I am an analyst working in several complex variables. Since approximately fifteen years, an important part of my research has been devoted to the study of bifurcations
within holomorphic families of endomorphisms of complex projective spaces. Besides complex analysis, my work on this subject uses pluripotential and ergodic theoretic
methods. More specifically, I often investigate the relations between geometrical properties of bifurcation loci and regularity properties of Lyapunov exponents.
A typical feature of my work is to stay at the border of one-dimensional and higher-dimensional holomorphic dynamics and to offer strong possibilities of enrichment between these two fields. This motivated me for visiting ICL for a long period to discuss these topics and share ideas with experts such as Davoud Cheraghi and Sebastian van Strien.
I spent three months at ICL and started a collaboration with Davoud on the geometry of Siegel domains for holomorphic dynamical systems in dimension at least two. We were interested in the possible existence of such domains with very regular boundaries and found families of transcendental automorphisms enjoying such properties. I plan to pursue this collaboration which opens many other challenging questions.
The ICL Maths departement is a wonderful place for research, it was an extremely nice opportunity for me to be there for a long period.
Host: Dr Davoud Cheraghi