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.
Anyon statistics are intermediate statistics between Fermi and Bose statistics and they have been used by physicists to describe the quantum Hall effect.
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.
The subject is two-sided estimates for the integral kernel of the semigroup of operators generated by the Schroedinger operators, with applications to NSE and spectral analysis.
The aim of the project is to explore algebraic geometry tools for the study of approximation methods based on piecewise polynomial functions, also known as splines.
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).
