Combinatorial and computational algebra of toric degenerations of varieties

Lead Research Organisation: University of Bristol
Department Name: Mathematics

Abstract

Toric varieties play an important role in algebraic geometry. There are several methods developed in polyhedral and combinatorial geometry to compute the invariants of a toric variety.

The student will work on toric varieties which are at the interface of algebra, combinatorics and geometry. Recently there has been a breakthrough in algebraic geometry making a direct connection between the theory of Newton-Okounkov bodies and tropical geometry, and in particular the toric varieties arising in both contexts. The main component of the student's project is to apply algebraic and combinatorial methods to further explore such connections.

Publications

10 25 50

Studentship Projects

Project Reference Relationship Related To Start End Student Name
EP/N509619/1 01/10/2016 30/09/2021
1953188 Studentship EP/N509619/1 18/09/2017 31/03/2021 Oliver Clarke