November 29, 2011
French university professor to give second M-Center lecture today
Slava Kharlamov, a professor at the University of Strasbourg in France, will give the second Mirror Symmetry and Tropic Geometry Research Center lecture at 2:30 p.m. today in 122 Cardwell Hall.
Kharlamov's lecture is titled "First Steps in Real Enumerative Geometry."
Surprisingly, in several real enumerative problems the number of real solutions happens to be comparable (for example, in logarithmic scale) with the number of complex ones. Currently such a phenomenon is best studied in the case of interpolation of real points on a real rational surface by real rational curves. The key tool here is given by 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, Kharlamov will explain what 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. Using this, Kharlamov will explain how to establish some basic properties of the invariants that imply, in particular, the abundance of real solutions.