Funded PhD Studentship: DTC MATH 40 - Topology and combinatorics of configuration spaces of points in tropical geometry

Swansea University is a UK top 30 institution for research excellence (Research Excellence Framework 2014), and has been named Welsh University of the Year 2017 by The Times and Sunday Times Good University Guide.

Swansea Science DTC is a community committed to undertaking world-class research that has a positive impact globally and we have a fully-funded PhD scholarship for 2017/2018 entry.

Swansea Mathematics is rated as one of the Top 25 mathematics departments in the UK, and are within the top third in the world (QS World University Rankings 2015).

The Department of Mathematics places a strong emphasis on developing graduate employability and this is evidenced by the fact that 94% of our graduates are in full-time employment or further study within six months of graduating. Graduates have been employed by a wide range of organisations including: AXA, BA, Deutsche Bank, Shell Research, Health Authorities, Zurich Financial Services, Local Government and others.

Description:

Tropical geometry is very recently-emerged field of mathematics that combines polyhedral geometry, matroid theory, and algebra to provide exciting new tools and invariants in areas such as algebraic geometry, and it has already produced some stunning results. In this project we will explore the topology and structure of Hilbert schemes of tropical point configurations in projective space. These spaces bring together ideas from homological algebra, the theory of symmetric functions, and matroids into fascinating geometric structures that have not yet been understood.