Research Programs and Projects at KdVI

1. Algebra, Geometry and Mathematical Physics
2. Pure, Applied and Numeric Analysis
3. Stochastics

  1. Algebra, Geometry and Mathematical Physics

Program Leader: Prof.dr G.B.M. (Gerard) van der Geer

The barycentre of the program lies in the dynamic area of mathematics where algebra and geometry are in strong interaction. One part of the dynamics of this area comes from new developments in pure mathematics, the other from developments in mathematical physics, especially string theory, which has supplied a new intuition for developing mathematical ideas. The program covers a wide area ranging from algebraic and arithmetic geometry, harmonic analysis on algebraic groups and random matrix theory to integrable systems and string theory. Instead of listing the subdisciplines involved, the program can better be described by two unifying characteristics. The first is the interplay of algebra and geometry. The second is the fact that many developments in subfields of our theme, such as quantum groups, moduli spaces, non-commutative geometry, were inspired or influenced by recent developments in mathematical physics, while intuition from physics is partially used as a tool to develop mathematics. Core areas are Algebraic Groups, Algebraic Geometry, Quantum groups and String Theory.

Projects:

1. Algebra and Geometry; project leaders Prof. dr G.B.M. (Gerard) van der Geer and Prof. dr E.M. (Eric) Opdam
2. Mathematical Physics; project leaders Prof. dr R.H. (Robbert) Dijkgraaf, Prof. dr E.M. (Eric) Opdam and Dr. S.V. (Sergey) Shadrin
3. Discrete Mathematics; project leader Prof. dr A. (Lex) Schrijver

Program members

Staff: Dr Ö. (Özgür) Ceyhan, Dr F.L.D. (Fabien) Cléry, Prof.dr R.H. (Robbert) Dijkgraaf, Prof.dr G.B.M. (Gerard) van der Geer, Dr J. (Jochen) Heinloth, Dr G.F. (Gerard) Helminck, Dr S. (Stefan) Kolb, Dr B.J.J. (Ben) Moonen, Prof.dr E.M. (Eric) Opdam, Dr H. (Hessel) Posthuma, Dr T. (Thomas) Quella, Prof.dr N.Y. (Nicolai) Reshetikhin, Dr J.P. (Jan Pieter) van der Schaar, Prof.dr A. (Lex) Schrijver, Dr S.V. (Sergey) Shadrin, Dr K. (Kostas) Skenderis, Dr J.V. (Jasper) Stokman

PhD Students: A.Y. (Alexandr) Buryak, A.W. (Adam) Bzowski, Drs M.C. (Maarten) Hoeve, Drs P.M.J. (Phyllis) Joris, N. (Niels) Kowalzig, A. (Andrey) Opimakh, Drs R. (Ruud) Salomon, Drs R.I. (Roland) van der Veen

Guests and Emeriti: Dr O.L.J. (Jonas) Bergstrom, Dr H.G.J. (Henk) Pijls, Dr R.W. (Rob) van der Waall

  2. Pure, Applied and Numerical Analysis

Program Leader: Prof.dr J.J.O.O. (Jan) Wiegerinck

Analysis is the part of mathematics which uses operations involving infinity, such as limits, convergent infinite series, differentiation and integration. Much of analysis involves functions and function spaces and the study of solutions of many kinds of equations involving functions. Traditionally, the modelling of real word phenomena uses analysis. Although nowadays many other parts of mathematics also contribute to modelling, the interaction between analysis and applications remains very strong, and keeps on to vitalize analysis with fresh ideas. Many new branches of analysis have started by combining analysis with some other part of mathematics. See for instance geometric analysis and dynamical systems, algebraic analysis and q-analysis, stochastic analysis, and numerical analysis driven by the need for efficient computer algorithms.

The KdV Institute only specializes in a few of the many parts of analysis. The main current directions are complex analysis within pure analysis, and dynamical systems and numerical analysis within applied analysis.

Projects:

1. Pure Analysis; project leader Prof. dr J.J.O.O. (Jan) Wiegerinck
2. Applied Analysis and Dynamical Systems; project leader Dr. A. J. (Ale Jan) Homburg
3. Numerical Analysis; project leader Prof. dr R.P. (Rob) Stevenson

Program members

Staff: Dr S.K. (Samir) Bhowmik, Dr J.H. (Jan) Brandts, Prof.dr.ir J. (Jason) Frank, Dr A.J. (Ale Jan) Homburg, Dr H. (Han) Peters, Prof.dr R.P. (Rob) Stevenson, Dr C. (Chris) Stolk, Prof.dr J.G. (Jan) Verwer, Prof.dr J.J.O.O. (Jan) Wiegerinck

PhD Students: Janis Bajars, S. (Svetlana) Dubinkina, Dr N. (Nabiolla (Nabi)) Godarzvand Chegini, Ir T.J. (Tim) Op 't Root, Drs R.J. (Ricardo) Reis da Silva, Drs S. (Sjors) van der Stelt

Guests and Emeriti: Dr W. (Walter) Hoffmann, Prof.dr T.H. (Tom) Koornwinder, Prof.dr J. (Jaap) Korevaar

  3. Stochastics

Program Leader: Prof.dr C.A.J. (Chris) Klaassen

All phenomena in science and society are ruled by randomness, sometimes partially or to a considerable extent. The branches of mathematics that enable one to understand, predict, and control such phenomena are Probability Theory, Statistics, Stochastic Operations Research, and Financial Mathematics. Collectively they go by the name Stochastics. All said branches are represented within the stochastics program of the research program of the Korteweg-de Vries Institute.

Probability Theory studies the behaviour of a stochastic system of which the underlying chance mechanism is known: given this chance mechanism certain system characteristics are analyzed. Probability Theory is rooted in Analysis, more specifically in Measure and Integration Theory, and it nourishes the other branches of Stochastics.

Observing the behaviour of a stochastic system of which the underlying chance mechanism is unknown, one may try to induce which is the true underlying chance mechanism. The mathematics of this problem is called Mathematical Statistics. Our statistics research is motivated by both theoretical issues and by problems raised in application areas.

Topics of a theoretical nature are found in nonparametric and semiparametric statistics, as well as in Bayesian statistics. Applied research is motivated by statistical problems in e.g. finance, neuroscience, systems biology, and forensic science.

Projects:

1. Mathematical Statistics; project leader Prof. dr C.A.J. (Chris) Klaassen
2. Probability Theory; project leader Prof. dr M.R.H. (Michel) Mandjes

Program members

Staff: Dr A.J. (Bert) van Es, Prof.dr C.A.J. (Chris) Klaassen, Dr B.J.K. (Bas) Kleijn, Dr A.J. (Andries) Lenstra, Prof.dr M.R.H. (Michel) Mandjes, Prof.dr A.N. (Albert) Shiryaev, Prof.dr M.J. (Marjan) Sjerps, Dr P.J.C. (Peter) Spreij, Dr R.G. (Robin) de Vilder

PhD Students: D.H. (David) Baillie, Drs P.A.G.J.M. (Paul) Gruntjes, A.P. (Ton) Hellings, Drs J. (Jevgenijs) Ivanovs, Drs B.P.H. (Benjamin) Kemper, K. (Kamil) Kosinski, Drs V.J.G. (Vincent) Leijdekker, C.E. (Chrissie) Schapers, Drs E. (Enno) Veerman, P.W. (Piotr) Zuraniewski

Guests and Emeriti: Dr A.A. (Guus) Balkema, Drs A. (Abdel) Es-Saghouani, Dr S. (Shota) Gugushvili, Drs M.P. (Marcel) Visser