PRR Project

Summary

Our research Unit has invested in a parallel computing cluster and meets all requirements for supporting research in the fields of Numerical Analysis and Computational Mathematics. This position has the potential to encompass several areas of expertise and applications, not only classical fields in Mathematics, but also Artificial Intelligence and Machine Learning. It may also be used to reinforce the group working on Mathematical Complexity leaded by a ERC grantee.Given that computational mathematics plays a crucial role in various fields such as engineering, physics, biology, and finance, where mathematical models need to be solved to understand and predict real-world phenomena, one expects the candidate to be able to use a wide range of techniques, including numerical analysis, optimization, numerical linear algebra, numerical differential equations, and Monte Carlo methods, among others.The scientific profile of the candidate should include some of the following topics and research lines:Numerical AnalysisNumerical Differential Equations (Finite elements, Finite differences, Finite volumes, Meshless methods, and variants)Numerical Linear Algebra (eigenvalue problems, matrix factorizations, etc)Discrete Mathematics (graphs, number theory, combinatorics)Computational optimization (including operations research, engineering design, and machine learning)Monte Carlo Methods, stochastic processes, statistical physics.Complexity (Algorithmic complexity, P vs. NP problem and variants)Computational algebra (Symbolic Computation, Polynomial Arithmetic and Factorization, Algebraic Geometry, Group Theory and Representation Theory, Number Theory, and Computer Algebra Systems (CAS))Computational mathematics and artificial intelligence (AI) are closely interconnected fields that often complement each other in solving complex problems. These AI-driven approaches can offer innovative solutions and enhance the efficiency of traditional computational methods.The successful candidate will perform research work on one or more of the topics mentioned above, and is expected to publish his/her research in the top journals of the field on a regular basis. Within CMAF-cIO, he/she will be strongly encouraged to apply for funding from FCT and from other European Sources.It is expected that the candidate collaborates scientifically with other colleagues, both in the CMAF-cIO Unit and in the Mathematics Department, and participates in organization of scientific events, such as seminars and workshops/conferences.It is also expected that the candidate will enroll in teaching of advanced courses in Computational Mathematics, at the Master or PhD level, and develop his own research group with the help of young researchers, PhD students and Postdocs, funded by CMAF-cIO grants.