# Interactions of Functional Analysis with Algebra, Geometry and Topology

**Brief description:**

This program falls within several interdisciplinary fields within Pure Mathematics. More precisely:

• Certain linear, non-linear, and geometric aspects of Analysis (such as Geometric Analysis, Differentiability, Geometry of Banach spaces, Lineability and Spaceability, and classical inequalities).

• Banach Spaces and Lattices, and operators between them. General Operator theory, Chaotic and Hypercyclic

Operators.

• The study of General Topology and Group Theory (Lie groups, semisimple groups, compact groups, Topological abelian groups, among others) via many different techniques from many other areas in Mathematics (such as, for instance, techniques inherited from Functional Analysis).

**Researchers:**

Juan Benigno Seoane (Proffessor, Faculty of Mathematics, UCM)

Jesús Ángel Jaramillo Aguado (Proffessor, Faculty of Mathematics, UCM)

Francisco Luis Hernández Rodríguez (Proffessor, Faculty of Mathematics, UCM)

Gustavo Adolfo Muñoz Fernández (Proffessor, Faculty of Mathematics, UCM)

Rutwig Campoamor Stursberg (Proffessor, Faculty of Mathematics, UCM)

María Isabel Garrido Carballo (Proffessor, Faculty of Mathematics, UCM)

Elena Martín Peinador (Proffessor, Faculty of Mathematics, UCM)

Juan Ferrera Cuesta (Proffessor, Faculty of Mathematics, UCM)

Mar Jiménez Sevilla (Associate Proffessor, Faculty of Mathematics, UCM)

**Expected results:**

The recent history and production of the proposed team in these lines is enough to, at least, partially achieve the desired results. In fact, the group is already obtaining some positive results in these areas.