Mathematics

Mathematics

Mathematics at Hull has a long history of cutting-edge research in pure and applied mathematics as well as probability and statistics. Our impact is measured in our interactions with industry and society, particularly through our public engagement activities.

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Faculty of Science and Engineering
Dr Siri Chongchitnan
Director of Studies

The Challenge

Our mission is to promote interdisciplinary research in mathematics (pure, applied, probability and statistics) nationally and internationally.

The Approach

  • In pure mathematics, we study group theory, semigroup theory, and computational algebra
  • In applied mathematics, we study fluid mechanics, environmental and industrial modelling, and cosmology
  • In probability and statistics, we study processes on complex networks, as well as statistical methods in astrophysics
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OUR AIMS

  • To use mathematics to make sense of the world around us through a wide range of pure and applied research
  • To disseminate our mathematics research through high-impact publications and inspiring public engagement

Projects

Abstract

Algebra

At Hull, we study algebra using pure and computational approaches. We develop mathematical tools and design algorithms for computation with algebraic structures represented by matrices and permutations.

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Fluid Mechanics

We investigate the Navier-Stokes equations governing fluid motion. We are especially interested in high Reynolds number flows (typical of water and air flows) as well as hydrodynamical instability.

Network

Processes on Complex Networks

At Hull, we use probability theory to investigate the behaviour of processes, such as opinion formation, the spread of information and epidemics, on complex networks such as social, information, technological and biological networks.

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Environmental and Industrial Modelling

We develop models to analyse river flows in estuaries and the impact on the growth of vegetation due to pollutants released further upstream. We also investigate and develop numerical methods to solve the model equations.

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Cosmology

We investigate mathematical theories that explain the large-scale structure and evolution of the Universe. Our interdisciplinary research is performed in collaboration with the E. A. Milne Centre for Astrophysics.

Sky and water

Public Engagement

We are passionate about sharing mathematics with school students, teachers and the general public through our annual Royal Institution Mathematics Masterclasses, Venn Lectures in Mathematics, on-campus enrichment events and school visits.

View all projects

Computational Algebra

Researcher: Dr Alla Detinko
Computational algebra is an innovative discipline interfacing mathematics and computer science. It focuses on the design and implementation of algorithms for algebra and its applications. In Hull, we design algorithms and software for symbolic computation with algebraic structures represented by matrices and permutations. These are applied to solve problems in mathematics and further afield via computer experimentation.

Group Theory

Researcher: Dr Wolfram Bentz
We examine how the advanced symmetries of a structure, which are encoded in its group of units or automorphisms, influence its properties. We do this by establishing connections between permutation groups, transformation monoids, graphs, and automata.

Cosmology

Researcher: Dr Siri Chongchitnan
We constrain the physics of cosmological inflation (a brief flash of exponential expansion in the early Universe) using a complementary suite of current and future observables.

Processes on complex networks

Researcher: Dr Sander Dommers
Large complex networks can be found everywhere, for example as social, information, technological and biological networks. Many of these networks share the property that they are scale-free i.e., the number of links of nodes have a power law distribution. At Hull, we use probability theory to investigate what the effect is of the scale-free nature of complex networks on processes on these networks, both in and out of equilibrium.

Hydrodynamic Instability

Researcher: Dr Richard Danyi
In fluid dynamics, the study of hydrodynamic instability aims to find out if a given flow is stable or unstable, and how instabilities cause the development of turbulence. At Hull, we investigate analytically the linearised equations of motion for absolute and global instabilities.

Members

Outputs and publications

Araújo J, Bentz W and Cameron P J, 'Orbits of Primitive k-Homogeneous Groups on (n-k)–Partitions with Applications to Semigroups', Transactions of the American Mathematical Society, 371, pp 105–136 (2019)

Bentz W, Gillibert P and Sequeira L, 'Finite Abelian Algebras are Fully Dualizable, Communications in Algebra, 46, pp 1539–1553 (2018)

Dommers S, Giardinà C, Giberti C and Van der Hofstad R, 'Large deviations for the annealed Ising model on inhomogeneous random graphs: spins and degrees', Journal of Statistical Physics, 173(3–4), pp 1045–1081 (2018)

Dommers S, 'Metastability of the Ising model on random regular graphs at zero temperature', Probability Theory and Related Fields, 167(1), pp 305–324 (2017)

Detinko A, Flannery D, Hulpke A, 'Zariski density and computing in arithmetic groups', Mathematics of Computation, 87, pp 967-986 (2018)

Detinko A, Flannery D, 'Linear groups and computation', Expositiones Mathematicae (2019)

Chongchitnan S and Hunt M, 'On the abundance of extreme voids II: A survey of void mass functions', Journal of Cosmology and Astroparticle Physics, 03, 049 (2017)

Inspired?

Our research impacts the world. Come and join us.

Be part of a vibrant research community at the University of Hull.

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