Mathematics Seminar - 5 April 2006

[Mabilo Koutou]

M A T H E M A T I C S   S E M I N A R S   2006

Series of Lectures in "Experimental Discoveries of Mathematical Facts"

Wednesday, 5 April, at 14.30 hrs.
Venue:  ICTP Seminar room (Main Building, first floor)

Professor V.I. Arnold
(Steklov Institute, Moscow, Russia)

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


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).


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