Alexandre Kirillov




Wednesday, February 23, 2005 - 4:00pm


MSTB 254

We consider only two fractals: Sierpinski and Apollonian gaskets. The
idea is to show on these two examples how geometry, analysis, algebra and
number theory are tied together in the simplest problems, related to
fractal sets.

We start with definitions, speculate on the general matrix numerical
systems, consider the analytic properties and the p-adic behavior of
harmonic functions, analyse the spectrum of the Laplace operator on the
Sierpinski gasket. Then we describe the geometry, group-theoretic
structure and arithmetic properties of the Apollonian gasket.

The final idea is to draw a parallel between the two fractals - an
unfinished program.