This is a proposal for an Advanced Instructional School on the topic of André-Quillen and Hochschild cohomology functors on commutative algebras. The lecture series will explore a family of results and conjectures in homological commutative algebra, each making predic- tions about the complexity of certain cohomological objects.
This school will introduce to early career researchers the above cohomology theories and highlight important connections to algebraic topology, and finally present state of the art arguments to uncover the structure of these cohomology theories.
