Department of Mathematics

  1. Representation Theory
  2. Mathematical Physics
  3. Mathematical Biology
  4. Events
  5. Research Grants
    1. Representation Theory
    2. Mathematical Physics
    3. Mathematical Biology
    4. Events
    5. Research Grants

Department of Mathematics

City’s Department of Mathematics brings together high-quality undergraduate education and an active research body of academics and PhD students.

The department has a good reputation for student satisfaction and enviable graduate employability. All undergraduate Mathematics courses can be extended to four-year MMath (Hons) degrees and are carried out in conjunction with a range of other departments, producing a truly interdisciplinary approach to the subject. The department’s research, in mathematical biology, mathematical physics, and representation theory, often conducted in collaboration with other institutions, regularly leads to publications in internationally excellent journals and presentations at global conferences.

Research

The Department of Mathematics contains three research groups undertaking fundamental research in pure and applied mathematics:

Representation Theory Research Group

The representation theory group focuses on modern aspects of the representation theory of finite groups, algebraic groups and related algebras, drawing motivation from geometry, statistical mechanics string theory.

Mathematical Physics Research Group

The mathematical physics group focuses on quantum mechanics, quantum field theory, string theory and fluid dynamics. One of the distinguishing features of the mathematical physics group is its strong expertise on integrable systems.

Mathematical Biology Research Group

The Mathematical Biology group applies mathematical methods to increase our understanding of the biological world, and the central focus is on the mathematical modelling of evolution. There are three main areas of research: evolutionary game theory, cultural evolution, and the modelling of evolution on networks.

Seminar series

Alongside a range of conferences and workshops, the department organises a regular seminar series. Seminars in 2014 (past and upcoming) are detailed below.

Date Speaker & Title Room
28/01/2014 Speaker: Chris Bowman (City University London)
Title: The Partition algebra and the Kronecker Problem
Abstract: The Kronecker problem asks for a combinatorial understanding of the tensor products of simple modules for the symmetric group. We shall introduce the partition algebra as a natural setting in which to study this problem and discuss new results concerning its representation theory. This is based on joint work with M. De Visscher, O. King, and R. Orellana.
CG04
04/02/2014 Ginestra Bianconi (QMUL)
Title: Statistical mechanics of multiplex networks
Abstract:A large variety of complex systems, from the brain to the weather networks and complex infrastructures, are formed by several networks that coexist, interact and coevolve forming a "network of networks". Modeling such multilayer structures and characterizing the rich interplay between their structure and their dynamical behavior is crucial in order to understand and predict complex phenomena. In this talk I will present recent works on statistical mechanics of multiplex networks. Multiplex networks are formed by N nodes linked in different layers by different networks. I will present models that generate multiplexes with different types of correlations between the layers, and characterize new percolation phenomena on multiplex networks, showing first order phase transitions, bistability or a complex phase diagram with tricriticals points and higher order critical points.
CG04
11/02/2014 Tobias Galla (University of Manchester) POSTPONED CG04
18/02/2014 Steven Donkin (University of York)
Title:Some Remarks on Gill's Theorems On Young Modules.
Abstract: In a recent paper C. Gill proves some results on the tensor product of Young modules for symmetric groups. Gill uses methods from the modular representation theory of finite groups. We here take a different point of view by first working in the context of representations of general linear groups and then applying the Schur functor (a point of view pioneered by J. A. Green). Our results are valid too (and no more difficult to obtain) in the quantised situation (of representation of quantum general linear groups and Hecke algebras). For the purposes of exposition we shall describe the situation in the classical context and then compare and contrast with the quantised context if time permits.
CG04
25/02/2014 Paul Martin (Leeds University)
Title:"Fun with partition categories"
Abstract: The Brauer category sits inside the partition category - both having elementary set-theoretic constructions. The Temperley-Lieb category sits inside these categories (in at least two different ways), but it's construction has a more geometrical flavour. We will consider geometrically defined extensions of the TL category in the Brauer and partition categories. These constructions are motivated in part by applications in computational physics, but here we will consider them from a representation theory perspective.)
C350
04/03/2014 READING WEEK
11/03/2014 Giuseppe Mussardo (Sissa) CG04
18/03/2014 Anne Davis (Cambridge) CG04
25/03/2014 John McNamara (Bristol) CG04
01/04/2014 Speaker: Peter Hydon (Surrey)
Title: "Difference equations by differential equation methods"
Abstract: Around twenty years ago, I heard an eminent numerical analyst say, "Any problem involving difference equations is an order of magnitude harder than the corresponding problem for differential equations." Research since that time has transformed our understanding of difference equations and their solutions. The basic geometric structures that underpin difference equations are now known. From these, it has been possible to develop systematic techniques for finding solutions, first integrals or conservation laws of a given difference equation. These look a little different to their counterparts for differential equations, mainly because the solutions of difference equations are not continuous. However, they are widely applicable and most of them do not require the equation to have special properties such as linearizability or integrability.
CG04
08/04/2014 TBC CG04
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