Research team
Expertise
My research concerns the study of conformally invariant differential operators: these appear in physics as the differential operators dictating the behaviour of elementary particles. In particular, I study higher spin versions in several dimensions. Also the connection with the underlying dual symmetry algebra is investigated (based on the concept of Howe duality), as this gives rise to applications in representation theory.
Special functions in several vector variables.
Abstract
Physical systems are often described in terms of differential equations. To find solutions for these systems, one can investigate the symmetries of the system: these are transformations which generate solutions, through well-defined relations in a specific algebra. Often, this leads to special solutions which are referred to as 'special functions' (a whole mathematical subject on its own). In this project, we will start from a specific type of equations (conformally invariant equations for massless particles of arbitrary spin) and investigate the special functions appearing in this framework.Researcher(s)
- Promoter: Eelbode David
- Fellow: Janssens Tim
Research team(s)
Project type(s)
- Research Project
Approach theory meets likelihood theory.
Abstract
Let the density of an unknown probability distribution belong to a family of densities which are determined up to an unknown parameter vector. Based on a sample of observations, the maximum likelihood estimator (MLE) then provides an estimate for the unknown parameter vector by picking the vector under which the chance of observing the particular given sample is maximal. Statisticians value the MLE because it behaves well asymptotically. This roughly means that the estimates given by the MLE will converge to the true value of the unknown parameter vector as the sample size grows to infinity. However, doubts about the applicability of the MLE have emerged as `misspecified models', i.e. models in which the density of the unknown probability distribution fails to belong to the family of densities producing the MLE, are common in realistic settings. Many researchers have investigated under which additional regularity conditions the MLE in a misspecified model continues to behave well asymptotically. Here we want to follow a different route. More precisely, instead of adding extra regularity conditions on the model (which may again destroy the applicability), we will try to establish results in which we measure how irregular a model is and then use this information to assess how asymptotically well the MLE behaves. To this end, we will use approach theory, a mathematical theory which is designed to cope rigorously with notions such as `almost behaving well asymptotically'Researcher(s)
- Promoter: Eelbode David
- Co-promoter: Lowen Bob
- Fellow: Berckmoes Ben
Research team(s)
Project type(s)
- Research Project
Construction of symmetry algebra realizations using Dirac operators.
Abstract
This project consists of three main topics: T1 Construction of new realizations of osp(1/2n) T2 Integral transforms associated with osp(1/2n) T3 Analysis related to the orthosymplectic transvector algebraResearcher(s)
- Promoter: Eelbode David
Research team(s)
Project type(s)
- Research Project