Mathematics

Applied Mathematics

Professor Nikolai Brilliantov

  • Kinetic theory of informationally connected active particles
  • Kinetic theory of dense granular gases of viscoelastic particles
  • Anomalous dynamics of an infinite set of Smoluchowski-like ordinary differential equations: Numerical and Analytical study
  • Mathematical Modelling of nano-actuators
  • Mathematical Modelling of icy geysers on icy satellites Enceladus and Europa

Professor Ruslan Davidchack

  • Detection of Unstable Periodic Orbits in Nonlinear Dynamical Systems
  • Generating Partitions, Homoclinic Tangencies, and Symbolic Dynamics in Non-Hyperbolic Systems
  • Free Energy Computation Methods with Application to Solid-Liquid Interfaces

Professor Alexander Gorban

  • Dimensionality Reduction in Data Analysis
  • Training Algorithms for Neural Networks
  • Dynamics of Systems of Physical, Chemical, and Biological Kinetics
  • Dynamics of Physiological Adaptation

Dr Bogdan Grechuk

  • Financial mathematics and economics, more concretely risk modelling and optimisation under risk
  • Discrete mathematics and optimisation
  • Mathematics formalization and formal proofs

Professor Jeremy Levesley

  • Theoretical Aspects of Approximation by Interpolation and Quasi-Interpolation of Manifolds using Polynomials and Radial Basis Functions
  • Solutions of Partial Differential Equations using Radial Functions and the Lattice Boltzmann Method
  • Fast solutions of Interpolation Equations
  • Practical Approximation of Physical Data

Dr Andrew Morozov

  • Mathematical Ecology and Population Dynamics
  • Dynamical systems, reaction-diffusion-advection models, optimisation, evolutionary game theory, integro-differential equations, pattern formation and chaos, disease modelling

Professor Sergei Petrovskii

Mathematical Ecology and Population Dynamics, in particular:

  • Mechanisms of Spatiotemporal Self-Organisation in a System of Interacting Species
  • Pattern Formation and Chaos
  • Biological Invasion
  • Population Waves
  • Coupling between Biological and Environmental Processes
  • Self-Organised Plankton Patterns in Turbulent Environment
  • Biologically Relevant Diffusion-Reaction Systems
  • Application of Nonlinear Partial Differential Equations in Biology and Ecology

Dr Ivan Tyukin

  • Dynamical systems
  • Asymptotic properties of solutions of systems of ODEs
  • Networks, synchronization, and controlled synchronization of dynamic networks
  • Control and Optimization in presence of uncertainties
  • Parameter estimation and Identification
  • Machine learning and data analysis
  • Computer vision
  • High-dimensional data analysis and measure concentration phenomena in machine learning
  • Neural networks

Dr Bo Wang

  • Nonparametric and semi-parametric modelling for longitudinal and functional data, and applications
  • Gaussian process methods for nonlinear regression
  • Stochastic mortality modelling and forecasting

Dr Aihua Zhang

  • Actuarial Science: Pensions, Annuities, longevity/mortality-linked products
  • Financial Mathematics: Asset Pricing, Portfolio maximisation
  • Economics: Economic Dynamics
  • Miscellany: Risk Management, Business Valuation, Accounting, and Carbon Finance

Pure Mathematics

Dr Alexander Baranov

  • Lie Algebras and Representation Theory
  • Direct Limits of Finite Dimensional Algebras, Groups, and their Representations

Dr Katrin Leschke

  • Differential Geometry
  • Conformal surfaces, in particular, minimal surfaces, CMC surfaces, HSL surfaces and Willmore surfaces
  • Quaternionic Holomorphic Geometry
  • Transformation theory
  • Integrable systems
  • Isoparametric manifolds
  • Visualisation
  • Shape recognition
  • Surfaces in 3D

Dr Andrey Mudrov

  • Algebra, representation theory, mathematical physics

Dr Frank Neumann

  • Algebraic Topology and Homotopy Theory, Cohomology of Finite Loop Spaces, and Generalized Homogeneous Spaces
  • Algebraic Invariant Theory
  • Applications of Homotopy Theory to Algebraic Geometry and Arithmetic Geometry, Etale Homotopy, and Cohomology of Stacks

Dr Simona Paoli

  • Category Theory
  • Homotopy theory
  • Interactions between higher category theory and algebraic topology

Dr Teimuraz Pirashvili

  • Homological Algebra
  • Functor Homology and Polynomial Functors.
  • Leibniz Algebras

Dr Sibylle Schroll

  • Representation Theory of Finite Dimensional Algebras. In particular, Quiver Representations
  • Homological Algebra
  • Cluster Algebras, especially Cluster Categories and Finite Dimensional Algebras related to Surface Cluster Algebras
  • Cohomology Theories: Hochschild cohomology and Extensions
  • Algebras related to modular representations of finite groups: Brauer graph algebras, special biserial algebras and their wild analogue
  • Non-commutative Groebner bases

Professor Nicole Snashall

  • Representation Theory of Finite Dimensional Algebras
  • Hochschild Cohomology and Support Varieties of Modules
  • Homological Algebra, Ext Algebra, Finiteness Conditions

Dr Andrew Tonks

  • Category theory, infinity groupoids
  • Homological algebra, K-theory
  • Homotopical algebra, operads, simplicial methods