Stochastic Loewner Evolution: Fractal shapes and curves
by
Hans Fogedby(Aarhus)
→
Europe/Stockholm
122:026
122:026
Description
The most exciting concepts in theoretical physics are
those that relate algebraic properties to geometrical ones.
Of course, the outstanding example of this is the
geometric meaning of the equations of general relativity,
and their realization in the shapes of possible universes and
in black holes. Other examples abound including the patterns
of the paths of Brownian motion, the forms of percolating clusters,
the shapes of snowflakes and the phase boundaries, and the beautiful
fingers of interpenetrating fluids and of dendrites.
An approach called Schramm-Loewner evolution (SLE) provides a
new method for dealing with a wide variety of scale-invariant
problems in two dimensions. This approach is based upon an
older method called Loewner Evolution (LE), which connects
analytical and geometrical constructions in the complex plane.
