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.
Mathematically, graphene could be considered as a two-dimensional object. Two dimensionality of graphene leads to a number of remarkable physical and mechanical properties which also give rise to new challenging mathematical problems.
This PhD project will investigate random field solutions of parabolic partial differential equations perturbed by random noises, including stochastic heat equations and parabolic Anderson models as prototype examples.
Front propagation is ubiquitous throughout science and beyond, from the invasion of species in population dynamics to the switching properties of liquid crystals to the spread of rumours, and is often modelled mathematically using initial-value problems and travelling waves for systems of reaction-diffusion equations and their non-local variants.
Applications of the Yang-Baxter equation range from the description of physical forces of the nature (quantum field theory, integrable Hamiltonian systems in particle and statistical physics), through classification of geometric and topological objects in mathematics (knot theory, group theory) to foundations of mathematics (braided monoidal categories).