Research Group

Mathematics

A young man with dark hair and glasses is writing a mathematical formula on a surface, the window through which the photo is taken is also covered in formulas.

Mathematics is an essential part of research in many other disciplines.

Our academics have links with research groups in other departments around the university, and work collaboratively on interdisciplinary projects with colleagues across the Faculty of Science and Health such as the Department of Psychology and the School of Computer Science and Electronic Engineering.

Mathematics research in our department covers three main areas: applied mathematics, pure mathematics, and mathematics education. Academics may have interests in more than one area, and some also carry out research within data science.

  • Algebra, Geometry and Discrete Mathematics theme (Jessica Claridge, Alastair Litterick, Jesus Martinez-Garcia, David Penman, Alexei Vernitski, Gerald Williams, Peter Higgins) - The recent departmental growth strategy has enabled an expansion in the theme’s scope, doubling its size from a core base of expertise in semigroup theory, combinatorial group theory, graph theory and combinatorics to now include researchers who work in algebraic geometry, finite group theory, and applications of finite field theory to network coding.
  • Analysis and Mathematical Physics theme (Murat Akman, Georgios Papamikos, Georgi Grahovski) - Theme members work on a broad range of topics in Mathematical Analysis and Mathematical Physics, including discrete and continuous integrable systems, Lie groups, Lie algebras and symmetries, analysis of PDEs, Harmonic analysis and Potential theory, algebraic methods in differential equations, and geometric analysis. 
  • Mathematical Applications theme (Chris Antonopoulos, Dmitry Savostyanov, Edd Codling, Hadi Susanto) - Theme members work on topics ranging from numerical mathematics and applications of linear algebra, through dynamical systems and nonlinear waves, to mathematical biology. Specific topics include complex systems, network analysis, network inference, random walk theory, collective behaviour, population dynamics, pattern formation, dynamical systems, soliton theory and nonlinear waves, nonlinear and atomic optics, spinor Bose-Einstein condensates, fluid mechanics, numerical mathematics, low-rank tensor product approximations, linear and multilinear algebra, matrix analysis, and the design of efficient numerical algorithms.

MESS (Mathematics Essex Seminar Series)

Throughout the academic year we run the Mathematics Essex Seminar Series. This series gives our staff and research students an opportunity to present and discuss their work with a diverse audience from around the University. We also invite mathematicians from other institutions across the world to present their research, helping raise awareness of research outside the university, and promoting inter-institutional collaboration.

Upcoming events

Summer term 2021

13th May 2021 - Fractional random Schrödinger operators, integrated density of states and localisation - Constanza Rojas-Molina, CY Tech - Institut des Sciences et Techniques - CY Cergy Paris Université.

6th May 2021 - The curious case of rapid entrainment after jet lag and how to get a single neuron to remember - Kyle Wedgwood, University of Exeter.

29th April 2021 - Mathematics Anxiety: general overview, what has been done and what we need to do to help learners - Frederica Armani, University of Essex.

Spring term 2021

25th March 2021 - Digraph groups and related groups - Mehmet Cihan, University of Essex.

18th March 2021 - Understanding the Notion of K-stability using 3-folds - Nivedita Viswanathan, University of Edinburgh.

11th March 2021 - Domino effects on networks of bistable oscillatory nodes - Jennifer Creaser, University of Exeter.

4th March 2021 - Spread and infinite groups - Charles Cox, University of Bristol.

25th February 2021 - Differentiable vs non-differentiable systems - Cristiana de Filippis, University of Oxford.

18th February 2021 - Our brain is not static - Kelly Iarosz, Universidade Tecnológica Federal do Paraná (UTFPR).

11th February 2021 - Relativistic chaotic scattering - Jesús Seoane Sepúlveda, Universidad Rey Juan Carlos.

4th February 2021 - A discrete Kakeya-type inequality - Marina Iliopolou, University of Kent.

28th January 2021 - Extreme events in nonlinear wave interactions (dragon king) - Antonio Marcos Batista, State University of Ponta Grossa, Paraná, Brazil.

Highlights of Autumn term 2020 events

Cod on the menu? Using mathematical modelling to provide fisheries management advice

In this seminar Dr Nicola Walker, a Fisheries Modeller for Centre for Environment, Fisheries and Aquaculture Science, presented the state-space assessment model (SAM) that is used to assess fish stocks, in this case using North Sea cod as an example. Such models inform scientific advice on the management of fish stocks, with results being derived from evidence including catches, research surveys and life history.

Dr Walker explained the diagnostics for assessing the quality of input data and model fits and highlighted some of the problems facing the assessment of this stock. The North Sea cod made an interesting case study, as this fish is believed to have stock that is below safe biological limits, even though the fishery was certified sustainable just two years ago.

Related papers

Nicola D. Walker, Robin Boyd, Joseph Watson, Max Kotz, Zachary Radford, Lisa Readdy, Richard Sibly, Shovonlal Roy, Kieran Hyder, A spatially explicit individual-based model to support management of commercial and recreational fisheries for European sea bass Dicentrarchus labrax, Ecological Modelling, Volume 431, 2020, 109179, ISSN 0304-3800

Roy, S., Walker, N. and Sibly, R. M. (2020) Potential consequences of climate and management scenarios for the northeast Atlantic mackerel fishery. Frontiers in Marine Science, 7. 639. ISSN 2296-7745.

