Colloquium Series

Spring 2026

March 6, 2026

Dylan Thurston, Boston College​

Topic: Rational maps and graph energies
Time: 4:00-5:00 pm
Location: JCC 280
Reception: JCC 501
Abstract: The dynamics of rational maps from the Riemann sphere to itself has long fascinated mathematicians and the general public with the intricate patterns they produce in their limit sets. But how to describe a rational map abstractly? We will show how to present rational maps and maps that look topologically like them by maps between graphs, and in turn extract information about the rational map from dynamics on the graphs, getting information about:​
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* whether a topological map can be geometrized and realized as a  rational map;​
* the conformal dimension of the limit set;​
* whether the limit set has Sierpinski-carpet behavior; and​
* just how expanding the map is as it acts on its limit set.

February 6, 2026

Laura DeMarco, Harvard University

Topic: The (Algebraic) Geometry of the Mandelbrot Set
Time: 4:00-5:00 pm
Location: JCC 160
Reception: JCC 535
Abstract: One of the most famous -- and still not fully understood -- objects in mathematics is the Mandelbrot set.  By definition, it is the set of complex numbers c for which the recursive sequence defined by x_1 = c and x_{n+1} = (x_n)^2+c is bounded.  This set turns out to be rich and complicated and connected to many different areas of mathematics.  I will present an overview of what's known and what's not known about the Mandelbrot set, and I'll describe recent work that (perhaps surprisingly) employs tools from number theory and arithmetic geometry.  The recent project is a special case of a broader conjecture in algebraic dynamical systems on the geometry of periodic points and joint work with Myrto Mavraki.