Tribone Tilings: Honeycombs to Benzels | Hrishik Koley | B. Math, 2022-25

Title: Tribone Tilings: Honeycombs to Benzels

Speaker: Hrishik Koley (B. Math, 3rd year)

Abstract: Tilings have been a very interesting field of algebraic combinatorics, since it’s dawn, and yet have a plethora of unanswered questions, partly owing to the fact that new shapes and new tiles never cease to arise, and being considered. From such wide classes of shapes and tiles, Conway and Lagarias considered and showed that certain roughly triangular regions in the hexagonal grid or honeycombs cannot be tiled by shapes Thurston later dubbed tribones. However, in 2021, Propp introduced a two-parameter family of roughly hexagonal regions in the hexagonal grid called benzels and showed that a tiling by tribones exists under certain constraints on these parameters. In this talk, we will look at both structures and try to understand their tribone tilings.

Prerequisites: Elementary ideas of graph theory, group theory, and topology might help, but the speaker would anyways introduce each and every idea required.

Date & Time: Saturday, 24th August 2024, 11:30 AM - 1:00 PM