About the programme
Analysis covers a huge part of mathematics and smoothly connects to other branches of mathematics such as geometry and stochastics. The analysis programme at KdVI consists of two research focus groups: Pure Analysis, and Dynamical Systems and Numerical Analysis.
Current directions of research in the first focus group are low-dimensional dynamical systems, both in real and complex variables, and the new direction micro-local analysis. These topics are closely connected; the research is driven by the fast developments in the field. Research is curiosity-driven but group members have an open eye for applications in other branches of mathematics and the sciences. A remarkable example is the NWO TOP-1 project of prof. Peters and dr. Regts, which connects complex dynamical systems, graph theory and statistical mechanics.
In the second focus group, research is directed towards the numerical solution of partial differential equations (PDEs) and to topics derived from that, such as numerical linear algebra and inverse problems. Research is both fundamental, e.g., concerned with well-posedness and optimality of numerical methods as well as application-driven in e.g. climate models and non-destructive testing. Prof. Crommelin is a member of the board of the Dutch Institute for Emergent Phenomena (DIEP), a joint effort of FNWI institutes IoP, KdVI, ILLC, HIMS and the Amsterdam Institute for Advanced Study (IAS).
The analysis programme is small, but analysis is of crucial importance in many aspects of the research in the other programmes. The analysis programme has close ties with the other programmes through these common research interests. The recent hiring of Dr. Leo Tzou is expected to further improve the scientific interaction between the two focus groups within the programme.