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# Prof Zurab Janelidze

## Formulas and forms in categorical algebra

Most mathematical structures of a given type can be added and multiplied, just like numbers. This leads to the development of arithmetic of mathematical structures. In this expository paper you will see how simple laws of such arithmetic are able to capture the inner complexity of certain mathematical structures, and how sometimes it becomes possible to reveal the inner shape of a structure through the organisation of the relationships between like structures. The notion of a ‘category’ was devised to express general principles of relationships between mathematical structures. A more refined notion of a ‘form’ is proposed, which makes it possible to reveal symmetry in these principles that up to now was a luxury of more specific types of structures. This is, however, not an end, but merely the beginning of new exploration.

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## Short biography

Zurab Janelidze is a professor of Mathematics in the Department of Mathematical Sciences. His research expertise is in categorical algebra, a merger of the fields of category theory and algebra. He serves on the editorial boards of Applied Categorical Structures and Cahiers de Topologie et Géométrie Différentielle Catégoriques, which are two of the three main international journals in category theory. He completed his university studies at Tbilisi State University in Georgia, where he obtained his PhD in 2006. During 2007-2008 he was a postdoctoral fellow at the University of Cape Town. In 2009 he was appointed at Stellenbosch University as a lecturer, and promoted to senior lecturer, associate professor and full professor in 2011, 2014 and 2019, respectively. He is the programme leader for Mathematical Sciences and convener of Foundations of Abstract Mathematics modules offered at second and third year level of undergraduate study.

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