Complex analysis, Banach spaces, and operators

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, number theory, geometry of Banach spaces and differential equations. More specifically, we address the following topics: 
1. Problems of Loewner Theory where aspects of geometric function theory and of differential equations (and deep connections with Physics) converges; 
2. Hyperbolic dynamics in complex domains (such as the unit disk) for both discrete iteration and continuous iteration;
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. In Number Theory, the study of the distribution of zeros of the zeta function and the complexity of the powers of 2;
6. The study of the asymptotic behavior of properties of convex sets in finite-dimensional spaces.

Our research team consists of seven 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. We expect to generate significant benefits for the participation in the team of some co-authors and international experts (from the Universisities of Rome 2 Tor Vergata, Stavanger, Helsinki, Artois, Federal de Minas Gerais, and Technical of Munich).