Iain Moffatt has been awarded a research grant for his research programme entitled “Hypermaps: polynomials, dualities and minors”.

Iain Moffatt

This project is funded by the Engineering and Physical Sciences Research Council (EPSRC) and is concerned with higher order interactions in networks. Mathematics has traditionally modelled networks using “graphs”. Graphs provide a highly powerful structure for modelling pairwise interactions of objects. However, effective modelling of many applications requires capturing simultaneous interactions of multiple objects, rather than just pairs. (For example, consider the structure of neurons in the brain.) In such applications “hypergraphs” or “hypermaps” are used.

Despite such higher order interactions being pervasive, their systematic study is only just receiving due attention and there is a pressing need to develop the corresponding combinatorial theory. This project will introduce a theoretical underpinning for these higher order interactions by developing combinatorial, topological and algebraic tools and structure for them. Motivated by applications in statistical physics, biomathematics and topology, our focus is on the “hypermap polynomials” that lie at
the intersection of these applications. It will develop a theoretical framework for hypermap polynomials by undertaking a systematic study of hypermap minors, dualities, and associated algebraic and combinatorial structures.