Marie Skłodowska-Curie Action EF LieLowerBounds

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The Marie Skłodowska-Curie Action ’’Lower bounds for partial differential operators on compact Lie groups’’ (LieLowerBounds) ‘’ is a project aiming to bring together the expertise of the experienced researcher, Dr. Serena Federico, and that of the supervisor, Prof. Michael Ruzhansky, in order to obtain some fundamental lower bounds for partial differential operators on compact Lie groups.
The project will be implemented at the University of Ghent (the beneficiary) while the University of Rennes I will contribute as the Partner Organisation. The duration of the project is 24 months.


Historically, the theory of partial differential operators is one of the most important branches of mathematics with several consequences in many other mathematical fields and with applications in other sciences. This project intends to investigate the validity of some fundamental lower bounds for partial differential operators, and in general for pseudo-differential operators, on compact Lie groups. The validity of such a priori estimates will lead to the development of results about interesting problems in the theory of partial differential operators, such as, for instance, in the solvability problem of partial differential operators on compact Lie groups. We will combine microlocal analysis techniques and noncommutative methods to define a new global approach to be applied to the resolution of problems in the setting of compact Lie groups.


Objectives

  • To perform a deep geometric analysis of operators on compact Lie groups through representation theory aiming to the development of new techniques to analyze the problem in the setting of compact Lie groups
  • To prove lower bounds for pseudo-differential operators on compact Lie groups
  • To apply the results to interesting open problems in the theory of partial differential operators on compact Lie groups, and, specifically, on the problem of solvability.

 

Role of Ghent University

Ghent University is the organisation where the project is implemented (the beneficiary). It recruits the experienced researcher and ensures the necessary training of the researcher.

 

Website

Serena Federico
Marie Curie project
Analysis project

 

Contacts

Dr. Serena Federico
Department of Mathematics: Analysis, Logic and Discrete Mathematics
Ghent University

Prof. Michael Ruzhansky
Department of Mathematics: Analysis, Logic and Discrete Mathematics
Ghent University