Abstract: ‘Nut graphs’ are graphs that have a single non-trivial kernel eigenvector, and this unique vector has no zero entries. Remarkably, this rather abstract mathematical definition has significant consequences for the chemistry and physics of π-conjugated systems. It gives a model for radicals with fully distributed spin density, and a model for molecules with exactly one non-bonding π molecular orbital that are omniconductors in the simplest model of ballistic conduction. Signed nut graphs provide models for molecular structures with these properties that have Möbius twists in their πsystems. This talk will give an introdution to these fascinating graphs.

Bio: Professor Patrick Fowler obtained his PhD in Chemistry from the University of Sheffield in 1981. He was a SERC Postdoctoral Fellow at the University of Cambridge from 1980 to 1983. In 1983 he spent a year as a Senior Demonstrator at the University of Durham, returning to a Postdoctoral Research Fellowship at the University of Cambridge in 1984. In 1985 he became a Lecturer in Physical Chemistry at the University of Exeter, where he was then promoted to Reader in 1990 and Professor in 1995. In 2005 he became Professor of Theoretical Chemistry at the University of Sheffield. He was elected Fellow of the Royal Society in 2012.

Professor Fowler is a leading figure in the field of mathematical and computational chemistry. His research ranges from chemical problems with an emphasis on applications, to combinatorial and graph theoretic problems that are of a more mathematical nature, but often loop back to chemistry and pictorial chemical models. The graphs used in his research typically serve as models for geometric and electronic structure of molecules and molecular electric and magnetic properties. The tools he applies come from theoretical chemistry as well as from mathematics and computer science, where he and his collaborators use implementations of efficient algorithms to tackle chemical problems. He is also interested in applications of symmetry in engineering.