The Existence of a Topos

Dessins d’enfants are coloured graphs that lie at the crossroads of combinatorics, topology, complex analysis, and number theory. Properties within these diverse fields of
mathematics can be inferred and related by considering the category of dessins d’enfants— furthering the understanding of these respective fields.This research project will study the combinatorial aspects of the category of dessins d’enfants; beginning with the notion of morphisms between dessins d’enfants, describing monomorphisms and epimorphisms of dessins, discussing the possibility of a topos, and calculating the Euler characteristic of a dessin. The research will then be proceeded by a
study of dessins d’enfants in a direction chosen by the applicant’s interests.

Lachlan Schilling

University of Adelaide

Lachlan Schilling is currently a 2nd-year student at the University of Adelaide studying a Bachelor of Mathematical Sciences (Advanced) and a Bachelor of Science (Advanced) – majoring in pure mathematics and theoretical physics. He is currently interested in abstract algebra, geometry, and particle physics.

In his spare time, Lachlan enjoys participating in capture the flag competitions. These are cyber security competitions where teams test and evaluate the security of technology. Furthermore, during the summer of 2021, Lachlan participated in the Mathematical Contest in Modeling (MCM) where he, along with two other students, successfully developed a mathematical model to profit from stock market trading.

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