An extended SIR model for the spread of COVID-19 in different communities

In early 2020 the novel coronavirus Covid-19 began to spread rapidly throughout the world. To understand the impact of the virus, and how to control infections, scientists looked towards data modelling to provide examples of the infection rate and the impact on communities.

In this seminar, Dr Chris Antonopoulos looked at the effectiveness of the modelling approach on the pandemic due to the spreading of the novel COVID-19 disease and develop an extended-susceptible-infected-removed (eSIR) model that provides a theoretical framework to investigate its spread within a community. A particular focus of this research has been the time evolution of different populations, and how to monitor diverse significant parameters for the spread of the disease in various communities, represented by countries and the state of Texas in the USA.

Dr Antonopoulos explained that the eSIR model can provide us with insights and predictions of the spread of the virus in communities that recorded data alone cannot. It was interesting to hear that the spread of COVID-19 can be under control in all communities considered, if proper restrictions and strong policies are implemented to control the infection rates early from the spread of the disease.

Related papers

Cooper, I., Mondal, A. and Antonopoulos, CG., (2020). A SIR model assumption for the spread of COVID-19 in different communities. Chaos, Solitons and Fractals. 139, 110057-110057

Cooper, I., Mondal, A. and Antonopoulos, CG., (2020). Dynamic tracking with model-based forecasting for the spread of the COVID-19 pandemic. Chaos, Solitons and Fractals. 139, 110298-110298

K-stability of Fano 3-folds

Dr Anne-Sophie Kaloghiros, a Senior Lecturer at Brunel University, joined us to discuss her work on K-stability of Fano 3-folds.

Fano varieties are geometric shapes which are positively curved. They arise in a wide array of fields from theoretical physics to phylogenetic trees. There are rich interactions between differential geometric and algebro-geometric properties of Fano manifolds (and more generally of Kahler manifolds).

An instance of this phenomenon was conjectured by Yau Tian and Donaldson (and proved by Donaldson, Chen and Sun): they proved that on Fano manifolds the existence of special canonical metrics is equivalent to a stability property. This is an equivalence between properties that are subtle, and still little understood.

In her talk, Dr Kaloghiros explained the algebro-geometric approaches to this problem, as well as recent developments in this area of research and their applications to our understanding of Fano surfaces and 3-folds.

Related papers

Ahmadinezhad, H. and Kaloghiros, A-S. (2015) 'Non-rigid quartic 3-folds'. Compositio Mathematica, 152 (5). pp. 955 - 983. ISSN: 1570-5846

Kaloghiros, AS. (2011) 'The defect of Fano 3-folds'. Journal of Algebraic Geometry, 20 (1). pp. 127 - 149. ISSN: 1056-3911

Our academics

Dr Murat Akman

Lecturer in Mathematics

Department of Mathematical Sciences, University of Essex

Research areas: Pure mathematics.

Dr Chris Antonopoulos

Lecturer in Applied Mathematics

Department of Mathematical Sciences, University of Essex

Research area: Applied mathematics.

Dr Jessica Claridge

Lecturer in Mathematics

Department of Mathematical Sciences, University of Essex

Research areas: Pure mathematics, mathematics education.

Professor Edward Codling

Professor of Mathematical Biology

Department of Mathematical Sciences, University of Essex

Research area: Applied mathematics.

Dr Georgi Grahovski

Senior Lecturer in Applied Mathematics

Department of Mathematical Sciences, University of Essex

Research areas: Applied mathematics, pure mathematics.

Professor Peter Higgins

Professor of Pure Mathematics

Department of Mathematical Sciences, University of Essex

Research area: Pure mathematics.

Dr Alastair Litterick

Lecturer in Mathematics

Department of Mathematical Sciences, University of Essex

Research area: Pure mathematics.

Dr Jesus Martinez-Garcia

Lecturer in Pure Mathematics

Department of Mathematical Sciences, University of Essex

Research area: Pure mathematics.

Dr Georgios Papamikos

Lecturer in Mathematics

Department of Mathematical Sciences, University of Essex

Research area: Applied mathematics.

Dr David Penman

Senior Lecturer in Pure Mathematics

Department of Mathematical Sciences, University of Essex

Research area: Pure mathematics.

Professor Christopher Saker

Professor of Mathematics Education

School of Mathematical Sciences, University of Essex

Research area: Mathematics education.

Dr Dmitry Savostyanov

Lecturer in Mathematics

Department of Mathematical Sciences, University of Essex

Research area: Applied mathematics.

Professor Hadi Susanto

Professor of Applied Mathematics

Department of Mathematical Sciences, University of Essex

Research area: Applied mathematics.

Dr Alexei Vernitski

Senior Lecturer in Mathematics

Department of Mathematical Sciences, University of Essex

Research area: Pure mathematics, mathematics education.

Professor Gerald Williams

Professor of Algebra

Department of Mathematical Sciences, University of Essex

Research area: Pure mathematics.