BBC+G

Organizers: János Pach, Dömötör Pálvölgyi, Géza Tóth

Starting September 2020, this is the joint Budapest Big Combinatorics + Geometry (BBC+G) Seminar of the Geometry Seminar of the Rényi Institute, the GeoScape Research Group and the Lendület Combinatorial Geometry (CoGe) Research Group.
The talks are typically on Friday 2-4 pm, but this can change depending on the time zone of the speaker.
Zoom link for the online lectures: https://zoom.us/j/96029300722 and the password is the first 6 terms from the Fibonacci sequence starting with 11.
Recordings of past online talks of the BBC+G Seminar can be watched at the BBC+G video archive.

2021 Fall Semester - every Friday at 14:00 in Main Hall of the Rényi Institute and online

October 15, 2021, 2 pm (CET)
András Bezdek: On colored variants of some two-player games

Abstract: Sprouts (Brussels sprouts, resp.) are two-player topological games, invented by Michael Paterson and John Conway (1967). The games start with p dots (p crosses resp.), have simple rules, last for finitely many moves, and the player who makes the last move wins. In the misere versions, the player who makes the last move loses. We make an attempt to make such games colored, preserving the esthetical interest and balance of them. The analysis of these colored games is a joint work with Alason Lakhani, Haile Gilroy and Owen Henderschedt at Auburn University.


October 8, 2021, 2 pm (CET)
Zsolt Lángi: An isoperimetric problem for three-dimensional parallelohedra

Abstract: Convex polyhedra whose translates tile the three-dimensional Euclidean space are called three-dimensional parallelohedra. Three-dimensional parallelohedra are among the best known convex polyhedra outside mathematics, their best known examples are the cube, the regular rhombic dodecahedron and the regular truncated octahedron. Despite this fact, in the presenter's knowledge, no isoperimetric problem has been proved for them in the literature. The aim of this note is to investigate isoperimetric-type problems for three-dimensional parallelohedra. Our main result states that among three-dimensional parallelohedra with unit volume the one with minimal mean width is the regular truncated octahedron. If time permits, in addition, we establish a connection between the edge lengths of three-dimensional parallelohedra and the edge densities of the translative mosaics generated by them, and use our method to prove that among translative, convex mosaics generated by a parallelohedron with a given volume, the one with minimal edge density is the face-to-face mosaic generated by cubes.


October 1, 2021
Szeged Geometry Day 2021

September 24, 2021, 2 pm (CET)
Dömötör Pálvölgyi: 666-uniform Unit Disk Hypergraphs are 3-colorable

Abstract: I will present some new tricks about coloring geometric hypergraphs that we have developed with Gabor Damasdi. These will allow us to show that any finite set of planar points can be 3-colored such that any unit disk containing at least 666 points contains two differently colored points. Earlier it was known that 2 colors are not always sufficient and that for (non-unit) disks sometimes even 4 colors are needed. Our proof uses a generalization of the Erdos-Sands-Sauer-Woodrow conjecture. If time permits, I'll also sketch our proof for this generalization, which builds on the recent proof of the original ESSW conjecture of Bousquet, Lochet, and Thomasse.


September 17, 2021, 2 pm (CET)
Alexandr Polyanskii: Colorful Tverberg revisited

Abstract: We will discuss the following colorful Tverberg-type result (and its monochromatic version): For a pair x,y of points in $R^d$, denote by D(xy) the closed ball for which the segment xy is its diameter. For any n blue points and n red points in $R^d$, there is a red-blue matching M such that all the balls D(xy), where $xy\in M$, share a common point. Joint work with O.Pirahmad and A.Vasilevskii.