Higher Algebra and Koszul Duality - Talk 28

Explore fundamental concepts of higher algebra in this 2-hour seminar talk delivered by Justin Campbell at the BunG Seminar. Delve into essential definitions of higher algebra, examining symmetric monoidal structures on higher categories, and understanding both associative and commutative algebras. Progress through the theory of operads, discovering how this framework accommodates various algebraic structures with particular emphasis on Lie algebras. Investigate the fascinating relationship between Lie algebras and commutative algebras through Koszul duality, gaining insight into why the tangent space of a group naturally possesses a Lie bracket structure. Learn these complex mathematical concepts through a clear, formula-free approach that emphasizes conceptual understanding.