Presented by: 
Michael Joswig, TU Darmstadt, Germany
Tue 20 Nov, 3:00 pm - 4:00 pm
Room 442, Building 67

It is known from theorems of Bernstein, Kushnirenko and Khovanskii from the 1970s that the number of complex solutions of a system of multivariate polynomial equations can be expressed in terms of subdivisions of the Newton polytopes of the polynomials.   For very special systems of polynomials Soprunova and Sottile (2006) found an analogue for the number of real solutions.  In joint work with Ziegler we could give a formula for the signature of foldable triangulation of a lattice polygon.  Via the Soprunova-Sottile result this translates into lower bounds for the number of real roots of certain bivariate polynomial systems.  This talk will focus on the combinatorial aspects of the subject.