Sarah Koch (University of Michigan)
Title: Mating habits of polynomials
Abstract: Given two complex polynomials, we can try to mathematically "paste them together" to obtain a rational function, through a procedure in complex dynamics known as mating the polynomials. In this talk, we focus on quadratic polynomials - we begin with a brief discussion of the dynamics of quadratic polynomials and parameter space (where the Mandelbrot set lives), we then discuss the mating of two quadratic polynomials, and finally we explore examples where the mating does exist, and examples where it does not. There will be many pictures and movies in this talk.
Alex Kontorovich (Rutgers University)
Title: Circles. Lots of Circles.
Abstract: Oh, and numbers too. (Did I mention the circles?)
Ezra Miller (Duke University)
Title: Topology for statistical analysis of brain artery images
Abstract: Statistics looks for trends in data. Topology quantifies geometric features that don't change when shapes are squished, stretched, or bent continuously. What does one have to do with the other? When data objects are already geometric, such as magnetic resonance images of branching arteries, topology can isolate information of statistical relevance. This talk explains what we have learned about the geometry of blood vessels in aging human brains using topological methods in statistics. The main results are joint with Paul Bendich, Steve Marron, Alex Pieloch, and Sean Skwerer (at the time, a Math postdoc, Stat faculty, Math undergrad, and Operations Research grad student).