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On the volume of basins of roots of polynomial systems

Ponente: Michael Shub
Institución: City University of New York
Tipo de Evento: Investigación
Cuándo 18/02/2016
de 13:00 a 14:30
Dónde Salon de Seminarios Graciela Salicrup
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Given a square system of complex homogenous polynomial equations , f , and a root x we define the basin of f as follows. Pick z at random in projective space and subtract s f(z) from f (homoginized). If the zero of "f-sf(z)" for s between 1 and zero starting at z continues to x we say 
z is in the basin of x. Are the volumes of the basins all equal? This would be kind of amazing from my perspective and useful. There is evidence both ways. I will discuss what I and coworkers  Carlos Beltran and Diego Armentano know about the problem.