Research Group

Mathematics

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.

Applied mathematics

Applied Mathematics covers a wide range of mathematical topics and application, such as engineering, natural sciences, or industry, that may involve appropriate formulation of equations describing the behaviour of the physical systems and analysis of the equations that may require various mathematical (analytical as well as numerical) techniques.

Pure mathematics

Pure mathematics studies abstract concepts that may be inspired by real life phenomena and that yield tools that can be applicable in other subject areas. Our academics contribute to well-established areas of mathematics such as algebra, including graph theory and group theory, and geometry.

Mathematics education

Research in mathematics education is primarily concerned with the tools, methods and approaches that facilitate practice or the study of practice. As demand for students with good mathematics skills increases, we must also improve the way that mathematics is taught.

Our research tries to underpin our own practice. What do we do well with educating our students and what can be done better, feeds through in to our research.

 

You can find out more about our academics areas of research interest using the staff list below.

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

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 Georgios Amanatidis

Lecturer in Mathematics

Department of Mathematical Sciences, University of Essex

Research area: 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.