Exploring the Euler Characteristics of Dessins d’Enfants

Dessins d’enfants were invented by Alexander Grothendieck. He pointed out their remarkable relationships to diverse areas of mathematics. The topic lies at a crossroads of combinatorics, topology, complex analysis, and number theory, and provides an opportunity to explore fundamental concepts of category theory in a hands-on manner. The focus will primarily be on the combinatorial aspects of dessins. We will aim to define and study non trivial properties of dessins. This includes, but is not limited to, define the notion of a morphism of dessins, describing monomorphisms and epimorphisms of dessins, investigate whether the category of dessins is a topos and developing a definition of the Euler characteristic of a dessin.

Paawan Jethva

University of Adelaide

Paawan Jethva is a second-year Bachelor of Mathematical Sciences (Advanced) student at the University of Adelaide. In 2022, he completed a summer research project on numerical methods for improved tsunami modelling. It involved numerically solving non-linear partial differential equations and investigating how to extend them to include dispersive effects. The same year, he participated in the Mathematical Contest in Modeling (MCM) in a team with two other students. Their chosen problem was designing an optimal trading strategy for Bitcoin and gold, which involved developing a price forecasting model and a portfolio rebalancing model to optimise future returns given past pricing data. Their team was designated a meritorious winner. His current interests include category theory, a field used in almost all areas of mathematics.

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