" SPECTRA OF SELF-SIMILAR LAPLACIANS ON THE
SIERPINSKI GASKET WITH TWISTS"
Baris Evren Ugurcan
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).
Place: Mathematics Seminar Room, SAZ-141