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Model Theory and Algebraic Analysis (MODALAN)
Start date: Dec 1, 2012, End date: Nov 30, 2014 PROJECT  FINISHED 

"The researcher Dr. Luca Prelli will carry out the interdisciplinary project""MODALAN"": Model Theory and Algebraic Analysis at the University of Lisbon,Portugal. At the host institution there is a scientific expertise that suits theresearcher's needs excellently since it houses young and activeresearchers in model theory plus it is home to some of the best specialists inalgebraic analysis. A contact between these two fields of mathematics is veryrare and, at the present point of his career, for the applicant it would beessential to acquire new cutting-edge skills.Within a period of 24 months, the aim of this research project is to developthe applicant's knowledge in algebraic analysis and geometry and acquire newskills in two different subjects: the algebraic study of PDE on one side andthe analytical model theory on the other. The nature of this proposal isstrongly multidisciplinary since it involves different branches of mathematicsas algebra, analysis, geometry and logic.In particular, concerning 1), we would like to extend classical methods ofalgebraic analysis and apply these new techniques to approach Cauchy problemswith growth conditions.Concerning 2), we intend to contribute to the development of the study of o-minimal sheaf cohomology in order to obtain a general solution of the Pillayconjecture.The applicant has already acquired professional maturity, independence and international visibility. He spent various research periods abroad, established collaborations and made scientific publications with other foreign researchers. The action can make a significant contribution to the applicant's professional maturity. He will be integrated into a high level foreign university structure and professionally recognized in another national context while having the possibility of expanding his knowledge and research qualities. In the long term perspective, this will support the applicant in furthering his academic career at an international level."
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