Applications of topology to soft matter physics

These projects are open to students worldwide, but have no funding attached. Therefore, the successful applicant will be expected to fund tuition fees at the relevant level (home or international) and any applicable additional research costs. Please consider this before applying. 

This project will address mathematical problems in the research field of algebraic topology, inspired by the theory of topological defects in soft materials.

In soft matter physics, one often considers materials whose molecules display discrete symmetries. Liquid crystals, for example, typically consist of rod-shaped molecules with no distinguished head or tail. The molecules of such a material tend to align with each other in local patches of the sample region, but there may be places where continuity of alignment breaks down. These so-called topological defects are responsible for interesting behaviours and properties at the mesoscopic scale, and it has long been recognised that tools from algebraic topology (such as fibre bundles and homotopy groups) play a vital role in understanding them.

Biaxial nematics are liquid crystals with more than one axis of reflectional symmetry. One of the goals of this project is to obtain a better understanding of the mathematics behind biaxial nematics and their topological defects. This will involve answering beautiful problems in the topology of manifolds, related to classical topics such as the vector field problem and the Poincaré-Hopf theorem.

Essential Background:

Decisions will be based on academic merit. The successful applicant should have, or expect to obtain, a UK Honours Degree at 2.1 (or equivalent) in Mathematics and a first course in Algebraic Topology is essential.

Application Procedure:

Formal applications can be completed online: https://www.abdn.ac.uk/pgap/login.php.

You should apply for Mathematics (PhD) to ensure your application is passed to the correct team for processing.

Please clearly note the name of the lead supervisor and project title on the application form. If you do not include these details, it may not be considered for the studentship.

Your application must include: A personal statement, an up-to-date copy of your academic CV, and clear copies of your educational certificates and transcripts.

Please note: you DO NOT need to provide a research proposal with this application.

If you require any additional assistance in submitting your application or have any queries about the application process, please don't hesitate to contact us at [Email Address Removed]