seminario Boris Shapiro
Boris Shapiro, Stockholm University
terrà un seminario
Giovedì 10 Ottobre alle 15.00
presso la sala conferenze Tricerri del Dipartimento di Matematica e Informatica su
Mystery of point charges after J.C.Maxwell, C.F. Gauss and M.Morse
Abstract. The fundamental question about how many points of equilibrium can a system of fixed point charges in R^3 have attracted substantial attention since the late 19-th century. In his famous book "The treatise of electricity and magnetism" J.C.Maxwell formulated an unexpected guess that the number of points of equilibrium of a system of N charges in R^3 never exceeds (N-1)^2. His proof although very interesting turned out to be completely false and his claim is still open already for 3 charges. I will discuss this topic and present some new results in this direction related to the fewnomial theory and real algebraic geometry. (No advanced material will be required for understanding, in fact , I will present some mathematical challenges for undergraduate students.)