Instructor: Bobby Wilson
Email: blwilson [at] math . uw .edu
Office: Padelford C-344
Office Hours: TBD
Lectures: M W F 1:30 pm - 2:20 pm, Padelford C-401
COURSE DESCRIPTION
This course will be based in geometric measure theory with a particular emphasis on questions concerning fractals, structure and geometric combinatorics. Specifically, we will use iterated function systems as a medium through which to study the various notions of dimension of sets and measures and their interplay. This will include the study of Hochman's \cite{hochman2014self} results using Shannon Entropy to approach the dimension drop conjecture. Furthermore, we will discuss projection theorems including Marstrand's projection theorem and Favard length (If there is time, we will discuss generalized projections of Peres and Schlag \cite{peres2000smoothness}). Finally, we will discuss topics of pairwise distances and Kakeya sets including recent progress in these directions. The texts of Falconer, Mattila, B\'ar\'any-Simon-Solomyak, and Guth. Prerequisites: MATH 524.
Prerequisites: 524
Text Book: "Self-Similar and Self-affine Sets and Measures", Barany, Simon and Solomyak
RECENT UPDATE
[09.24.2025] Welcome to the fall quarter! Here is the Syllabus