Dr. Pedro Antunes, a postdoc of the Group of Mathematical Physics of the University of Lisbon (GFM-UL), has been awarded a grant within the scope of the 2009 edition of the Research Stimulus Program of the Gulbenkian Foundation in the area of Mathematics. The project, entitled Shape Optimization for Eigenvalue Problems in Partial Differential Equations, will be developed within the GFM-UL during one year under the supervision of Prof. Pedro Freitas, also of GFM-UL.

The problems under study have applications in a manifold of areas ranging from Physics to Engineering and Biology, and are related to the determination of the optimal shape for specific quantities associated with the vibration frequencies (spectrum) of the object under consideration. Such questions have a long history in Mathematics, going back to at least the nineteenth century and to the work of Rayleigh on membranes and plates. This was followed by several developments thoroughout the twentieth century by mathematicians such as Hilbert, Weyl, Pólya, Szegö, S.-T. Yau and others.

The main purpose of the project will be to combine analytical techniques with a quantitative analysis based on meshless numerical methods that allow for the treatment of vast amounts of data with enough accuracy, in order to explore situations for which theoretical methods alone are not yet sufficiently developed to yield results. The more theoretical side of the study will be based on links between geometry and partial differential equations. This combined approach also illustrates the growing importance of computacional methods in Mathematics, including in more conceptual aspects.

The prize consists of a grant of €12.500, with €2500 going to the researcher and the remaining €10.000 for GFM-UL to support the execution of the proposal. The public award cerimony will take place at the Gulbenkian Foundation headquarters on the 2nd of March 2010, at 17:00.