Projects and Assignments in Pure Mathematics

Infinite reflection groups

Finite reflection groups are treated, for example, in J E Humphreys, "Reflection groups and Coxeter groups" (Cambridge). Affine reflection groups on finite spaces (which are infinite groups) are also treated there, but the geometry of polytopes defined by reflection walls starts to get quite interesting, and more can be said than Humphreys finds room for in his book. In the project one would develop an understanding of the construction of these groups (or a subset of them), and study the combinatorics of the corresponding geometries.

Prerequisites

Some level 1 group theory and level 2 linear algebra. Ideally also a level 3 module on groups and symmetry.

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