July 27-28 2015 5E102, Inha University |

**Lecture 1****. 2:00-3:00 July 27 (Mon), 2015**

**Poincare variational principle in
potential theory**

The talk will translate in modern
language Poincare's famous Acta Mathematica 1897
article, complemented by Torsten Carleman
doctoral dissertation and the work of M. Schiffer on Fredholm eigenvalues of a planar domain.

**Lecture
2****. 4:00-5:00 July 27 (Mon), 2015**

**The Friedrichs operator**

The Hilbert space angle between Bergman
space and its complex conjugate was studied by Friedrichs
in connection with problems of planar elasticity. I will trace some ideas derived
from Friedrichs influential work, in the context of
modern approximation theory. In particular I will bring into focus Hankel
forms, complex symmetric operators and spectral analysis in a vector space
endowed with two norms.

**Lecture
3****. 1:00-2:00 July 28 (Tues), 2015 **

**The ellipse revisited**

Among all planar algebraic curves the
ellipse is distinguished by carrying Bergman space orthogonal polynomials
enjoying a three term relation. And secondly by not possessing a Riesz-Fejer type decomposition for positive polynomials,
but still enjoying a special sub-normal quantization. Other aspects of modern
mathematical physics, such as Laplacian Growth phenomena, single out the
ellipse.