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

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