"Chemical space: challenges and opportunitites at the border of chemistry, mathematics and computer sciences."

Modelling the evolution of the chemical space requires the development of mathematical and computational frameworks that encode the dynamics of the entire network linking chemicals through chemical reactions. In this presentation, I will explore some of the current computational ontologies for chemistry, their importance and shortcomings, and the need for a stable ontological framework for the future of chemistry and its computational scope. Additionally, I will provide a mathematical framework that relates the various ontologies of chemistry and their interconnections.

In the second part of the talk, I will examine the available models for chemical space, focusing particularly on those based on hypergraphs, in contrast to the traditional graph- based approaches. I will discuss the advantages of the hypergraph framework, along with its associated challenges. Some results will be presented on the use of hypergraphs, covering the evolution of the chemical space from 1800 to the present day. I will also address the significance of random hypergraphs and their chemical relevance, as well as recent advances in exploring the mathematics behind these random structures. Lastly, I will highlight the role of generative models for hypergraphs, along with their chemical significance and implications.