# Real and Functional Analysis

## Members

The research in the Real Analysis and Functional Analysis area in the Department of Mathematics (DM) is mainly focused on: *Operator algebras* (symbols for non-local algebras, fredholm index theory, asymptotic analysis of non-fractal algebras of operator sequences, Lie algebras and JC*-algebras, operator algebras of operators in Bergman spaces); *Operator theory* (formulas for the index of singular integral operators with shifts, fredholm theory of convolution-type operators, properties of truncated Toeplitz operators, spectral theory of non-selfadjoint operators); *Spaces of analytic functions and Riemann - Hilbert problems* (factorization of quasi - periodic functions, factorization in Riemann surfaces and applications to integrable systems, corona problems, invariant subspaces, properties of spaces of poly-analytic functions).

Patrícia Gonçalves is the leader of the research program in *Hydrodynamic Limits and Equilibrium Flutuations: universality from stochastic systems* under a grant from the European Research Council (ERC).

The members of the scientific area of Real Analysis and Functional Analysis of the DM collaborate with members of other scientific areas of the DM, namely the area of Algebra and Topology and the area of Mathematical Fysics and maintain close scientific collaboration with mathematicians from the University of Algarve the University of Minho and the University of Aveiro as well as with various researchers in foreign universities.

Most of the members of the scientific area of Real Analysis and Functional Analysis are integrated in the Center for Functional Analysis, Linear Structures and Applications and in the Center for Mathematical Analysis, Geometry, and Dynamical Systems.

## Seminars

- Functional Analysis, Linear Structures and Applications
- Seminar in probability and statistical mechanics/Probability and stochastic analysis

## Future and Recent Events

- Oberwolfach May 2025
- PSPDE Lisboa November 2023

## Other links

Members of the scientific area maintain close scientific collaborations with investigators from the following institutions:

- England: University of Leeds, University of Reading, University of Liverpool, University of London and University of Oxford
- France: Université de Lorraine, Université de Bordeaux
- Georgia: A. Razmadze Mathematical Institute, Academy of Sciences
- Germany: Technische Universitat Chemnitz and Technische Universitat Darmstadt
- Mexico: Universidad Autónoma del Estado de Morelos
- Poland: University of Agriculture in Krakow
- USA: New York University in Abu Dhabi
- Spain: Universidad Complutense de Madrid
- Russia: St Petersburg State University and Southern Federal University