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Dear all, Please join us for Dan's defense. This is the last scheduled talk for the semester. Details below. Best, Iddo. Title: Geometric methods in analysis on fractals Speaker: Daniel Kelleher (UCONN) Friday, April 25, 2014 3:00 pm MSB 109A Abstract: Analysis on fractals revolves around the development of a harmonic structure on the fractal. Harmonic structures describe the Dirichlet form on these spaces, which is equivalent to a self-adjoint operator analogous to the classical Laplacian, and is also equivalent to a diffusion process on the space. I will include a brief discussion about results concerning the construction of harmonic structures on p.c.f. fractals, and determining the properties of this structure, such as calculating the spectrum of the Laplacian operator. I will then discuss results pertaining to the relationship between p.c.f. self-similar structures and self-similar groups, and how these groups of automorphisms of rooted trees generate fractals and help in their analysis. When lifting the p.c.f. assumption, analysis on these spaces becomes much harder, and few examples are know. I will talk about some results about the construction of a harmonic structure on the non-p.c.f. hexacarpet. Finally, if time permits, I will talk about applications to neurobiology.