Speaker: Dr. Coline Emprin (Stockholm University)

Title: Kaledin Classes and Formality Criteria

Time: 15:00-17:00 June 3, 2026 (Wednesday)

Place: MCM110 & Online (Zoom ID: 3329836068  Password: mcm1234)

Abstract: A differential graded algebra A is said to be formal if it is connected to its homology H(A) by a zigzag of quasi-isomorphisms preserving the underlying type of algebraic structure. Formality can be studied using cohomological operations called Massey products. If a differential graded algebraic structure is formal, then all its Massey products vanish. However, the converse is false.

Kaledin classes were introduced as a refinement of these Massey products, providing a complete characterization of formality for associative algebras over a field of characteristic zero. In this talk, I will present a generalization of Kaledin classes to arbitrary coefficient rings, as well as to other algebraic structures (encoded by operads). I will also prove new formality criteria based on these classes and discuss some examples.