An introduction to graph homomorphisms and topological methods

For this first meeting, I will give an introductory talk to graph homomorphisms in general, and especially to the topological aspects of the subject. The original application was to use topological methods (in particular, the Borsuk-Ulam Theorem) to put lower bounds on chromatic numbers of graphs, and since then this idea has been understood much more generally. We will discuss in particular the seminal paper L. Lová, "Kneser's conjecture, chromatic number, and homotopy". J. of Comb. Theory A. 25 (1978), and briefly survey more recent work in the area, including E. Babson and D. Kozlov, "Proof of the Lovasz conjecture" Annals of Math. 165 (2007).