Elias We gert\, TU Bergakademie Freiberg\, Germany

T hough Bernhard Riemann'\;s thesis is commonly k nown as the source of the

celebrated Riemann ma pping theorem\, Riemann himself considered conform al

mapping just as an example to illustrate his ideas about a more general

class of nonlinear boundary value problems for analytic functions.

The talks aim on making these Riemann-Hilbert pro blems more popular\, to

encourage further resea rch and to find novel applications.

In the first part we address the existence and uniqueness of solutions

for different problem classes and present two applications: potential

flow past a porous object\, and a free boundary value proble m in

electrochemical machining.

In the s econd part\, a connection between Riemann-Hilbert problems and a

class of extremal problems is es tablished. Solutions to Riemann-Hilbert

problem s are characterized by an extremal principle which generalizes

the classical maximum principle an d Schwarz'\; lemma. We briefly sketch an

app lication to the design of dynamical systems.

In the end\, a class of nonlinear transmission probl ems is considered.

As a special result\, we obt ain a hyperbolic version of the Riesz decompositio n

of functions on the unit circle into an analy tic and an anti-analytic part. LOCATION:Seminar Room 2\, Newton Institute CONTACT:info@newton.ac.uk END:VEVENT END:VCALENDAR