**ODTÜ-B****Ý****LKENT
ALGEBRAIC GEOMETRY SEM****I****NAR**

**“Towards the generalized Shapiro and Shapiro conjecture”**

by

**Alexander
Degtyarev**

**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 --> P**^{1} 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>d*^{2}/3+O(*d*). In the talk, we improve the
above inequality to *g>d*^{2}/4+O(*d*).

** **

**Date:** 3 April 2009 Friday

**Time:** 15:40

**Place:** Bilkent, Mathematics Seminar
Room SA-141

** **

**Tea and cookies will be served before the
talk.**