Hans Fogedby (Aarhus University)
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.