Lie Algebras and Homotopy Theory - Jacob Lurie

Explore the intricate connections between Lie algebras and homotopy theory in this comprehensive seminar presented by Professor Jacob Lurie at the Institute for Advanced Study. Delve into the origins of Lie algebras in mathematics and their fundamental structures. Examine the concept of fundamental groups and their significance in topology. Uncover the Whitehead bracket and its role in homotopy theory. Investigate homotopy operations and their applications, including the Hilton Milner Theorem. Analyze rational homotopy and its implications for algebraic topology. Study Quillen's Theorem and its impact on understanding the relationship between differential graded Lie algebras and homotopy theory. Gain insights into derived categories and their relevance to modern algebraic geometry and homological algebra.

Intro
Definition of Lie Algebra
How Lie Algebra arose in mathematics
The fundamental group of X
The fundamental group structure
The Whitehead bracket
Lie algebras
Why Homotopy
Homotopy Operations
Hilton Milner Theorem
Rational Homotopy
Quillins Theorem
Differential Graded Lie Algebra
Quillens Theorem
Quilllens Theorem
Defining Lie Algebra
Defining A
Derived Categories