Operad理论短期课程
数学专题报告
报告题目(Title)：Operad理论短期课程
报告人(Speaker)：王凯（中国科学技术大学特任副研究员）
地点(Place)：新主楼1220报告厅
时间(Time)：2024年9月19日、20日、23日、26日,14:10-15:10
邀请人(Inviter)：刘玉明
报告摘要
Operads were introduced by Boardman and Vogt in 1968 and later by Peter May in 1972 to describe iterated loop spaces. Today, operads have become essential tools in the study of algebraic structures, with applications ranging from homotopy theory to deformation quantization, the Deligne conjecture, Higher algebras, among others.
This mini-course will provide a concise introduction to algebraic operads and their Koszul duality theory. Developed by Ginzburg and Kapranov in 1994, Koszul duality offers a powerful framework for explaining duality phenomena in rational homotopy theory and has since become a cornerstone of operad theory. Through this perspective, one can derive the deformation theory of algebraic structures and minimal models of operads in a canonical way. As a concrete example, we will explore how the Hochschild cochain complex of associative algebras and the concept of A-infinity algebras naturally emerge from the Koszul dual of the operad of associative algebras.
First talk: Some basics on algebraic (co)operads
Second talk: Bar-Cobar duality for operads
Third talk: Quadratic operads and their Koszul duals
Fourth talk: Minimal model of operads and deformation complex of algebraic structures
