the structure of their mirrors, as well as the moduli space of Calabi-Yau pairs. It is also intimately related to the theory of cluster algebras and wall-crossing structures. Tony Yue Yu was awarded the Clay Research Fellowship in 2016, and an European Research Council (ERC) starting grant in 2020.

ZOOM INFO

ID: 829 3178 8351

Password: 362374

Join Zoom Meeting

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