Name Responsible Activity "Department of Mathematics: Analysis, Logic and Discrete Mathematics" "Leo Storme" "Within the analysis track we work on harmonic analysis, functional analysis, partial differential equations, operator theory, asymptotic analysis and non-standard analysis. The research in functional analysis focuses on the study of function spaces, functional inequalities and generalized functions. Generalized functions are examined both in a linear and in a non-linear context, often using Fourier analysis, shear theory, complex analysis and analysis on varieties. Various problems in asymptotic analysis lead to the development of real and complex Tauber positions for integral transformations, with which problems are solved in analytic number theory, spectral theory and analytical combinatorics. Within the department there is also the international Analysis and PDE research center which also offers support for problems in applied sciences that are related to partial differential equations.Within the logic track, research is carried out on proof theory, notation systems for ordinal numbers and phase transitions for Gödel incompleteness. This topic also relies for a large part on complex analysis and analytical combinatorics. Furthermore, logical limit laws are also studied through analytical combinatorics. The notation systems for ordinals find their applications in proof-theoretic analyzes, sub-recursive hierarchies, and combinatorial independences. Recently, research has been done into generalized Goodstein rows that give rise to representations of ordinals through natural, directed limit structures. Good quasi-orders form a broad research area that is close to representation systems for ordinals. These orders are central to the study of terminating algorithms. Finally, research is also carried out into modal logic, provability logic, computer-controlled evidence, mathematics and computability theory.Within discrete mathematics, research is carried out into substructures in finite projective spaces and finite classical polar spaces, with applications in other domains such as algebraic combinatorics, coding theory and extremal graph theory. Research is being conducted into examples of substructures, characterizations of substructures, and improvement of parameters related to these substructures. Many of these sub-structures are being investigated because of their intrinsic geometrical importance, but many of these sub-structures are also related to other research domains, or come from other research domains." "Educational Centre for Mathematics, Education, Econometrics and Statistics (main work address Brussels)" "The Research Centre for Mathematics, Education, Econometrics and Statistics joins staff members who teach courses on mathematics, econometrics or statistics. The research of the group is rather heterogeneous and pertains to domains of mathematics (e.g., differential geometry), education (e.g, strategy choice and strategy development, numerical and mathematical cognition, problem solving, mathematics learning), econometrics (portfolio optimization and visualization methods, non-parametric production theory, cost function estimates for convex and non-convex technologies), and statistics (e.g., extreme value analysis, multilevel analysis, choice modelling, construction of composite indicators, time series analysis)." Mathematics "The department DWIS includes research groups dealing with: - Algebra (ALGB) with research focussed on ring theory, groups and semi-groups; - stochastics (TWIS) - Topology, Algebraic Topology and Approximation theory (AATO)with focus on analytical and categorical topology, on algebraic topology and Approximation theory in Banach spaces. -CAMP (applied mathematics)" "Analysis, Mathematics in Education" "The implementation of Computer Algebra Systems (CAS) is proving to be a revolution in education and research, and demands an entirely new approach to reach complete integration. For the treatment of specific problems new modules have to be written in the described CAS environment. Research is done to investigate the extent to which abstract notions can be implemented in a CAS. A CAS system can also be used as a basis for programs and for the teaching of the principles of informatics, and the efficiency of this should be investigated. For educational purposes an interactive interface between user and CAS system has to be developed. Through comparison with control groups which benefited from more traditional education, research is been undertaken on the extent to which this new technology improves the quality of traditional education. This is happening in a school department with large student numbers." "Applied Mathematics" "Applied mathematics" "Karel In't Hout" "The research topic of our group is the development, analysis and application of numerical methods. Here our main focus is on time-dependent partial differential equations - PDEs, for short. PDEs are of key importance in mathematics and a broad variety of application areas. The mathematical models in present-day science and engineering almost always have multiple underlying variables, leading to PDEs that are multidimensional. In our research, we are actively involved in four application areas: