News and events archive

2/3 Update Unfortunately, we have just learnt that Professor Hans Zanna Munthe-Kaas has been quarantined because of the corona virus and he had to cancel his trip to Brno. The lecture on Wednesday is cancelled and will be rescheduled to one of the future terms. Hans Munthe-Kaas is professor of mathematics at the University of Bergen. His research is centred around foundational questions in computational mathematics and applications of Lie groups, symmetries and differential geometry in structure preserving discretisations of differential equations. Munthe-Kaas is chair of the Abel prize committee, managing editor of the journal “Foundations of Computational Mathematics”, President of the Norwegian Mathematical Society, and President of the scientific council of Centre International de Mathématiques Pures at Appliquées (CIMPA) in Nice. Abstract Symmetry is a topic which has inspired artists and mathematicians from ancient to modern times. A fundamental problem is the classification of discrete groups of isometries, such as the 17 planar wallpaper groups, which have been used in mosaics since medieval ages and were classified by Fedorov in 1891 in a complicated proof. Conway’s Magic Formula can be used to classify discrete symmetries for spherical, plane and hyperbolic surfaces and yields the 17 wallpaper groups, the 7 frieze patterns and all discrete spherical symmetries as special cases. The formula and its proof is so simple that it is accessible to advanced high school students. Recently, Munthe-Kaas was involved in the design of a mathematical maze in Bergen Botanical garden. Inspired by Conway, he ended up with a highly symmetric design. Under some reasonable assumptions, only one of the 17 wallpaper groups fulfils his original design criteria. The labyrinth, called `Archimedes’ labyrint` consists of 1234 yews (Taxus baccata, Tis červený) in 2m height and covers an area of about 800 m^2. It was presented in Science Magazine, October 2018. In the last part of this talk we move beyond Conway, and discuss the problem of multivariate polynomial interpolation. Based on kaleidoscopic symmetry groups (Coxeter groups), we find interpolation points with remarkable properties. We show that for any d and k, there exists a unisolvent set of interpolation points for d-variate polynomial interpolation of order k. These points have optimal Lebesque constants and allow fast computation by symmetric fast Fourier transforms. Coffee Break at 4.00 PM The lecture starts at 4.30 PM, however, you can arrive earlier at 4 PM to attend an informal coffee break, during which you can engage in a discussion with the speaker himself and get first-hand knowledge. Where? Mendel Museum's Augustinian Abbey Refectory at Mendel Square