Guillem Cazassus (Oxford) will speak in the differential geometry seminar on 26/02/2024 at 2pm in the Salle des Profs (9th floor building NO). Guillem’s title is “Extending down Donaldson-Floer theory” and his abstract is below.
The Donaldson polynomials are powerful invariants in Low
Dimensional Topology: for example they are able to distinguish smooth
manifolds that are homeomorphic, but not diffeomorphic. They are
rooted in theoretical physics (Yang-Mills gauge theory) and are
difficult to compute, as they involve solving a PDE (the
Anti-Self-Dual equation).
I will present a program aimed at computing these by “cut-and-paste”
operations. Specifically I will explain how to recast these into an
“extended Topological Field Theory”. This will involve going from
Gauge Theory to Symplectic Geometry, Hamiltonian actions and
Homotopical Algebra.