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## Organisation

# Department of Mathematics: Analysis, Logic and Discrete Mathematics

### Department

Main organisation:Faculty of Sciences

Lifecycle:1 Jan 2019 → Today

Organisation profile: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.

Keywords:Logic, Analysis, Discrete Mathematics

Disciplines:Differential geometry, Algebraic geometry