Research in Pure Mathematics in the School of Mathematical Sciences at Queen Mary, University of London is carried out accross a broad range including Algebra, Combinatorics, Geometry, Number Theory, Topology, Analysis, Probability, and Logic. This page describes the research in more detail and gives a few highlights.

The weekly seminars (held on Mondays at 4:30pm in the Mathematics Seminar Room) cover topics in all of these areas. Information can be found under "Seminars and Events" in the left-hand panel. Information about other mathematics seminars can be found under "Seminars". Lists of our recent publications can be found under "Publications", and individuals' research interests and profiles under "People".

### Algebra

The Algebra group in the School is one of the strongest in Great Britain. Our traditional strength is in group theory, especially finite simple groups, linear groups and algebraic groups, geometric, topological and combinatorial aspects of group theory, finite *p*-groups, and computational group theory. The group also has strengths in representation theory, quantum algebras, and algebraic geometry, including non-commutative geometry, model theory, and higher algebra.

The department participates in the University of London Algebra Colloquium, which meets every week during the academic year. Postgraduate courses in algebra are always offered: these vary in level from beginning graduate courses to advanced research-oriented courses.

We host the website of the Atlas of Finite Group Representations, and we also keep records of the London Algebra Colloquium which are essentially complete since the start of the colloquium in 1950.

Members of staff pursuing research in Algebra include Bray, Cameron, Chiswell, Fayers, Leedham-Green, Macintyre, Majid, Müller, Noohi, Soicher, Tomašić, Wehrfritz, and Wilson. Their Web pages give further details of their research.

### Combinatorics

A very active group works both on topics within combinatorics (especially finite geometry, design theory, graph and matroid theory, statistical mechanics, extremal combinatorics, algorithms and asymptotics) and on links with algebra (permutation groups and subgroup counting), logic (model theory), information and coding theory, and design of experiments.

A weekly study group is held during term time.

There are close links with researchers in Algebra, Probability, and Statistics.

Members of staff pursuing research in Combinatorics include Bailey, Cameron, Ellis, Hilton, Hodges, Jackson, Jerrum, Johnson, Macintyre, Müller, Preece, Soicher, Stark, and Walters.

We host the site DesignTheory.org and the British Combinatorial Committee webpage, and keep a list of Web-based resources for design theory and related areas of mathematics and statistics (including coding theory, combinatorics, finite geometry, and graph theory).

### Geometry and Topology

The London University Geometry and Topology Seminar meets several times each term and invites speakers from all areas of geometry and topology. In addition, there is a weekly reading group, usually on a topic which is of interest to other mathematicians as well as to specialists. The Geometry and Analysis Seminar includes geometry on manifolds and the Quantum Algebra Seminar includes algebraic geometry and noncommutative geometry. There are also close links with researchers in dynamical systems.

Members of staff pursuing research involving Geometry and Topology include Bullett, Chu, Majid, Noohi, and Tomašić.

### Number Theory

Areas being pursued within Number Theory include algebraic number theory and Diophantine approximation. Number Theory also features in connection with research in other areas in the School including in group theory and dynamical systems.

Members of staff pursuing research involving Number Theory include Chiswell, Tomašić and Vivaldi.

### Analysis

Research in Analysis is mostly in the areas of harmonic analysis and integral equations on groups; Jordan algebras and analysis on infinite-dimensional manifolds; operator algebras and functional analysis; and non-commutative geometry. There are links with group representations, non-associative algebras, differential geometry, probability theory, and mathematical physics. There is a weekly seminar on Geometry and Analysis which typically includes functional analysis.

Members of staff pursuing research involving Analysis include Bandtlow, Chu, Ellis, Jenkinson, Majid, and Müller.

### Probability

Research in Probability within Pure Mathematics focuses on randomised algorithms, Markov chains (especially mixing time of combinatorially or geometrically defined Markov chains), probabilistic existence proofs of combinatorial structures, and use of random combinatorial structures as models for physical or computational systems. There is also a group in applied probability elsewhere in the school.

Members of staff pursuing research involving Probability include Gnedin, Jerrum, Stark and Walters.

### Logic

Research in Logic is mainly in Model Theory, with other activity in Linguistics and History. Within Model Theory, there is great interest in connections with algebraic geometry, model theory of the Frobenius map, geometry of fields with measure, (nonstandard) cohomology theories and motivic integration.

Members of staff who do research in Logic include Hodges, Macintyre, and Tomašić.