Group actions and geometric combinatorics in 𝔽 q d $\mathbb{F}_{q}^{d}$

Combinatorial Curvatures, Group Actions, and Colourings: Aspects of Topological Combinatorics

3 Introduction In the first part of this thesis we discuss a new notion of curvature for cell complexes, introduced by Forman [26], and some variations of it. This notion is purely combinatorial and uses local data to define a combinatorial curvature, enabling us to deduce global topological properties. Before we outline Part I, we point out important differences to earlier attempts to extend t...

Torus Actions and Combinatorics

These are lecture notes for a “Tapas” course given at the Fields Institute in November, 2017.

Lectures in Geometric Combinatorics

The fourteen lectures in this book were prepared for the advanced undergraduate course at the Park City Mathematics Institute on Geometric Combinatorics in July 2004. They begin with the basics of polytope theory with an emphasis on geometry via the theory of Schlegel and Gale diagrams. The lectures lead up to secondary and state polytopes arising from point configurations. These polytopes are ...

Topics in Geometric Combinatorics

Geometric Quotients of Unipotent Group Actions

This article is devoted to the problem of constructing geometric quotients of a quasiaffine scheme X over a field of characteristic 0 by a unipotent algebraic group G. This problem arises naturally if one tries to construct moduli spaces in the sense of Mumford's 'geometric invariant theory' for singularities of algebraic varieties or for modules over the local ring of such a singularity. Indee...