DMS Colloquium: Lori Alvin

Speaker: Lori Alvin, Furman University

Title: Investigating One-dimensional Dynamical Systems

Abstract: The study of dynamical systems originally arose from the modeling of physical phenomena like the motions of the planets or the molecules in a gas. When considering all the possible dynamical systems in the world, it does not initially seem as if the study of one-dimensional dynamical systems can yield much insight into the most difficult problems. Although very simple to define, unimodal maps exhibit extremely complicated behaviors. In this talk we investigate unimodal maps from two families: the symmetric tent maps and the logistic maps. We look at several examples and try to understand the long-term behavior of points within each system.

Biography:

Lori Alvin is an Assistant Professor of Mathematics at Furman University in Greenville, SC. She is interested in topological dynamics, symbolic dynamics, and continuum theory. She earned her PhD in 2011 from the University of Wisconsin at Milwaukee under the direction of Karen Brucks, where she was first introduced to unimodal maps, adding machines, and inverse limit spaces. Most recently Lori has started investigating the dynamics of set-valued maps.

Sponsored by the AWM chapter, departmental colloquium

Faculty host: Krystyna Kuperberg