PIRSA:23010069

Effective algebro-homotopical constructions and a question of Kapustin

APA

Medina-Mardones, A. (2023). Effective algebro-homotopical constructions and a question of Kapustin. Perimeter Institute. https://pirsa.org/23010069

MLA

Medina-Mardones, Anibal. Effective algebro-homotopical constructions and a question of Kapustin. Perimeter Institute, Jan. 13, 2023, https://pirsa.org/23010069

BibTex

          @misc{ pirsa_23010069,
            doi = {10.48660/23010069},
            url = {https://pirsa.org/23010069},
            author = {Medina-Mardones, Anibal},
            keywords = {Mathematical physics},
            language = {en},
            title = {Effective algebro-homotopical constructions and a question of Kapustin},
            publisher = {Perimeter Institute},
            year = {2023},
            month = {jan},
            note = {PIRSA:23010069 see, \url{https://pirsa.org}}
          }
          

Anibal Medina-Mardones Sorbonne University

Abstract

In recent years, the classification of fermionic symmetry protected topological phases has led to renewed interest in classical constructions of invariants in homotopy theory. In this talk, we focus on the description of Steenrod squares for triangulated spaces at the cochain level, introducing new formulas for the cup-i products and discussing their universality through an axiomatic approach. We also examine the interaction between Steenrod squares and the algebra structure in cohomology, providing a cochain level proof of the Cartan relation as requested by Kapustin. Time permitting, we will also study the Adem relation from this perspective.

Zoom link:  https://pitp.zoom.us/j/98288876236?pwd=cHJVM3M1K3FsUmdtbENZenhKMnBkdz09