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For many years,the employment of the Wienr-Hopf technique to acoustics

and other physical problems, was the only manifestation in applications

of the Riemann-Hilbert formalism. However, in the last 50 years this

formalism and its natural generalization called the d-bar formalism, have

appeared in a large number of problems in mathematics and mathematical

physics. In this lecture, I will review the impact of the above formalisms

in the following: the development of a novel, hybrid numerical-analytical

method for solving boundary value problems (Fokas

Method,www.wikipedia.org/wiki/Fokas_method), the introduction of new

algorithms in nuclear medical imaging, and most importantly, a novel

approach to the Lindelof Hypothesis (a close relative of the Riemann

Hypothesis).