Matroid theory

Host Faculty: Engineering
General Subject Area: Pure Mathematics
Project Level: PhD
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Matroids (combinatorial geometries) are precisely the geometric structures underlying the solution of many combinatorial optimisation problems. These problems include scheduling and timetabling, and finding the minimum cost of a communications network between cities. Given this, it is surprising that matroid theory also unifies the notions of linear independence in linear algebra and forests in graph theory as well as the notion of duality for graphs and codes. Current and recent postgraduate projects have included studying matroids with a cyclic arrangement of circuits and cocircuits, developing tools analogous to Tutte's Wheels-and-Whirls Theorem, and using tree decompositions to unravel the behaviour of crossing separations.


Supervisor: Charles Semple

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