Department Colloquium
No upcoming colloquium.Past Department Colloquia
Date: Friday, November 11
Time: 4 PM onward
Venue: Eckhart 206 (Departmental address, contact information)
Speaker: Viatcheslav Kharlamov (IRMA, Strasbourg)
Title: First steps in real enumerative geometry.
Abstract: Surprisingly, in a quite a number of real enumerative problems the number of real solutions happens to be comparable (for example, in logarithmic scale) with the number of complex ones. For the moment, such a phenomenon is studied quite in depth in the case of interpolation of real points on a real rational surface by real rational curves. The key tool here are the Welschinger invariants (which can be seen as a real analogue of genus zero Gromov-Witten invariants). In this talk, based on joint works with I. Itenberg and E. Shustin, I will remind how Welschinger invariants look like in the case of surfaces, point certain modifications, and present some recursive formulas that allow to control Welschinger invariants in the case of Del Pezzo surfaces and by these means to establish some basic properties of the invariants that imply, in particular, the abundance of real solutions.