PIRSA:21120024

Video URL

https://pirsa.org/21120024

Reflection in algebra and topology

Mazel-Gee, A. (2021). Reflection in algebra and topology . Perimeter Institute for Theoretical Physics. https://pirsa.org/21120024

Mazel-Gee, Aaron. Reflection in algebra and topology . Perimeter Institute for Theoretical Physics, Dec. 10, 2021, https://pirsa.org/21120024 

          @misc{ scivideos_PIRSA:21120024,
            doi = {10.48660/21120024},
            url = {https://pirsa.org/21120024},
            author = {Mazel-Gee, Aaron},
            keywords = {Mathematical physics},
            language = {en},
            title = {Reflection in algebra and topology },
            publisher = {Perimeter Institute for Theoretical Physics},
            year = {2021},
            month = {dec},
            note = {PIRSA:21120024 see, \url{https://scivideos.org/pirsa/21120024}}
          }

Aaron Mazel-Gee University of Southern California

Talk numberPIRSA:21120024
DOI10.48660/21120024
Source RepositoryPIRSA
Collection
Talk Type Scientific Series
Subject

Abstract

In this talk, I will discuss a new duality that was recently discovered in joint work with David Ayala and Nick Rozenblyum, which we refer to as reflection.

In essence, reflection amounts to two dual methods for reconstructing objects, based on a stratification of the category that they live in. As a classical example, an abelian group can be reconstructed on the one hand in terms of its p-completions and its rationalization, or on the other (reflected) hand in terms of its p-torsion components and its corationalization; and these both come from a certain "closed-open decomposition" of the category of abelian groups.

Examples and applications of reflection are abundant, because stratifications are abundant. In algebra, reflection recovers the derived equivalences of quivers coming from BGP reflection functors (hence the terminology "reflection"). In topology, reflection is closely related to Verdier duality, a generalization of Poincaré duality that applies to singular spaces. Moreover, an explicit description of reflection leads to a categorification of the classical Möbius inversion formula, a Fourier inversion theorem for functions on posets.

Zoom Link: https://pitp.zoom.us/j/92439401154?pwd=cGZsUGJGcmNXdFZuclREL3gyYnhQdz09