April 4, Wednesday, 15:30, room 211

By definition, a determinantal representation of a plane curve C is a matrix triple (A_0,A_1,A_2) such that the zero set of the equation det(x_0 A_0+x_1 A_1+x_2 A_2)=0 is C. In the talk I am going to present the proof (due to V. Vinnikov) of the theorem stating that every smooth plane curve over complex numbers admits such a representation. We will also discuss an analogous result over real numbers, in particular, various relations between the signature of the defining matrices and the topological type of the curve C(\R).