Various maps arising in topology look like they should come from algebraic geometry, if only one could allow them to take values « at infinity ». This is the case for the little disks operad, whose underlying spaces have the homotopy type of the configuration spaces of points on the affine line, but whose operadic maps are not algebraic in any obvious way. I will explain how to solve this...
Unimodular rows are fundamental objects in algebraic K-theory as they classify stably free projective modules. Geometrically, they correspond to morphisms to punctured affine space and may thus be thought of as an algebro-geometric analogue of maps to spheres in topology. The latter give rise to Borsuk's cohomotopy groups, a counterpart to which was constructed purely algebraically by van der...
By a result of Heuts-Moerdijk, the oo-category of simplicial diagrams on the nerve of a discrete category A is equivalent to that of left fibrations over the nerve of A. This is an instance of the well known Grothendieck-Lurie straightening-unstraightening theorem.
In this talk, we will explain how one can generalize this result to the operadic case. More specifically, by working with the...
