Zoom link:

https://umontreal.zoom.us/j/94366166514?pwd=OHBWcGluUmJwMFJyd2IwS1ROZ0FJdz09

The classical Pontryagin–Thom isomorphism equates manifold bordism groups with corresponding stable homotopy groups.  This construction moreover generalizes to the equivariant context.  I will discuss work which establishes a Pontryagin--Thom isomorphism for orbispaces (an orbispace is a "space" which is locally modelled on Y/G for Y a space and G a finite group; examples of orbispaces include orbifolds and moduli spaces of pseudo-holomorphic curves).  This involves defining a category of orbispectra and an involution of this category