Abstracts for Higher Differential Geometry Seminar

I will explain how to obtain the T-duality isomorphism discovered by Peter Bouwknegt, Jarah Evslin, and Varghese Mathai in 2004 from the point of view of dg-manifolds. As a byproduct of this approach, one can recover the exceptional $B_n$ generalized geometry defined recently by Baraglia as the derived dg-Leibniz algebra of the fixed points of the T-dual automorphism acting on the symmetries of a self T-dual dgmanifold.

A supermanifold is called split if it is isomorphic to a vector bundle with a purely even base and purely odd fiber. In the smooth category, all supermanifolds are known to be split (although non-canonically). In contrast with that, complex-analytic supermanifolds are not necessarily split.

In this talk I will discuss a construction of holonomies for connections with values in $L$-infinity algebras which is based on an $A$-infty version of de-Rham's theorem. Then I will explain how this construction, applied to the Severa-Willwacher connections, is related to the proof of formality of the little $d$-disks operad. This talk is based on work in progress joint with F. Schaetz.