Special Seminar

Very recently, J.Y. Welschinger introduced a set of invariants for real varieties that give lower bounds on the number of real algebraic curves satisfying certain incidence relations. After J. Solomon's homological interpretation, these invariants opened a new gate to reconsider the quantum cohomology of real varieties. In this talk, I will discus Gromov-Witten-Welschinger (GWW) classes and their applications. In particular, Horava's definition of quantum cohomology of real algebraic varieties will revisited and it will be (re)introduced as a DG-operad. In light of this study, I will speculate about mirror symmetry for real varieties.