Mathematics

The group is dedicated to the following research activities:

The research activities of the Group focus on:

- Regularity properties for the solutions of Partial Differential Equations and for the minimizers of some integral functionals of the Calculus of Variations;

- Functional Spaces and their applications in Probability and Statistics;

- Interpolation spaces and applications of the interpolation theory to PDE’s;

- Integral operators. 

The research activities of the Mathematics Analysis Group focus on:

- Construction of class of representations of discrete hyperbolic fundamental groups of surfaces.

- Construction of mathematical transforms defined in the spectral domain of finite graphs and applications to compression, denoising and reconstruction of signals defined on large graphs.

The group is dedicated to the following research activities:

1) Construction of mathematical models based on partial and ordinary differential equations linked to the description of phenomena arising in different applied fields, in particular ecology and engineering;

2) Extension of nonlocal elasticity theories based on stress-driven spatial convolutions;

Economic statisticians employ specialised methodologies to delve into a variety of themes. The research activities of our statisticians group are primarily centred around three key areas: 1) statistical analysis of sustainability across its multifaceted aspects, including economic, social, environmental, and energy sustainability; 2) statistical models to examine corporate innovation and its impact on the labour market and human capital; 3) statistical models for finance, including the analysis of extreme values and forecasting, enhanced by sentiment analysis techniques.

The research activities of the Applied Mathematics Group of the UPN focus on the development of mathematical models, methods and algorithms and simulation procedures to solve complex problems in the financial-economic sector and support the growth of both traditional financial institutions, such as banks and insurance companies, and innovative companies. Research topics include, but are not limited to:

The Smart System Laboratory (SSLab) comprises three specialized units [https://smartsys.ualg.pt], namely:

Fields of research:

• Statistics for Stochastic Processes in Continuous Time 
• Time Series Analysis
• Econometrics
• Nonparametric Statistics

• Graph theory and its applications
• Extreme graph theory
• Combinatorics
• Algorithms and data structures
• Computational complexity
• Discrete optimization (task scheduling)
• Discrete and computational geometry
• The theory of concurrency
• Stochastic networks and their reliability