Applications of Riordan arrays in the analysis of two-dimensional lattice walks and polygons ( Ref WD_2020_31_WSCH_4)

Post summary

Applications are invited to submit applications to undertake a PhD entitled ‘Applications of Riordan arrays in the analysis of two-dimensional lattice walks and polygons.’

Riordan arrays are a group of matrices that was first defined in 1991, originally defined as a matrix group that unified many themes in enumeration. However, In recent times, Riordan matrices have been identified as a powerful tool in solving algebraic and enumerative combinatorial problems. Applications of these matrices have been found in many areas such as algorithm analysis, cryptography, wireless communications and structural biology.

The primary objective of this 4 year PhD study is to use Riordan matrix techniques to study combinatorial models of two-dimensional lattice walks and polygons. These models occur in various applications in physics, biology and computer science. In particular, they can be seen as simple models of biological vesicles or polymers. Of particular of interest in the models, is understanding their behaviour around certain critical points which correspond physically to phase transitions.

Person specification

Qualifications

Essential

• Applicants must have a relevant Mathematics degree (minimum level 2.1).

Desirable

• A relevant Masters in Mathematics or a related discipline is desirable.

Knowledge & Experience

Essential

• Applicants must be familiar with relevant mathematics software (eg. Mathematica, Sage or MATLAB).

Desirable

• Experience using LaTeX is desirable.

Skills & Competencies

Essential

• Applicants whose first language is not English must submit evidence of competency in English, please see WIT’s English Language Requirements for details.