Follow-Up Workshops

The word "period" is used to designate any number represented by the integral of an algebraic differential form over a cycle in an algebraic variety over the rationals (or the algebraic numbers). These include many numbers of interest in number theory and mathematical physics (multiple zeta values, Mahler measures, superstring amplitudes, ...), and also have deep connections with special values of motivic L-functions. The trimester covered five topics in depth: Motives Regulators Amplitudes Picard-Fuchs Equations Hypergeometric Motives The aim of this workshop is to “take stock” of — and to report on — recent developments in this area, since the original activity.

Many physical processes in materials science or geophysics are characterised by inherently complex interactions on a multitude of inseparable scales in space and time. The resolution of all features on all scales in a computer simulation easily exceeds today's computing resources. Observation and prediction of physical phenomena therefore requires insightful computational multi-scale models and methods for adaptive selection of relevant scales and effective representation of unresolved scales. This workshop will discuss the latest algorithms and models for this purpose, as well as the mathematics behind them, which enable reliable and efficient numerical simulation of challenging multiscale problems in modern high-performance computing environments.