Parametrisation of Algebraic Surfaces: developing geometric techniques that can be utilised to address fundamental questions in other sciences and in practical applications

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Project Detail:

This project is part of a 5-student centre for doctoral training at Loughborough University within the area of Geometry and its applications.

The overall aim of this project is to develop geometric techniques that can be utilised to address fundamental questions in other sciences and in practical applications. The main emphasis is on applications of algebraic geometry in the theory of kinematics of robots, parametrisation of surfaces and complexity theory, while the core of the projects will remain focused on developing new theoretical foundations in geometry. Several aspects of algebraic geometry, such as birational techniques, singularity theory, and higher secant varieties, as well as integrable systems will be used in various projects.

Parametrisation of Algebraic Surfaces:

Parametrising surfaces lies at the heart of geometric design. Deciding whether a surface is parametrisable or not can be answered by the Castelnuovo rationality criterion. However, giving an actual parametrisation of a surface is a very challenging problem and existing methods do not perform well in practice. This project will develop new techniques for parametrising singular surfaces of degree at least four. Our approach is based on working with singular models of surfaces, but substantially decreasing the complexity of the computations by avoiding resolution techniques. We will instead aim to give a thorough analysis of the singularities and the birational geometry of these surfaces.

Entry requirements:

Applicants should have, or expect to achieve, at least a 2:1 Honours degree (or equivalent) in Mathematics or a related subject. A relevant Master’s degree and/or experience in Algebraic Geometry will be an advantage, but not essential.

Contact details:
Name: Dr Hamid Ahmadinezhad
Email address: [Email Address Removed]
Telephone number: 01509 222628

How to apply:

All applications should be made online at http://www.lboro.ac.uk/study/apply/research/. Under programme name, select ‘Mathematical Sciences’

Please quote reference number: GEOM3/MA/HA

Note that applicants to one of the projects in this cohort will automatically be considered for other projects. Please contact us for further information.

Application details:
Reference number: GEOM3/MA/HA
Start date: 1/10/2017
Closing date: 5/5/17

Supervisors:
Primary supervisor: Dr Hamid Ahmadinezhad