Friday November 13, 2009
4:00 - 5:00 pm
Milner Hall 317
4:00 - 5:00 pm
Milner Hall 317
Mihai Putinar, UC Santa Barbara
Mathematical aspects of elliptic growth
A 2D boundary dynamics, obtained as the idealization of a fluid flow between two narrow plates, or electrodeposition, or bacterial growth leads to a simple mathematical idealization: the boundary velocity is proportional to the normal derivative of the Green function of the domain surrounded by the moving interface. Remarkably, this highly non-linear, non-equilibrium dynamical system admits many close solutions and an array of specific qualitative features which were repeatedly and independently been discovered during the last half-century. The lecture will be centered on three different linearizations of this growth process, all revealing complementary aspects: complete integrability of a 2D Toda lattice type, a statistical/quantum interpretation involving random normal matrices and a potential theoretic one having a natural Hilbert space operator realization.
Mathematical aspects of elliptic growth
A 2D boundary dynamics, obtained as the idealization of a fluid flow between two narrow plates, or electrodeposition, or bacterial growth leads to a simple mathematical idealization: the boundary velocity is proportional to the normal derivative of the Green function of the domain surrounded by the moving interface. Remarkably, this highly non-linear, non-equilibrium dynamical system admits many close solutions and an array of specific qualitative features which were repeatedly and independently been discovered during the last half-century. The lecture will be centered on three different linearizations of this growth process, all revealing complementary aspects: complete integrability of a 2D Toda lattice type, a statistical/quantum interpretation involving random normal matrices and a potential theoretic one having a natural Hilbert space operator realization.