Program
Ilia Itenberg (Paris)
Signed enumeration of real algebraic curves
Abstract: Cramer's theorem states that, for any positive integer d, through d(d+3)/2 points in general position in the real plane one can always trace a unique algebraic curve of degree d. We discuss several similar enumerative problems, taking into account, in addition, the genus of curves under consideration. In particular, we suggest new invariants of the projective plane (and, more generally, of certain toric surfaces) that arise from appropriate enumeration of real algebraic curves of genus 1 and 2 (joint work with E. Shustin).