Abstract: We deal with the following generalized version of the Shapiro and Shapiro total reality conjecture: given a real curve C of genus g and a regular map C --> P1 of degree d whose all critical points are distinct and real (in C), the map itself is real up to a Mőbius transformation in the target. The generalization was suggested by B. and M. Shapiro in about 2005, after the original conjecture was proved, and it was shown that the statement does hold for g>d2/3+O(d). In the talk, we improve the above inequality to g>d2/4+O(d).
Date: 3 April 2009 Friday
Place: Bilkent, Mathematics Seminar Room SA-141
Tea and cookies will be served before the talk.