The research unit PEAD studies Non-archimedean functional analysis. The term "non-archimedean" refers to the fact that the scalars, which in classical functional analysis are real or complex numbers, are now elements of a valued field K with non-archimedean valuation. I.e. a valuation that satisfies the strong triangle inequality |x+y| £ Max{|x|, |y|}. The best known examples of such fields are the fields of p-adic numbers, p a prime number ...
The main research topics of the department WISK are: 1. p-adic analysis The functions studied in the mathematical analysis have real and complex values. One can replace the real or complex numbers by other numbers: the p-adic numbers (p is a prime). These numbers have properties that are rather different from the properties of real numbers. For instance when calculating with p-adic numbers rounding errors do not occur. The analysis built on ...
TOPIC A : p-adic analysis (Van Hamme L.) : Normal bases in the space of continuous functions : The p-adic moment problem : Application of p-adic analysis to number theory - - TOPIC B : ring theory (Caenepeel S. ) : Computing the Brauer-Long group ofa Hopf algebra : Computing Taylor's extended Brauer group : Clifford theory for infinite dimensional Hopf algebra's - - TOPIC C : Institutional research (Geivaerts M.) : Research in higher ...
NUMBER THEORY AND ALGEBRAIC GEOMETRY
1) Study of the number of solutions of polynomial equations in several variables over finite fields and residue class rings, with emphasis on the relation to geometric and topological invariants of the equations, Igusa's local zeta function, p-adic exponential sums.
2) Connections between (1) and the theory of singularities, resolution of singularities, Log Minimal Model Program, topological ...