Uncertainty principles and Schrodinger operators on fractals

Analysis Seminar
Wednesday, October 23, 2019 - 1:55pm for 1 hour (actually 50 minutes)
Skiles 005
Kasso Okoudjou – University of Maryland and M.I.T. – kasso@math.umd.eduhttps://www.math.umd.edu/~okoudjou/
Christopher Heil

In the first part of this talk, I will give an overview of a theory of harmonic analysis on a class of fractals that includes the Sierpinski gasket. The starting point of the theory is the introduction by J. Kigami of a Laplacian operator on these fractals. After reviewing the construction of this fractal Laplacian, I will survey some of the properties of its spectrum. In the second part of the talk, I will discuss the fractal analogs of the Heisenberg uncertainty principle, and the spectral properties a class of  Schr\"odinger operators.