Analysis seminar: Shanna Dobson (UCR)

Title: The Chronicles of Fractal Geometry: Fractal Strings, and Functorial Harps

Abstract: In this talk, we explore the colorful analytical world of fractal geometry. We introduce fractal strings in the sense of Lapidus, both intuitively and by way of rigorous constructions. We examine rich illustrations of higher dimensional fractals and p-adic fractal strings. Then, we use artistic dimensions to postule new mathematical definitions; namely, universal properties of fairy tales. We propose a new categorical definition of fractal strings. We conclude with our conjectures on categorical p-adic fractal strings, which I call functorial harps.