∞-Categories and Deformation Theory Trinity 2024 Starting with André-Quillen's cohomology of commutative rings, Koszul-Moore duality has played a role in several developments in algebraic geometry. In this course, we will explore applications to deformation theory, including the classification of deformations by Lie algebras and the unobstructedness of Calabi-Yau varieties. Along the way, we will introduce the required higher categorical background. Prerequesites Familiarity with classical scheme theory, category theory, and a tolerance for abstraction are required. General Information The first meeting will be held in hybrid form (via the TCC Teams link or at the TCC room (CV1) in Oxford's Mathematical Institute). Notes Lecture 1 Lecture 2 Lecture 3 Lecture 4 Lecture 5 Lecture 6 Lecture 7 Lecture 8 Lecture 9