PIRSA:24110061

Derived differential geometry and applications

Steffens, P. (2024). Derived differential geometry and applications. Perimeter Institute. https://pirsa.org/24110061

Steffens, Pelle. Derived differential geometry and applications. Perimeter Institute, Nov. 07, 2024, https://pirsa.org/24110061 

          @misc{ pirsa_PIRSA:24110061,
            doi = {10.48660/24110061},
            url = {https://pirsa.org/24110061},
            author = {Steffens, Pelle},
            keywords = {Mathematical physics},
            language = {en},
            title = {Derived differential geometry and applications},
            publisher = {Perimeter Institute},
            year = {2024},
            month = {nov},
            note = {PIRSA:24110061 see, \url{https://pirsa.org}}
          }

Pelle Steffens

Talk number
PIRSA:24110061
Collection
Talk Type
Subject
Abstract

I will review some recent progress in derived differential geometry, in particular pertaining to moduli stacks of solutions of elliptic partial differential equations on manifolds (with boundaries, and also with `logarithmic' boundaries, which include, for instance, manifolds with asymptotically cylindrical ends). In particular, this framework allows one to work efficiently with the compactified moduli spaces of symplectic topology and gauge theory. In another direction, I will explain some work in progress on the derived geometry of jet spaces, which can be used to endow moduli stacks of solutions of EOMs of a classical field theory with shifted symplectic structures.