Funded PhD Studentship: DTC MATH 41 - Probability measures on infinite dimensional spaces and umbral calculus: Sheffer polynomial sequences

Swansea University is a UK top 30 institution for research excellence (Research Excellence Framework 2014), and has been named Welsh University of the Year 2017 by The Times and Sunday Times Good University Guide.

Swansea Science DTC is a community committed to undertaking world-class research that has a positive impact globally and we have a fully-funded PhD scholarship for 2017/2018 entry.

Swansea Mathematics is rated as one of the Top 25 mathematics departments in the UK, and are within the top third in the world (QS World University Rankings 2015).

The Department of Mathematics places a strong emphasis on developing graduate employability and this is evidenced by the fact that 94% of our graduates are in full-time employment or further study within six months of graduating. Graduates have been employed by a wide range of organisations including: AXA, BA, Deutsche Bank, Shell Research, Health Authorities, Zurich Financial Services, Local Government and others.

Description:

The classical umbral calculus is a study of Sheffer polynomial sequences on the real line. This theory has numerous connections with algebra, analysis, probability theory, mathematical physics, topology etc. In this project, you will study: (a) Sheffer polynomial sequences defined on an infinite dimensional space that are orthogonal with respect to a certain probability measures; (b) extensions of the theory to the noncommutative (quantum probability) setting.