QM Research Seminar: Refined invariants for real curves

The talk is devoted to several real and tropical enumerative problems. We suggest new invariants of the projective plane (and, more generally, of certain toric surfaces) that arise from appropriate signed enumeration of real algebraic curves of genus 1 and 2.These invariants admit a refinement (according to the quantum index) similar to the one introduced by Grigory Mikhalkin in the genus zero case. It turns out that two different rules of signs in the enumeration surprisingly lead to the same collection of refined invariants.The proof of the latter fact uses the tropical counterparts of the invariants under consideration.

This is a joint work with Eugenii Shustin.