 
Summary: TOOLS FROM HIGHER ALGEBRA
Noga Alon
Department of Mathematics
Raymond and Beverly Sackler
Faculty of Exact Sciences
Tel Aviv University
RamatAviv, Tel Aviv 69978
ISRAEL
Table of Contents
1. Introduction.
Explicit constructions:
2. Group theory and graphs with large girth.
3. Expanders and superconcentrators.
4. Character sums and pseudorandom graphs.
More mathematical tools:
5. Real varieties and sign patterns of polynomials.
6. The ChevalleyWarning theorem, Abelian groups and regular graphs.
7. More polynomials.
8. Hyperbolic geometry and triangulations of polytopes and polygons.
9. The Erd¨osMozer Conjecture and the hard Lefschetz Theorem.
