Transcendental Julia sets with fractional packing dimension
Jack Burkart (Stony Brook University)
Abstract: In this talk, we will define and compare different definitions of dimension (Hausdorff, Minkowski, and packing) used to analyze fractal sets. We will then define the basic objects in complex dynamics, and discuss some history of results about the dimension of the fractal Julia sets that famously show up in this area. No prior knowledge of complex dyanmics will be assumed. We will conclude by discussing my recent construction of a Julia set of a non-polynomial entire function with packing dimension strictly between one and two. We will see that Whitney decompositions, a foundational tool in harmonic analysis, play a vital role in the dimension calculation.
analysis of PDEsclassical analysis and ODEs
Audience: researchers in the topic
Series comments: Description: A senior graduate student/postdoc series in harmonic analysis, geometric measure theory, and partial differential equations.
Meetings will be weekly, and usually will occur on Monday, with some exceptions. For each talk, the Zoom link is made available in the website too. Contact Bruno Poggi at poggi008@umn.edu if you would like to subscribe to the seminar mailing list.
| Organizers: | Bruno Poggi*, Ryan Matzke, Jose Luis Luna Garcia* |
| *contact for this listing |