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 range of areas in group theory, representation theory, algebraic combinatorics, algebraic geometry, logic, number theory, homological/categorical algebra, and computational methods.

FACULTY MEMBERS PhD STUDENTS
John Bray Imen Belmokhtar
Cecilia Busuioc Amanda Cameron
Matt Fayers Rhys Evans
Alex Fink Rachael King
Wajid Mannan Diego Millan Berdasco
Thomas Müller Ben Smith
Behrang Noohi Yegor Stepanov
Tomasz Popiel Louise Sutton
Leonard Soicher (Head of Group)  
Ivan Tomašić  
Rob Wilson (Emeritus)  

Faculty members in other groups whose research includes high levels of Algebra include Xin Li (GA), Shahn Majid (GA), and Hugo Maruri-Aguilar (PA).

Seminars

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

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

News

  • We are pleased to announce that Behrang Noohi and Ivan Tomašić have joined the Algebra Group.

    Behrang is interested in higher categorical/derived structures in algebra and geometry. More specifically: algebraic/differentiable/topological stacks, moduli problems, higher dimensional groups and higher Lie theory, and string topology.

    Ivan studies model theory and its applications in algebraic geometry and number theory. More specifically, his interests include difference algebra and geometry (relating to the arithmetic aspects of the Frobenius automorphism), measurable structures, (nonstandard) cohomology theories, and motivic integration.

  • Madhusudan Manjunath has left QMUL and has taken up 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.
  • 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 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, algebraic graph theory, matroids and tropical geometry, finite geometry;
  • homological algebra, higher categorical/derived structures in algebra and geometry;
  • model theory and its applications in algebraic geometry and number theory, K-theory of number fields;
  • exceptional groups and Lie algebras, and applications to physics.

Recent publications

  • J. Bamberg, S. P. Glasby, T. Popiel and C. E. Praeger, Generalised quadrangles and transitive pseudo-hyperovals, J. Combin. Des. 24, (2016) 151-164.
  • J. Bamberg, S. P. Glasby, T. Popiel, C. E. Praeger and C. Schneider, Point-primitive generalised hexagons and octagons, J. Combin. Theory Ser. A 147 (2017), 186-204.
  • J. Bamberg, T. Popiel and C. E. Praeger, Point-primitive, line-transitive generalised quadrangles of holomorph type, J. Group Theory 20 (2017), 269-287.
  • J. Bamberg, T. Popiel and C. E. Praeger, Simple groups, product actions, and generalised quadrangles, arXiv:1702.07308 (2017), 21 pages, submitted for publication.
  • S.A. Basarab and T.W. Mueller, Group actions, deformations, polygroup extensions, and group presentations, submitted for publication.
  • Kai Behrend and Behrang Noohi, Moduli of non-commutative polarized schemes, arXiv:1507.07054v1, 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 accepted to FPSAC 2016, full version forthcoming.
  • Amanda Cameron and Dillon Mayhew, A splitter theorem for connected clutters, arXiv:1703.00945 (2017), 10 pages.
  • Z. Choo, W.H. Mannan, R. Garcia-Sanchez and V.P. Snaith, Computing Borel's regulator, Forum Math. 27 (2015), 131-177.
  • J. Chuang, A. Lazarev and W.H. Mannan, Cocommutative coalgebras: homotopy theory and Koszul duality, Homology Homotopy Appl. 18 (2016), 303-336.
  • J. Chuang, A. Lazarev and W.H. Mannan, Koszul-Morita Duality, J. Noncommut. Geom. 10 (2016), 1541-1557.
  • B. P. Corr, T. Popiel and C. E. Praeger, Nilpotent-independent sets and estimation in matrix algebras, LMS J. Comput. Math. 18 (2015), 404–418.
  • Thomas Coyne and Behrang Noohi, Singular chains on topological stacks. I, Adv. Math. 303 (2016), 1190-1235.
  • 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, Electronic J. Combin. 23 (2016) #P4.32.
  • Matthew Fayers, Dyck tilings and the homogeneous Garnir relations for graded Specht modules, J. Algebraic Combin. (2016), doi:10.1007/s10801-016-0734-2.
  • 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, J. Algebraic Combin. 44 (2016), 1009–1046.
  • Alex Fink, David E. Speyer and Alexander Woo, A Gröbner basis for the graph of the reciprocal plane, arXiv:1703.05967 (2017), 10 pages.
  • Alex Fink and Richard Guy, The outercoarseness of the n-cube, submitted for publication.
  • Gregory Ginot and Behrang Noohi, Group actions on stacks and applications to equivariant string topology for stacks, arXiv:1206.5603v1, 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.
  • C. Krattenthaler and T.W. Müller, Normalising graphs of groups, Monatsh. Math., 18 pages, available online, doi: 10.1007/s00605-016-0992-z
  • Václav Linek, Leonard H. Soicher and Brett Stevens, Cube designs, J. Comb. Des. 24 (2016), 223-233.
  • Madhusudan Manjunath and Ben Smith, Commutative Algebra of Generalised Frobenius Numbers, arXiv:1703.10884 (2017), 26 pages.
  • W.H. Mannan, Explicit generators for the relation module in the example of Gruenberg-Linnell, Math. Proc. Cambridge Philos. Soc. 161 (2016), 199-202.
  • W.H. Mannan, Duality in the homology of 5-manifolds, Homology Homotopy Appl. 19 (2017), 171-179.
  • L. Morgan and T. Popiel, Generalised polygons admitting a point-primitive almost simple group of Suzuki or Ree type, Electron. J. Combin. 23 (2016), #P1.34.
  • A.C. Niemeyer and T. Popiel, Finding involutions with small support, Bull. Aust. Math. Soc. 94 (2016), 43-47.
  • A.C. Niemeyer, T. Popiel and C. E. Praeger, Abundant p-singular elements in finite classical groups, J. Algebra 408 (2014), 189-204.
  • Behrang Noohi, Fibrations of topological stacks, Adv. Math. 252 (2014), 612–640.
  • Behrang Noohi, Group actions on algebraic stacks via butterflies, arXiv:0704.1010v2, submitted for publication.
  • 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), doi:10.1007/s10623-016-0223-6
  • Ivan Tomašić, Direct twisted Galois stratification, arXiv:1412.8066 (2014), 23 pages.
  • Ivan Tomašić, A twisted theorem of Chebotarev, Proc. Lond. Math. Soc. 108 (2014), 291-326.
  • Ivan Tomašić, Galois stratification and ACFA, Ann. Pure Appl. Logic 166 (2015), 639-663.
  • Ivan Tomašić, Twisted Galois stratification, Nagoya Math. J. 222 (2016), 1-60.
  • Ivan Tomašić and Michael Wibmer, Strongly étale difference algebras and Babbitt's decomposition, arXiv:1512.00495 (2015), 19 pages.
  • 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.