Guillermo Restrepo: Graphs and chemical reactions

Chemical reactions encode a wealth amount of information on the transformation of chemical substances. In this talk we will discuss how to mathematically model them at the level of atoms involved in the molecules interacting in the chemical reaction. Here molecules are regarded as graphs, whose transformation are modelled by rewriting rules acting upon the graph of starting materials and yielding the graph of products of the chemical reaction. Leaving aside reactions as ensembles of atoms and their transformations, reactions can also be modelled at the level of substances, where the important information is which starting materials relate to each other to produce the final products. Here, the model we use is that of directed hypergraphs.

As chemical reactions reported by chemists grow exponentially, the hypergraph representing them turns very large. In general, large networks are treated by devising statistics gauging several aspects of such structures, some statistics are, e.g. vertex degree distributions, centrality, and several others. Recently, curvature of edges and vertices has been incorporated to this statistics and we will show how the curvature can be extended to hypergraphs, which actually generalise graph results.

In the last part of the talk we will discuss open questions about the growth of chemical reaction networks and how to model them.