The underlying motivation for this project is the establishment of a solid basis for the creation of a research group in the Computational Mathematics area. There are several reasons for this resolution: the University of Aveiro has stated the need for the development of Informatics and Computer Science research groups, the Mathematics Department has expressed the need for research in Computer Science and the FCT s Mathematics Evaluation Panel has regularly pointed out the need for research in Computational Mathematics within portuguese R&D units. We believe that the existence of this project can play an important role in the motivation and recruitment of young researchers in this area.
- Objectives on Complexity Theory: the search for a theoretical framework for the classification of the Instances of NP-hard Problems, in terms of their computational cost.
- Objectives on Computational Geometry: to develop approximation algorithms and heuristics for the Minimum Vertex Guard Problem, to study de Vertex PI-Floodlights Problem for Orthogonal Polygons and to characterize the visibility graphs of certain classes of polygons.
- In the field of Quantum Computation, our work focus on the design of quantum arithmetic circuitry, particularly on the use of generalized redundant number systems, as well as on the problem of quantum computing simulation.