Boris Shapiro: New aspects of Descartes’ rule of signs
Tid: Må 2018-11-26 kl 11.00 - 12.00
Föreläsare: Boris Shapiro (Stockholm University
Plats: Room 31, building 5, Kräftriket, Department of Mathematics, Stockholm University ￼
The classical Descartes’ rule of signs claims that the number of positive roots of a real univariate polynomial is bounded by the number of sign changes in the sequence of its coefficients and it coincides with the latter number modulo 2. Similarly, the number of negative roots is bounded by the number of sign preservations and coincides with it modulo 2.
Strangely enough it is still unknown which combinations (p,n) of the numbers of positive and negative roots can be realized by polynomials of a given degree having a given sequence of signs of their coefficients. I will present some information related to this question and a number of open problems.