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math PhD Projects, Programs & Scholarships

We have 41 math PhD Projects, Programs & Scholarships

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  DTC MATH 10 - Probability measures on infinite dimensional spaces and umbral calculus
  Prof E Lytvynov
Applications accepted all year round
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.
  DTC MATH 11 - Quasi-free states on the algebra of the anyon commutation relations
  Prof E Lytvynov
Applications accepted all year round
Anyon statistics are intermediate statistics between Fermi and Bose statistics and they have been used by physicists to describe the quantum Hall effect.
  DTC MATH 12 - Mathematical analysis of Thomas-Fermi theory of charge screening in graphene
  Dr V Moroz
Applications accepted all year round
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.
  DTC MATH 13 - Heat kernel for Schroedinger operator - applications to NSE and spectral analysis
  Dr Z Sobol
Applications accepted all year round
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.
  DTC MATH 14 - Algebraic spline geometry methods in approximation theory
  Dr N Villamizar
Applications accepted all year round
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.
  DTC MATH 15 - Analysis of stochastic evolution equations - investigation of random field solutions of partial differential equations perturbed by random noises
  Prof JL Wu
Applications accepted all year round
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.
  DTC MATH 16 - Delay McKean-Vlasov stochastic differential equations and applications to finance
  Dr C Yuan
Applications accepted all year round
In this project, we shall investigate a class of delay McKean-Vlasov stochastic differential equations (SDEs), also known as mean-field delay SDEs.
  DTC MATH 17- Spreading speeds and traveling waves
  Dr E Crooks
Applications accepted all year round
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.
  DTC MATH 2 -Facets of noncommutative smoothness and foundations of noncommutative geometry
  Prof T Brzezinski
Applications accepted all year round
Noncommutative geometry combines ideas from geometry and noncommutative algebra and equips noncommutative rings with geometric meaning.
  DTC MATH 3 - Trusses - detailed study of properties and the nature of trusses with application to the Yang-Baxter equations
  Prof T Brzezinski
Applications accepted all year round
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).
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