The research of the chair of Analysis focusses on two main themes: functional analytic methods in partial differential equations and stochastic evolution equations, and spectral theory and noncommutative analysis.
- Stochastic Evolution Equations in Banach spaces
Project leader: Jan van Neerven
Stochastic partial differential equations with random perturbations can be studied in a functional analytic framework as stochastic evolution equations governed by a semigroup generator in an infinite-dimensionalspace. For Hilbert spaces, the theory of stochastic evolution equations has witnessed a rapid developement during the past two decades. One of its ingredients is the extension to the Hilbert space context of the classical Ito stochastic integral. In collaboration with Mark Veraar (Delft, now Karlsruhe) and L. Weis (Karlsruhe), the classical stochastic Ito integral has been extended to UMD Banach spaces. This permits a full treatment of semilinear stochastic evolution equations in the L^p scale. Current work focusses on understanding qualitative properties of solutions of stochastic evolution equations and understanding the connections between stochastic analysis on the one hand and harmonic analysis on the other. stochastic integral to stochastic integrands and on exploring connections between stochastic integration in Banach spaces and the geometry of the underlying space. This project is currently supported by and NWO VIDI grant (Mark Veraar). Previous grants include an NWO VIDI and NWO VICI grant (Jan van Neerven) and an NWO VENI grant (Mark Veraar).
- Noncommutative Analysis and Representation theory
Project leaders: Martijn Caspers en Bas Janssens