Talk by Dr. David Ayala (Mathematical Sciences, MSU)

08/31/2020  4:10-5:15pm  WebEx Meeting


``Reconstruction’’ summarizes a host of results in algebra and topology: decompose an object into atomic parts, then assemble the global object from these parts. For instance, a natural number is a product of primes; a finite abelian group is a product of cyclic groups; stratified space is a union of its strata; a group action on a space is codified by its fixed-point loci for each subgroup.
Through three desperate examples, this talk will motivate the notion of a stratified category, and will detail a general reconstruction result of such in terms of its strata.
         • Stratified spaces. Eg, concerning configuration spaces, Grassmannians, and knots;
         • Adelic reconstruction. Eg, prime-torsion decompositions of abelian groups;
         • Equivariant homotopy theory. Eg, vector spaces with cyclic group actions.
A novel application of this reconstruction will be presented: an identification of the Picard group of C_{p^n}-equivariant vector spaces.