# Abstract: Spectral Landscape Theory

The notion of an {\em adaptive landscape} has proved to be a valuable concept in theoretical investigations of evolutionary change, combinatorial optimization, and the physics of disordered systems. Landscape theory has emerged as an attempt to devise suitable mathematical structures for describing the static'' properties of landscapes as well as their influence on the dynamics of adaptation. Here we focus on the connections of landscape theory and algebraic combinatorics that form the basis of spectral approach to understanding landscape structure.