*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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