Secants and Birational Geometry of Toric Varieties

Algebraic geometry studies geometric objects, called algebraic varieties, that are the solution sets of systems of polynomial equations. Algebraic varieties can be thought of as subsets embedded in projective space; the interplay between the intrinsic properties of a variety and the properties of its embedding forms a major theme in classical algebraic geometry. However, many interesting algebraic varieties come with natural embeddings into other ambient spaces, such as toric varieties, and there has been a recent growth of interest in understanding the properties of these embeddings as well. The aim of this project is to improve our understanding of these issues by studying constructions such as secant varieties in the context of toric embeddings. The results will be applied to study the birational geometry of blowups of toric varieties, giving a clearer picture of the class of Fano-type varieties in higher dimensions. The successful applicant will join the Geometry and Mathematical Physics Research Group, which currently includes 12 permanent academic staff along with several research associates and PhD students. The group has a vibrant research culture, with activities including weekly research seminars, weekly meetings between students and supervisors, and excellent links with groups in neighbouring institutions. 94% of Loughborough’s research impact is rated world-leading or internationally excellent. REF 2021

The standard University IELTS English language requirement is 6.5 overall with 6.0 in each individual element (reading, writing, listening and speaking).

International students: £23,100

UK students: £5,238

UK/Home: £5,238

International: £23,100

October 2026, February 2027, July 2027

31 July 2026

• Loughborough, United Kingdom