8-9 March: Math. Phys. seminars at SISSA

[Emanuele Tuillier Illingworth]

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Mathematical Physics Seminars the 8th and 9th of March

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Tuesday 8th of March rm 136 11.00am

title: Riemann-Hilbert Approach to
        Scattering Problems in Elastic Media

Speaker: Elizabeth Its,
  Indiana University-Purdue University Indianapolis

Abstract:

We are developing Riemann-Hilbert (RH) approach to scattering problems in
elastic media. The approach is based on a version of RH method introduced
in nineties by A. Fokas for studying boundary problems for linear and
integrable nonlinear PDEs. The suitable Lax pair formulation of the
elastodynamic equation is obtained. The integral representations obtained
from this vector Lax pair   are applied to Rayleigh  wave  propagation  in
an elastic quarter space and half space. This reduces the problem to the
analysis of certain underdetermined matrix RH problem  on a torus.
We showed that the problem can be in fact re-formulated as a well-posed RH
problem with a shift. Some results of the described analysis will be
discussed. Part of this work is done jointly with Alexander Its and Julius
Kaplunov.

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Wednesday the 9th of March rm 134, 11.00am

Title: On the Riemann-Hilbert approach to the  normal matrix model.

Speaker: Alexander Its,
Indiana University Purdue University  Indianapolis

Abstract:
We present an  alternative way to build-up  the Riemann-Hilbert formalism
for the normal matrix model which was recently suggested by P. Bleher and
A. Kuijlaars. Our approach is an extension of the  Lax-pair construction
of R. Teodorescu, E. Bettelheim, O. Agam, A. Zabrodin, and P. Wiegmann,
and it  mimics the  isomonodromy technique  which was used in the early 90s
for the Riemann-Hilbert formulation of the Hermitian matrix model.

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