Seminar on Discrete Geometry: Tilings
This seminar will look at tilings.
We start with planar tilings, their properties, their generation e.g. by crystallographic groups, as well as at attempts of classification. (This quickly leads us to unsolved problems. For example, which pentagons tile the plane by congruent copies?)
Then we look at 3-dimensional tilings and their properties. New questions arise here: Which (combinatorial types of) polyhedra can be used to tile space? How many faces can a polyhedron have whose congruent copies tile space?
-- this seminar will mostly take place in English --
Seminar Dates + Topics:
18. October -- Discussion of topics
25. October -- Further discussion, fixing the program
8. November - Tilings with dominos: matching and algorithms -- Estela
15. November - Conway's tiling group I -- Johannes
22. November - Conway's tiling group II -- Barbara
6. December - Which pentagons tile space? -- Danijela
13. December - Tilings with dominos: the arctic circle theorem -- Justine, Ihab **
10. January - There are 17 wallpaper groups (symmetry groups of tile-transitive tilings?) -- Laith
17. January - The Penrose tilings -- Felix L.
24. January - What is a quasicrystal? Definitions -- Marie, Sophia **
31. January - Given a set of tiles .... undecidability -- Felix C.
7. February - The Euler equation for tilings, in the plane and in space. Why heptagons don't tile -- Andrés
14. February - Tilings in R^3 with large tiles -- Jorge
** Double-header meetings: start 2pm sharp, ends by 4pm sharp.
Federico Ardila und Richard P. Stanley: Pflasterungen, Math. Semesterberichte 53 (2006), 17-43.
John H. Conway and Jeffrey C. Lagarias: Tiling with polyominoes and combinatorial group theory, J. Combinat. Theory, Ser. A, 53 (1990), 183-208.
David Eppstein, John M. Sullivan and Alper Ungor: Tiling space and slabs with acute tetrahedra, Comput. Geometry: Theory & Applications 27 (2004), 237-255.
Branko Grünbaum and Geoffrey C. Shephard: Tilings with congruent tiles, Bull. Amer. Math. Soc. 3 (1980), 951-973.
Branko Grünbaum and Geoffrey C. Shephard: Tilings and Patterns, Freeman 1987.
Egon Schulte: Tilings, in: Handbook of Convex Geometry (P. Gruber and J. Wills, eds.), North-Holland, Amsterdam 1993, 899-932.