" SPECTRA OF SELF-SIMILAR LAPLACIANS ON THE

SIERPINSKI GASKET WITH TWISTS"

**By**

**Baris Evren Ugurcan**

**Bilkent University**

**Department of Mathematics**

** **

Abstract: We
study the spectra of the self-similar Laplacians on the Sierpinski gasket (SG)
with twists. By this we mean that instead of the usual IFS (iterated function
system) that yields SG as its invariant set, we compose each mapping with a
reflection to obtain a new IFS that still has SG as its invariant set, but
changes the definition of self-similarity. Using recent results, we are able to
approximate the spectra of these Laplacians by two different methods. To each
Laplacian we associate a self-similar embedding of SG into the plane, and we
present numerical evidence that the method of outer approximation, when applied
to this embedding, yields the spectrum of the Laplacian (up to a constant
multiple).

**Date: ****Thursday, October 12, 2006**

**Time: ****14.40**

**Place: ****Mathematics Seminar Room, SAZ-141**