In the spring of 2024, I visited Imperial College London for a three-month research stay. During this period, I experienced a productive and engaging academic environment. I benefitted in particular from many discussions with members of the dynamical systems and geometry groups or visiting scholars, and from attending various seminars and events. Outside of my research, I found London to be a culturally rich city, which complemented the academic experience well.
My field of research is holomorphic dynamics in one or several complex variables. The primary research focus during my stay was the starting point of a project with my host, Dr Davoud Cheraghi, on the bifurcation measure in moduli spaces of polynomial maps. This measure detects maximal bifurcations of polynomials seen as holomorphic dynamical systems. Using perturbation techniques developed by Arnaud Chéritat (University of Toulouse), we were able to prove that cubic polynomials with a capture type Siegel disk belong to the support of this measure, despite being stable along a one-dimensional subfamily in parameter space.
This work forms the basis for a longer-term project aimed at quantitatively analysing bifurcation and stability in one-dimensional complex rational dynamics.
Host: Davoud Cheraghi
