Oleg Musin - Chebyshev systems, convex curves and polyhedra | MoCCA'20

The talk “Chebyshev systems, convex curves and polyhedra“ by Oleg Musin on the Moscow Conference on Combinatorics and Applications at MIPT. Annotation: It is not hard to see that any Chebyshev system of functions defines a convex curve in d-dimensional Euclidean space. In this talk we consider ф generalization of the sign changes Hurwitz theorem for convex curves in R^d. The convex hull of any finite set of points on a convex curve is a polytope which is combinatorially equivalent to a cyclic polytope. We will consider a construction defining an alternative centrally symmetric polytope. Using this polytope, a proof of Ky Fan's theorem and its extension can be obtained directly from the Hopf degree theorem. The full schedule of the conference -