financial mathematics, physics, chemistry and biology. In general, solutions to PDEs from applications cannot be expressed in closed analytic form. Accordingly, one resorts to numerical schemes for their approximate solution. The development, analysis and application of such schemes takes a central place in numerical mathematics. In our group, we perform research into two general classes of numerical methods: operator splitting schemes and iterative methods." "Applied Mathematics" "This research unit has two permanent members: U. Einmahl (Probability and Mathematical Statistics) and T.Kadankova (Stochastic processes and their applications). The other two members, J. Dony (postdoc) and A. Van Messem (Ph. D. Student), do research in mathematical and applied statistics. The research by Uwe Einmahl focuses on limit theorems of probability in general spaces. Classical probability theory deals mainly with random variables taking values in the real line is well developed, but there are many open questions for random variables taking values in infinite-dimensional spaces. For instance, there is no natural extension of the classical central limit theorem to Banach spaces. Also the so-called law of the iterated logarithm which in the classical setting was established in 1942 has only relatively recently (1986) been obtained for infinite-dimensional spaces. The most recent research by U. Einmahl has addressed not only theoretical questions such as refinements of the basic limit theorems, but also applications to statistics such as density estimation which are possible via so-called empirical processes since these processes can be considered as random elements in a suitable infinite-dimensional space. Tetyana Kadankova's research is concerned with Lévy processes, especially with so-called one- and two-sided exit problems for such processes. A problem which she has recently investigated is determining the laws of the first passage of a level (the first exit time from a fixed interval) by such processes. Lévy processes are considered interesting objects both for the theory and applications. For this reason, this class of stochastic processes has received much attention during the last years. Some important applications of this topic come from financial mathematics and insurance. Oscillating Lévy processes serve also as governing processes for oscillating queueing systems and thus they are also important in queueing theory. Another part of her research is devoted to semi-Markov random walks and compound renewal processes. Additionally, she studies stochastic processes reflected at their infimum (supremum) which serve as governing processes in various applications. Julia Dony has an FWO postdoc position (2008-2011) and she works on applications of empirical process theory to nonparametric statistics. This is the continuation of her Ph.D. Thesis (under the guidance of U. Einmahl and D. Mason, co-promotor) which she defended in May 2008 at the VUB. Arnout van Messem currently works on a Ph. D. Thesis (under the guidance of U. Einmahl and A. Christmann, co-promotor) which he will defend during the academic year 2010/11. The main topic of this thesis are so-called support vector machines which are important objects in "" robust"" statistics." "Applied Statistics, Operations Research and Mathematics for Human Sciences" "The department Applied Statistics, Operations Research and Mathematics for Human Sciences is dealing with the diverse applications of quantitative techniques in the different fields (say mathematical modelling), e.g. Data analysis, Manpower planning, Location problems, Hydrology, Demography, and Multicriteria analysis." "Computational and Applied Mathematics Programme" "1) mathematical and computational physics -study of sparse representations of functions -application to inverse problems (L1-penalization) -regularization methods for linear ill-posed problems -stability of inverse problems -design of fast reconstruction algorithms 2) Inverse problems in imaging and image processing -tomographic image reconstruction in nuclear medicine -related problems in applied mathematics -2D or 3D tomographic image reconstruction from incomplete data, such as in computer tomography (CT) 3) Design of new geometrical representations for images and video -study of geometrical basis functions related to scalable image compression -design of geometrical decompositions for video representation -design of scalable robust video codecs -compression 4) non-linear ill-posed inverse problems -Cauchy problem for elliptic partial differential equations -application to electrical impedance tomography 5) Finite group theory, incidence geometry, error correcting codes, connection with graph theory" "Computational Mathematics" "Annie Cuyt" "The research at our group has been targeted at two distinct areas related to the algorithmic and numeric side of scientific computing: -In the area of computer arithmetic we are most involved and known for developing algorithms for the reliable computation of special functions with the focus on validated evaluation. -In the area of numerical techniques we are most engaged with the data-driven modelling, with the focus on linear regression and non-linear regression by rational functions."