In topological field theories, extended operators organise into an algebraic structure known as an En-algebra. Inspired by this, we study the deformations of En-monoidal k-linear ∞-categories, where k is a field. During this talk, I will review En-algebras, their formalisation through operads and Jacob Lurie’s framework of derived deformation theory. I will discuss the curvature problem encountered in the deformation of En-algebras and show that, under suitable conditions, deformations of a En-monoidal k-linear ∞-category C over the formal power series k[[t]] avoid this issue. More precisely, I will prove that deformations of C over the formal power series k[[t]] are equivalent to the actions of k[u] on C, where u is a degree −n − 2 variable. This talk is based on work done in collaboration with Pranav Pandit.
Zoom link: https://icts-res-in.zoom.us/j/93172534538?pwd=3que0i6jTb8rNhaMMoQdSxD6HbMujg.1
Meeting ID: 931 7253 4538
Passcode: 050607