School of Mathematical Sciences

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Algebra Group

The Algebra Group at QMUL has a long and distinguished history, going back to such names as Kurt Hirsch, Karl Gruenberg and Ian G. Macdonald. Having made its reputation primarily in group theory, it now covers a wide range of areas of finite and infinite group theory, representation theory and related combinatorics, computational methods including algorithm design and database construction, as well as applications in combinatorics, statistics and physics.

FACULTY MEMBERS POSTDOC FELLOWS PhD STUDENTS AFFILIATED FACULTY
John Bray Madhusudan Manjunath Imen Belmokhtar Cecilia Busuioc
Matt Fayers   Amanda Cameron Xin Li  (GA)
Alex Fink   Rhys Evans Shahn Majid  (GA)
Thomas Müller   Diego Millan Berdasco Wajid Mannan
Leonard Soicher (Head of Group)   Ben Smith Hugo Maruri-Aguilar  (PA)
    Yegor Stepanov Tomasz Popiel
    Louise Sutton Rob Wilson (retired)

Please consult the People section for more detailed information on Algebra Group faculty members and their research.

Seminars

We normally hold our Algebra Seminar on Mondays at 4.30pm. We aim for this seminar to be informal and accessible.

In conjunction with Imperial College and City University we run the weekly London Algebra Colloquium, which has been running continuously since 1950. We shall be hosting this Colloquium in Winter 2017, during which time our Algebra Seminar is suspended.

News

  • Madhusudan Manjunath has been awarded a Leibniz Fellowship to visit Oberwolfach from January to March 2017.
  • Algebra group members Matt Fayers and Alex Fink, together with Thomas Prellberg and Mark Walters, are organisers of the 2017 International Conference on Formal Power Series and Algebraic Combinatorics here at QMUL. Alex was on the programme committee for FPSAC 2015.
  • Alex Fink was awarded EPSRC grant EP/M01245X/1 with value £100,118 for the research project Algebra and Geometry of Matroids, taking place 01/07/2015 to 31/12/2016.
  • Leonard Soicher is part of the EPSRC-funded CoDiMa project EP/M022641/1, a Collaborative Computational Project running from 01/03/2015 to 29/02/2020, to support the development and use of the open-source GAP and SAGE mathematics systems.

Main areas of research

  • finite simple groups, their structure and representations;
  • representations of symmetric groups and Hecke algebras;
  • growth functions on finitely-generated groups, their combinatorics and number-theoretic properties;
  • computational group theory, development of algorithms and databases;
  • algebraic combinatorics, matroids and tropical geometry;
  • algebraic graph theory and design theory, and applications to statistics;
  • exceptional groups and Lie algebras, and applications to physics.

