Equivariant localization in quadratic enumerative geometry

We explain how to adapt the classical Atiyah-Bott torus localization methods to the computation of invariants, such as degrees of Euler classes, in the Grothendieck-Witt ring of quadratic forms, These quadratic enumerative invariants lift the usual integer-valued ones via the rank function, and for fields contained in the reals, the signature gives invariants for problems over the reals. Examples include quadratic counts of twisted cubic curves on hypersurfaces and complete intersections, this last is joint work with Sbarina Pauli.

For more information see:  https://personal.math.ubc.ca/~jbryan/Zoominar-UBC-ETH/