Emmy-Noether-Seminar

Quadratic refinements of enumerative problems

Marc Levine (Essen)

Abstract: Using a variety of methods, ranging from classical algebraic geometry to modern motivic homotopy theory, a number of classical enumerative invariants, such as Euler characteristics or counts of rational curves, have been refined to invariants in the Grothendieck-Witt ring of quadratic forms. These refinements yield the classical invariants by taking the rank and signature over the reals. We illustrate the theory with a number of examples.