PIRSA:19100081

Equivariant localization and Atiyah-Segal completion for Hochschild and cyclic homology

Chen, H. (2019). Equivariant localization and Atiyah-Segal completion for Hochschild and cyclic homology. Perimeter Institute. https://pirsa.org/19100081

Chen, Harrison. Equivariant localization and Atiyah-Segal completion for Hochschild and cyclic homology. Perimeter Institute, Oct. 24, 2019, https://pirsa.org/19100081 

          @misc{ pirsa_PIRSA:19100081,
            doi = {10.48660/19100081},
            url = {https://pirsa.org/19100081},
            author = {Chen, Harrison},
            keywords = {Mathematical physics},
            language = {en},
            title = {Equivariant localization and Atiyah-Segal completion for Hochschild and cyclic homology},
            publisher = {Perimeter Institute},
            year = {2019},
            month = {oct},
            note = {PIRSA:19100081 see, \url{https://pirsa.org}}
          }

Harrison Chen

Cornell University

Talk number
PIRSA:19100081
Collection
Talk Type
Subject
Abstract

There is a close relationship between derived loop spaces, a geometric object, and Hochschild homology, a categorical invariant, made possible by derived algebraic geometry, thus allowing for both intuitive insights and new computational tools.  In the case of a quotient stack, we discuss a "Jordan decomposition" of loops which is made precise by an equivariant localization result.  We also discuss an Atiyah-Segal completion theorem which relates completed periodic cyclic homology to Betti cohomology.