Join us on Friday February 9 at 3PM in Rocky 300 for the second of two Asprey Lecturers delivered by Professor Laura DeMarco. Harvard University.

Title: The Mandelbrot set today: what we know and what we don’t know

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 {c, c^2+c, (c^2+c)^2+c, …}, defined by x_1 = c and x_{n+1} = (x_n)^2+c, is bounded.  But this set turns out to be rich and complicated and related 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 arithmetic geometry to study these systems.  The new work is a collaboration with Myrto Mavraki.