PRR Project

Summary

In recent years, three professors in this area retired or went on permanent leave, of which one was full professor and an emeritus member of the center. Moreover, in the near future (before the end of the next period in 2029) at least one full professor will retire, prominent member of the center and head of the NADE group for years. This justifies the opening of 2 positions in Analysis. These positions are open in all sub-areas, all of which (except Financial mathematics) are active lines of research in our center. The various sub-domains of Analysis embraced by the position are(i)Differential Equations (DE)(ii) Partial Differential Equations (PDE)(iii) Dynamical Systems (DS)(iv) Calculus of Variations & Optimization (CVO)(v) Functional analysis (FA)(vi) Operator theory (OT)(vii) Measure theory (MT)(viii) Financial mathematics (FM)(ix) Stochastic analysis (SA)(x) Numerical Analysis (NA)Among these areas, the first and second have a long tradition in our center, being ODE also the field of Biomathematics and the study of Delay Differential Equations (DDE), all being offered at Master and/or at post-graduate level (our center has currently one PhD student in Biomathematics)l. It also embraces Rational mechanics and Mathematical Methods in Sciences (offered at undergraduate level) that are prerequisites for advanced training and research in mathematical modeling and the analysis of models in Continuum mechanics, including Solid and Fluid mechanics. PDEs, in turn, embrace Continuum mechanics, Mathematical Methods in Physics, Optimal transportation, all offered at Master and/or at post-graduate level, as well as fractional Calculus and Free boundaries and Obstacle problems, leading to research (doctoral or post-doc) in Mathematical modeling in all areas represented by NADE group (currently we have one PhD student in Fractional PDEs with applications to Peridynamics). Dynamical systems and Ergodic theory is an area represented by two integrated members of our center, with several students in post-graduate training. Numerical analysis, Functional analysis, Measure theory (both offered at Master and post-graduate levels) and Operators theory are currently not very active areas in our center on their own, but there exists numerous connections with Mathematical modeling and Mathematical physics that could be activated by hiring such a profile. Eventually, Financial mathematics is not a priority for our center, though Stochastic analysis is a field of growing importance, not only in FM but also in Mathematical Physics.Justification for research:Special emphasis should be put on PDE profiles, since it is a strength in our group (Schrödinger-type equations, Obstacle problems, Solid and Fluid mechanics, Continuum mechanics), and on Dynamical systems, also a unique feature of our center, whose group is extremely productive and high-level but his group is lacking critical mass.Other research lines where our center is strong are Delay Differential Equations (ODE) and Mathematical Physics (SA, FA). We also stress the importance for our center of profiles in Calculus of Variations and Geometric Measure Theory, for their connections with Mathematical Modeling in Solid mechanics. To align with the center strategic lines, this position should be in the sub-area of (in decreasing order of priority) : DS, DDE, PDE, CVO, (G)MT, ODE, FA&MT, OT, SA, NA, FM.