CANCELLED: Seminar Series - Symmetry: From Conway’s Magic Theorem to Archimedes’ Labyrinth
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
