Canceled

Unfortunately, the speaker Hans Zanna Munthe-Kaas got into the quarantine because of the new coronavirus in recent days and he had to cancel his trip to Brno.

We shall find a new timeslot in the future, but the lecture will not take place this Wednesday.

March 4, 2020 from 4:30 PM at Mendel Museum´s Augustinian Abbey Refectory at Mendel Square

Hans Munthe-Kaas

Symmetry: From Conway’s Magic Theorem to Archimedes’ Labyrinth and Beyond

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.

Seminar of differential equations will continue on February 24, 2020 at 12pm in lecture room M5.

Kodai Fujimoto, Ph.D. (Ústav matematiky a statistiky, PřF MU)

Asymptotic behavior of solutions for differential equations with φ-Laplacian

Dear Friends of Hikes and Mathematics,

you are invited to our 29th mathematical hike planned on February 29th. Meet at 9:38 at the bus station in Slavkov u Brna. We go by bus at 9:15 from the bus station Zvonařka in Brno, you can join us there.

We have planned a 17 km hike following a green path from Slavkov to Bučovice. Return to Brno by train.

All information and photos can be found at http://conference.math.muni.cz/vylety/. (in CZ)

Have a nice February and see you soon,

Jana Bartoňová and Jonatan Kolegar, organizers
Jan Slovák, Director of the Department of Mathematics and Statistics

We will continue on Thursday, February 13, in M5 at 1pm by the talk

F. Pakhomov

Dilators and Ptykes

Abstract:
Dilators are endofunctors D:WO->WO preserving pullbacks and directed co-limits, where WO is the category of well-orderings and strictly monotone maps. This notion was introduced by J.-Y. Girard as one of central notions within his approach to certain problems in proof-theory (calculation of proof-theoretic ordinals). Some more sophisticated applications motivate higher-order generalizations of the notion of dilator, known as ptykes. For example, ptykes of the type (WO->WO)->WO are functors from the category of dilators Dil to WO that preserve pullbacks  and  directed co-limits (here Dil is the category of dilators and Cartesian natural transformations).

In the first part of the talk I plan to discuss dilators, some basic results about them, and give some idea about their applications in proof-theory.  Next I plan to talk about my approach to the theory of ptykes, where  types of ptykes are interpreted as classes of relational structures that are closed under substructures.