Vector Riemann-Hilbert problems

With Yuri Antipov (Louisiana State University)

Vector Riemann-Hilbert problems: methods of Riemann surfaces and automorphic and hypergeometric functions

Vector Riemann-Hilbert problem of the theory of analytic functions attracts attention of pure and applied mathematicians for more than a century.
This talk presents some efficient techniques for its solution from perspective of the theory of hypergeometric functions, elliptic and hyper elliptic functions and automorphic functions generated by the Schottky symmetry groups. Illustrative examples from fracture, diffraction theory and fluid mechanics will be given.

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