Permanents, permutations and polynomials

Permutations are one of the most fundamental mathematical concepts. We aim to develop the combinatorial theory of permutations in several related contexts. Our theoretical advances will help us make significant progress on a number of open problems, some of which have defied attack for decades. The project links several areas of pure mathematics (combinatorics, graph theory, linear algebra, group theory, coding theory) and is likely to find future applications in information and communication technology.