|DATE||October 19 (Mon), 2020|
|HOST||Bhamidi, S.S Sreedhar|
|TITLE||[GS_M_3W] Three W's Seminar: Approaching the space of knots with higher categories|
A knot K is an embedding from S^1 into R^3 . Because embeddings are, in particular, injective, K induces a map between the spaces of configurations of finite subsets of S^1 and R^3 of some fixed cardinality r. The homotopy-types of such configuration spaces organize as an ∞-category, the construction of which makes use of stratified spaces and exit-path ∞-categories thereof. The goal of this talk is to supply the constructions of these ∞-categories and motivate the use of them in studying the space of knots.