Lugar: Gradu Aretoa, ZTF, Leioa

Día: 2026/04/22

Hora: 11:45

Prof. Laura DeMarco (Harvard University)

The (algebraic) geometry of the Mandelbrot set

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.

Prof. Mihnea Popa (Harvard University)

Hodge symmetries of singular varieties

The Hodge diamond of a smooth projective complex variety contains essential topological and analytic information, including fundamental symmetries provided by Poincaré and Serre duality. I will describe recent progress on understanding how much symmetry there is in the analogous Hodge-Du Bois diamond of a singular variety, and the concrete ways in which this symmetry reflects the singularity types. In the process, we will see how invariants from commutative algebra and higher dimensional geometry influence the topology of an algebraic variety, for instance by means of new weak Lefschetz theorems.