September 12, 2023

**Title:** *Lie algebras in homotopy theory (MI talk) *

**Speaker:** Gijs Heuts

Lie algebras have played an important role throughout the development of homotopy theory. I'll start with the Whitehead bracket, which gives a Lie algebra structure on homotopy groups that extends the usual commutator on the fundamental group of a space. Then we'll see how Quillen used Lie algebras to completely describe algebraic topology "with rational coefficients". Time permitting, we'll then move on to the more modern development of Lie algebras "up to homotopy" and their role in describing topological spaces.