I spent 3 months as an ICL-CNRS Fellow at Imperial College, between April and July 2018. This visit allowed me to discuss and interact with experts both in algebraic geometry (in particular with my host Johannes Nicaise and his collaborators and students), and in holomorphic dynamical systems (in particular with Fabrizio Bianchi and Davoud Cheraghi).
With Fabrizio Bianchi, we investigated examples of degeneration of Green potential associated to meromorphic families of polynomial maps, and found interesting connections with the corner locus of the tropical polynomial given by the tropicalization of such families.
While taking part to the fervent research activity at ICL, especially through seminars and workshops, I could enter in contact and interact with several colleagues.
In particular, I could discuss with Mirko Mauri about possible generalization to higher dimensions of a recent work about characterizations of sandwiched singularities in terms of selfsimilarity properties. While a general statement in higher dimensions seems quite ambitious at the moment, interesting results can be obtained by focusing on cone singularities, and studying the analogous problem in the global setting, related to Fano varieties.
Finally, with Sara Filippini, we started investigating the relations between normal families of finite non-invertible maps on cusp singularities and mirror symmetry. In fact, the problem of classifying dynamical behaviors of such maps seems related to constructing a canonical dual of a given map to the dual cusp. Understanding this phenomenon could enlighten new connections between the two topics.
The working conditions at the Imperial college were ideal, the mathematics department is scientifically very active. This visit allowed me to learn a lot of new mathematics, and to develop new collaborations, which would not have been possible otherwise.
Host: Dr Johannes Nicaise