Recent publications

  • Spencer Backman and Madhusudan Manjunath, Explicit Deformation of Lattice Ideals via Chip Firing on Directed Graphs, J. Algebraic Combin. 42 (2015), 1097-1110.
  • S.A. Basarab and T.W. Mueller, Group actions, deformations, polygroup extensions, and group presentations, submitted for publication.
  • Andrew Berget and Alex Fink, Matrix orbit closures, arXiv:1306.1810 (2015), 29 pages.
  • Andrew Berget and Alex Fink, Equivariant Chow classes of matrix orbit closures, Transformation Groups, available online.
  • John N. Bray, Richard A. Parker and Robert A. Wilson, Finding 47:23 in the Baby Monster, LMS J. Comput. Math. 19 (2016), 229-234.
  • John N. Bray and Henrik Bäärnhielm, A new method for recognising Suzuki groups, J. Algebra, to appear.
  • Amanda Cameron and Alex Fink, A lattice point counting generalisation of the Tutte polynomial, arXiv:1604.00962 (2016), 11 pages, extended abstract, full version forthcoming.
  • Dustin Cartwright, Andrew Dudzik, Madhusudan Manjunath and Yuan Yao, Embeddings and Immersions of Tropical curves, Collectanea Mathematica 67 (2016), 1-19.
  • Tevian Dray, Corinne A. Manogue and Robert A. Wilson, A symplectic representation of E7, Commentat. Math. Univ. Carol. 55 (2014), 387-399.
  • Matthew Fayers, A generalisation of core partitions, J. Comb. Theory, Ser. A 127 (2014), 58-84.
  • Matthew Fayers, The irreducible representations of the alternating group which remain irreducible in characteristic p, Trans. Am. Math. Soc. 368 (2016), 5807–5855.
  • Matthew Fayers and Liron Speyer, Generalised column removal for graded homomorphisms between Specht modules, J. Algebraic Combin. 44 (2016), 393-432.
  • Matthew Fayers, (s,t)-cores: a weighted version of Armstrong's conjecture, arXiv:1504.01681 (2015), 28 pages, submitted for publication.
  • Matthew Fayers, Irreducible projective representations of the symmetric group which remain irreducible in characteristic 2, submitted for publication.
  • Alex Fink, Aviezri S. Fraenkel and Carlos Santos, LIM is not slim, Int. J. Game Theory 43 (2014), 269-281.
  • Alex Fink and Felipe Rincón, Stiefel tropical linear spaces, J. Comb. Theory, Ser. A 135 (2015), 291–331.
  • Alex Fink and Luca Moci, Matroids over a ring, J. Eur. Math. Soc. 18 (2016), 681–731.
  • Alex Fink, Jenna Rajchgot and Seth Sullivant, Matrix Schubert varieties and Gaussian conditional independence models, arXiv:1510.04124 (2015), 31 pages, to appear in J. Algebraic Combin.
  • Alex Fink and Richard Guy, The outercoarseness of the n-cube, submitted for publication.
  • Gary R.W. Greaves and Leonard H. Soicher, On the clique number of a strongly regular graph, arXiv:1604.08299 (2016), 13 pages, submitted for publication.
  • C. Krattenthaler and T.W. Müller, Generalised Apéry numbers modulo 9, J. Number Theory 147 (2015), 708-720.
  • C. Krattenthaler and T.W. Müller, Truncated versions of Dwork’s lemma for exponentials of power series and p-divisibility of arithmetic functions, Adv. Math. 283 (2015), 489-529.
  • C. Krattenthaler and T.W. Müller, Periodicity of free subgroup numbers modulo prime powers, J. Algebra 452 (2016), 372-389.
  • Václav Linek, Leonard H. Soicher and Brett Stevens, Cube designs, J. Comb. Des. 24 (2016), 223-233.
  • Ye Luo and Madhusudan Manjunath, Smoothing of Limit Linear Series of Rank One on Saturated Metrized Complexes of Algebraic Curves, arXiv:1411.2325 (2014), 41 pages.
  • Madhusudan Manjunath, Syzygies over the Polytope Semiring, arXiv:1606.07395 (2016), 21 pages.
  • Madhusudan Manjunath, Tropical Graph Curves, arXiv:1603.08870 (2016), 23 pages, submitted for publication.
  • Madhusudan Manjunath, Frank-Olaf Schreyer and John Wilmes, Minimal Free Resolutions of the G-Parking Function Ideal and the Toppling Ideal, Trans. Am. Math. Soc. 367 (2015), 2853-2874.
  • Patric R.J. Östergård and Leonard H. Soicher, There is No McLaughlin Geometry, arXiv:1607.03372 (2016), 19 pages, submitted for publication.
  • Leonard H. Soicher, On cliques in edge-regular graphs, J. Algebra 421 (2015), 260-267.
  • Leonard H. Soicher, The uniqueness of a distance-regular graph with intersection array {32,27,8,1;1,4,27,32} and related results, Des. Codes Cryptogr., available online (open access).
  • Robert A. Wilson, Classification of subgroups isomorphic to PSL2 (27) in the Monster, LMS J. Comput. Math. 17 (2014), 33-46.
  • Robert A. Wilson, A quaternionic construction of E7, Proc. Am. Math. Soc. 142 (2014), 867-880.
  • Robert A. Wilson, Every PSL2(13) in the Monster contains 13A-elements, LMS J. Comput. Math. 18 (2015), 667-674.
  • Robert A. Wilson, Is Sz(8) a subgroup of the Monster?, Bull. Lond. Math. Soc. 48 (2016), 355-364.
  • Robert A. Wilson, Introduction to the finite simple groups, in: Algebra, Logic and Combinatorics, vol. 3 of LTCC Advanced Mathematics Series, World Scientific, 2016, pp. 41-68.