This book is primarily a textbook introduction to various areas of discrete geometry. In each
area, it explains several key results and methods, in an accessible and concrete manner. It …

A number of important results in combinatorics, discrete geometry, and theoretical computer
science have been proved using algebraic topology. While the results are quite famous …

These lecture notes for the IAS/Park City Graduate Summer School in Geometric
Combinatorics (July 2004) provide an overview of poset topology. These notes include …

This book is a revised version of my 2005 thesis [71] for the degree of Doctor of Philosophy
at the Royal Institute of Technology (KTH) in Stockholm. The whole idea of writing a …

We use the Laplacian and power method to compute Betti numbers of simplicial complexes.
This has a number of advantages over other methods, both in theory and in practice. It …

We generalize the definition and enumeration of spanning trees from the setting of graphs to
that of arbitrary-dimensional simplicial complexes $\Delta $, extending an idea due to G …

Let I (G) denote the independence complex of a graph G=(V, E). Some relations between
domination numbers of G and the homology of I (G) are given. As a consequence the …

We introduce anew approach to the study of dynamic (or continuous) packet routing, where
packets are being continuously injected into anetwork. Our objective is to study what …

Bárány's “topological Tverberg conjecture” from 1976 states that any continuous map of an
N-simplex Δ N Δ _ N to ℝ d R^ d, for N≥(d+ 1)(r− 1), maps points from r disjoint faces in Δ N …

The Kneser conjecture (1955) was proved by Lovász (1978) using the Borsuk-Ulam
theorem; all subsequent proofs, extensions and generalizations also relied on Algebraic …