PI: Contreras Márquez, Manuel D.
Abstract: The project can be situated within the general framework of analytic and harmonic functions in planar domains or in other special domains in several variables or spheres and its relationships with, or applications to, other fields of Mathematics. Our global objective is to deepen further our understanding of several aspects of complex functions, be they analytic or harmonic: 1) their geometric and analytic properties as members of certain spaces or special classes, 2) their dynamics (iterations of applications of a domain into itself), 3) their applications to some specific types of operators that act in such spaces or families of functions.
Regarding the applications, we intend to focus on the “concrete” operator theory and on some topics in Mathematical Physics such as Hele-Shaw flows. Our intention is to study various extremal problems, some of them related with the Schwarzian derivative, conformal and quasi-conformal maps, behavior of maximal functions, integral and composition operators and semigroups of conformal self-maps of the unit disk, dynamics of analytic self- maps of the disk, Loewner chains and Stochastic (Schramm-)Loewner Equation, among others.
Source of Funding: 2012 National Plan / MTM2012-37436-C02-01
Implied entities: Universidad de Sevilla, Tor Vergata University (Rome, Italy), University of Bergen (Norway).
iMAT research line: ⊕ RL10. Mathematical Analysis
Researchers:
Filippo Bracci (Tor Vergata University, Rome)
Santiago Díaz Madrigal
Carmen Hernández Mancera
Alexander Vasiliev (University of Bergen).
