seminar @ Sissa

[Emanuele Tuillier Illingworth]

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MATHEMATICAL PHYSICS SECTOR ACTIVITIES
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SEMINAR ON:
"Boutroux curves: equilibrium measures without solving a minimization problem"

Prof. Marco BERTOLA (Concordia University)

Abstract:
The nonlinear steepest descent method for rank-two systems relies on the notion of $g$-function. For the case of asymptotics of generalize orthogonal polynomials with respect to varying {\em complex} weights we can recast the requirements  for the Cauchy-transform of the equilibrium measure into a  problem of algebraic geometry and harmonic analysis and completely solve the existence and uniqueness issue without relying on the minimization of a functional. This addresses and solves also the issue of the ``free boundary problem'', determining implicitly the curves where the zeroes of the orthogonal polynomials accumulate in the limit of large degrees and the support of the measure. A numerical algorithm to find these curves in some cases is also explained. (With animations!)

Wed. 11 July 2007 @ 14.30
SISSA - Main Building - lower ground floor - room D