Mathematics Colloquia and Seminars

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Welschinger invariants are real analogues of genus zero Gromov-Witten invariants. Their general theory is still under construction but they gave already a number of non-trivial applications, especially in real enumerative geometry where they remain the main source of lower bounds on the number of real solutions (one may mention as one of the first applications of the Welschinger invariants the proof of the existence of real solutions in the problem of interpolating real points by real rational plane curves of given degree). No preliminary knowledge on the subject is supposed. Some down-to-years definition of Welschinger invariants will be given and it will be shown how some elementary tropical geometry helps to understand the behavior and properties of these invariants in some simple cases, like small Del Pezzo surfaces, that is the blow-ups of projective plane in a small number of points.