# Erwan Brugallé (Université de Nantes): Relation among complex, real and tropical enumerative invariants of plane curves part I

**Abstract: **A classical problem in enumerative geometry is to determine the number

of plane algebraic rational curves of degree d passing through 3d-1

points (eg the number of lines passing through two points). We will

address several generalizations of this problem in real, tropical, and

symplectic geometries. The first part will mainly be devoted to tropical

refined invariants defined by Block and Göttsche, and generalized by

Göttsche and Schroeter. Relations discussed there are suggested by a

formula relating enumerative invariants of two real symplectic

4-manifolds differing by a surgery along a real Lagrangian sphere. This

formula, whose origin can be traced back to a work by Abramovich and

Bertam, will be discussed in the second part. We will give as well

applications to Welschinger invariants of rational symplectic 4-manifolds.

**This talk is the first part of in a series of lectures by Brugallé in relation to his BFS invited professorship.**