Bryan L. Shader
University of Wyoming (ILAS Speaker)
The classic Perron-Frobenius Theory shows that combinatorial, algebraic and spectral properties of nonnegative matrices are closely related, and this powerful tool has been successfully used in the analysis of Markov chains. The talk develops the analogous relationships between k-tuples of n by n nonnegative matrices, the combinatorics of colored digraphs, and the analysis of higher dimensional dynamical systems. The techniques discussed are then applied to solve a weak version of the famous road-coloring conjecture that arose in finite automata and symbolic dynamics.
Return to Program