**Date/Time**

Date(s) - 21/09/2023*4:30 pm - 5:30 pm*

**Location:** HH 312

**Speaker:** Aleksandar Milivojevic’s (University of Waterloo)

**Title:** Formality and non-zero degree maps

**Abstract: **A non-zero degree map between closed orientable manifolds induces an injection of rational cohomology algebras. The key property used in this quick argument, namely Poincare duality, in fact sees more than just the ring structure: as shown by L. Taylor, a non-trivial triple Massey product (an operation taking in three rational cohomology classes) is pulled back to a non-trivial triple Massey product under a non-zero degree map. I will discuss a recent result with J. Stelzig and L. Zoller showing that formality is preserved under non-zero degree maps. Namely, if the domain manifold is formal, then so is the target. A formal manifold is one whose differential graded algebra of forms is determined by the cohomology algebra alone; on such a manifold, all triple and higher-order Massey products are trivial. Some geometric applications, old and new, will be given.