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CATEGORIES:Cambridge Analysts' Knowledge Exchange
SUMMARY:Construction of the Global Parametrix for the Kiss
ing Polynomials - Andrew Celsus\, University of Ca
mbridge
DTSTART;TZID=Europe/London:20190306T150000
DTEND;TZID=Europe/London:20190306T160000
UID:TALK121243AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/121243
DESCRIPTION:When trying to implement the Deift-Zhou method of
nonlinear steepest descent to recover uniform asym
ptotics of orthogonal polynomials\, one needs to c
onstruct solutions to a model Riemann-Hilbert prob
lem (RHP). The solution to this model problem is k
nown as the global parametrix. Typically\, these m
odel RHPs are of a standard form\, and the global
parametrix can be constructed with the use of thet
a functions on a certain Riemann surface. In the c
ase when one is dealing with orthogonality in the
complex plane and the limiting distribution of zer
os is supported on multiple arcs\, the associated
model RHP is not of this standard form\, and as su
ch\, new methods are needed to construct solutions
to this problem. The goal of this talk is to outl
ine the construction of the global parametrix whic
h arises when one is trying to study asymptotics o
f a family of complex polynomials known as the Kis
sing polynomials. This is joint work with Guilherm
e Silva of the University of Michigan.
LOCATION:MR14\, Centre for Mathematical Sciences
CONTACT:Georg Maierhofer
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