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Recent MSc and PhD topics

MSc Dissertations

  • Mathematical Modelling of the Spead of Disease using Contact Networks
  • A Classical and a Bayesian Approach to Linear Ill -Posed Inverse Problems
  • Infinite antichains of permutations and permutation graphs
  • Building up the bigger picture of turbulence, Including the tripple cascade
  • Introduction to Momentum Maps
  • Topics in Bayesian Inverse Problems
  • Bifurcations of Transition States
  • The Duflo Isomorphism for Lie Algebras and Lie Superalgebras
  • Investigation into the Spectra of Selected Operators Associated with Determinantel Point Processes
  • McShane's Identity
  • Optimal Vaccination Strategies for Spatially Structured SIR Disease Models
  • 2D Discrete Radon Transform for Digital Data
  • Continuous Rankings of infinite utility Streams
  • Multi-Scaling in Reaction-Diffusion Systems: a Kinetic Monte Carlo approach
  • Calculating the number of rational points on elliptic curves with j-invariant 0 or 1728 over finite fields
  • Fermi Acceleration in the Fermi-Ulam Model
  • Topics on Bianchi Modular Groups
  • Ratner's Theorem on SL(2,R) - Invariant Measures
  • Geodesic Flows of Anosov Type
  • Varifolds and Vector-Valued Measures

PhD Theses

  • Representation Theory of Rank Two Kak-Moody Groups
  • Six-Wave Systems in One Dimensional Wave Turbulence
  • Rational Maps with Clustering and the Mating of Polynomials
  • Detection and Decoding Algortihms for nanoscale data Storage.
  • Heights on Elliptic Curves Over Number Fields, Period lattices and Elliptic Logarithms.
  • Modular Symbols Over Number Fields
  • S-Integral Points on Hyperelliptic Curves
  • Some Topics In Horogenization
  • Modular and Reciprcity Approaches to a family of Diophantine Equations
  • On Embeddings and Dimensions of Global Attractors Associated with Dissipative Partial Differential Equations
  • Pseudo-Differential Operators, heat calculus and index theory of groupoids, satisfying the Lauter-Nistor condition
  • On the Lebesque-Nagell Equation and Related Subjects
  • Exponentially Small Splitting of Invariant Manifolds near Hamiltonian-Hopf Bifurcations.
  • Categorical and Geometric aspects on non-commutative algebras: Mutations, tails and perversities.
  • Universal Frechet Sets
  • Resolutions of Foliations of real lie algebras
  • Applications of Mohl Methods on Function Spaces
  • Conjugacy and Subgroups of Hyperbolic Groups
  • Complete Non Compact CMC Surfaces in Hyperbolic 3-Space
  • Deformations of Plane Curve Singularities and the S-Constant Stratum
  • Some Examples of the Spatial Evolution of Two-Parameter Processes with Non-Adapted initial conditions
  • Approximation Methods for Multidimensional Problems Applications in Exotic Option Pricing
  • Infinite Dimensional Sampling
  • Analysis of Gradient Descents in Random Energies: Applications to Heat Baths
  • Transient Growth in Separated Flows
  • Irregular Sets and Conditional Variational Principles in Dynamical Systems
  • Some Examples of the Spatial Evolution of Two-Parameter Processes with Non-Adapted initial conditions
  • Key Varieties for Surfaces of General Type
  • Stochastic Travelling waves driven by One-Dimensional Wiener Processes
  • Generalizations of non-commutative unique factorization rings
  • Stability and Instability of Hamiltonian Systems with Two Time Scales
  • Meshfree Numerical Methods and their Application in Cell Biology
  • Slowly-Coalescing Brownian Motion on the Line