Complex analysis, Banach spaces, and convexity

PI1: Manuel D. Contreras Márquez

PI2: Luis Rodríguez Piazza

Abstract: The aim of this project is to develop several research topics in the frame of Mathematical Analysis touching different areas as complex variable, operator theory, geometry of Banach spaces, differential equations, and convex geometry. More specifically, we address the following topics:
1. Problems of Loewner theory where aspects of geometric function theory and of differential equations converges (and with deep connections with Physics);
2. Hyperbolic dynamics in complex domains (such as the unit disk) for both discrete iteration and continuous iteration (semigroups of holomorphic functions);
3. The study of some classical (essentially composition and integral) operators between spaces of analytic functions, semigroups of such operators and the study of spaces of Dirichlet series;
4. Issues related to the classical invariant subspace problem;
5. The study of the asymptotic behavior of properties of convex sets in finite-dimensional spaces.

Our research team consists of six researchers from the University of Seville with extensive experience in the previous topics, formed by the union of two groups that have been continuously involved in research projects over the last 20 years. Five of them are consolidated researchers (either full or associated professors) and the other one with a Juan de la Cierva post-doc position. We expect to get important benefits for this project with participation in the work plan of recognized international experts and our collaborators (whose names and universities we will detail in each block of the scientific memoir in which they will collaborate).