Tid: 20 oktober 2008 kl 15.15-16.00 .

Plats : Seminarierummet 3733, Institutionen för matematik, KTH, Lindstedts väg 25, plan 7. Karta!

Föredragshållare: Alan Sola, Matematik, KTH

Titel: Loewner evolutions and random growth models.

Sammanfattning: The Loewner differential equation is a highly useful tool in complex analysis. It allows us to parametrize conformal mappings, and hence sets in the complex plane, in terms of a unimodular driving function. By letting these driving functions be given by some stochastic process, one obtains random evolutions of conformal maps, and hence random families of sets in the plane.

I will report on recent joint work with Fredrik Johansson (KTH). We have studied the hulls of Loewner evolutions driven by Lévy processes, and in particular the compound Poisson process. The discontinuities of the driving processes cause the evolving sets to be branched, in contrast to the curves of standard Schramm-Loewner evolution (SLE) that correspond to Brownian motion. I will explain how our work relates to random growth models in physics and discuss some results that we have obtained.

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