UCalgary Peripatetic Seminar: Alice Rolf

Embedding calculus is a powerful tool which is useful in making quantitative and qualitative conclusions about the topology of embedding spaces. In this talk, we will give a geometric description of the fiber of $\mathrm{Emb}(M,M)\to T_{\mathrm{\infty }}\mathrm{Emb}(M,M)$using smooth structures as well as an algebraic description of its delooping using automorphisms of the little disk operad. In the second part of the talk, we will describe some known properties of that automorphism space and will then explain some ideas that go into the proof of showing that the endomorphisms of the framed little disk operad agree with the automorphisms.