Mathematics Seminar - 5 April 2006

[mabilok at ictp.it]

Seminar Title:
Statistics of topological structures of smooth functions, of polynomials, of trigonometric polynomials, of affine Coxeter groups  and the Sixteenth Problem of Hilbert. (Lecture 1)

Series of Lectures in "Experimental Discoveries of Mathematical Facts"

Date:Wednesday, 5 April 2006
Start Time:14:30:00
Location:ICTP
Contact:Mabilo Koutou
Contact Email:math at ictp.it
Room:Main Building Seminar Room
Speaker:Prof. V.I. Arnold (Steklov Institute, Moscow, Russia)

Abstract:

One associates to a smooth function a graph, defined as the topological  space whose points are the connected components of the level hypersurfaces of the function.  The talk describes the structures of these graphs for the Morse functions with a fixed number of critical points and for the polynomials and trigonometric polynomials of given degree or a given spectrum (provided, for instance, by the Newton polyhedron of that trigonometric polynomial for an affine system of  roots).