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, number theory, algebraic combinatorics, algebraic geometry, logic, 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
Steve Lester Diego Millan Berdasco
Wajid Mannan Ben Smith
Thomas Müller Yegor Stepanov
Behrang Noohi Louise Sutton
Tomasz Popiel  
Abhishek Saha  
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

We normally hold our Algebra Seminar during term 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.

News

  • We are pleased to announce that the newly appointed lecturers in number theory, Steve Lester and Abhishek Saha have joined the Algebra Group.

    Steve is interested in analytic number theory, especially L-functions, multiplicative functions, classical automorphic forms, and mathematical physics, especially quantum chaos.

    Abhishek is interested in classical and higher rank modular forms, automorphic representations and the L-functions attached to them.

  • 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.

Main areas of research

  • group theory: structure of finite groups, growth functions on finitely-generated groups and their combinatorics and number-theoretic properties, computational group theory and group-theoretical databases;
  • representation theory: representations of finite groups, representations of symmetric groups and Hecke algebras;
  • number theory: K-theory of number fields, analytic number theory, L-functions, multiplicative functions, classical automorphic forms, classical and higher rank modular forms, automorphic representations;
  • algebraic combinatorics: algebraic graph theory, matroids and tropical geometry, finite geometry, computation;
  • homological algebra: higher categorical/derived structures in algebra and geometry;
  • model theory and its applications in algebraic geometry and number theory;
  • mathematical physics: exceptional groups and Lie algebras and applications to physics, quantum chaos.

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.
  • H.M. Bui, S.J. Lester and M.B. Milinovich, On Balazard, Saias, and Yor's equivalence to the Riemann Hypothesis, J. Math. Anal. Appl. 409 (2014), 244-253.
  • 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.
  • A. Corbett and A. Saha, On the order of vanishing of newforms at cusps, Math. Res. Let., to appear.
  • 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
  • Y. Lamzouri, S. Lester and M. Radziwiłł, Discrepancy bounds for the distribution of the Riemann zeta-function with applications, J. Anal. Math., to appear.
  • Y. Lamzouri, S. Lester and M. Radziwiłł, An effective universality theorem for the Riemann zeta-function, Comment. Math. Helv., to appear.
  • Stephen J. Lester, On the distribution of the zeros of the derivative of the Riemann zeta-function, Math. Proc. Cambridge Philos. Soc. 157 (2014), 425-442.
  • Stephen J. Lester, The distribution of the logarithmic derivative of the Riemann zeta-function, Quart. J. Math. 65 (2014), 1319-1344.
  • Stephen J. Lester, a-Points of the Riemann zeta-function on the critical line, Int. Math. Res. Not., 9 (2015), 2406-2436.
  • Stephen J. Lester, On the variance of sums of divisor functions in short intervals, Proc. Amer. Math. Soc. 144 (2016), 5015-5027.
  • S. Lester, K. Matomäki and M.Radziwiłł, Small scale distribution of zeros and mass of modular forms, arXiv:1501.01292 (2015), 31 pages, submitted for publication.
  • S. Lester and M. Radziwiłł, Quantum unique ergodicity for half-integral weight forms, arXiv:1606.04119 (2016), 61 pages.
  • S. Lester and Z. Rudnick, Small scale equidistribution of eigenfunctions on the torus, Comm. Math. Phys. 350 (2017), 279-300.
  • S. Lester and N. Yesha, On the distribution of the divisor function and Hecke eigenvalues, Israel J. Math. 212 (2016), 443-472.
  • 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.
  • P. Nelson, A. Pitale and A. Saha, Bounds for Rankin-Selberg integrals and quantum unique ergodicity for powerful levels, J. Amer. Math. Soc. 27 (2014), 147-191.
  • 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.
  • A. Pitale, A. Saha and R. Schmidt, Transfer of Siegel cusp forms of degree 2, Mem. Amer. Math. Soc. 232 (2014).
  • A. Pitale, A. Saha and R. Schmidt, Representations of SL2(R) and nearly holomorphic modular forms, RIMS Kokyyroku 1973 (2016), 141-153.
  • A. Pitale, A. Saha and R. Schmidt, Local and global Maass relations, Math. Z. (2017), DOI:10.1007/s00209-016-1840-5.
  • Abhishek Saha, A relation between multiplicity one and Böcherer's conjecture, Ramanujan J. 33 (2014), 263-268.
  • Abhishek Saha, On ratios of Petersson norms for Yoshida lifts, Forum Mathematicum 27 (2015), 2361-2412.
  • Abhishek Saha, Large values of newforms on GL(2) with highly ramified central character, Int. Math. Res. Not. 13 (2016), 4103-4131.
  • Abhishek Saha, Hybrid sup-norm bounds for Maass newforms of powerful level, Algebra and Number Theory 11 (2017), 1009-1045.
  • Abhishek Saha, On sup-norms of cusp forms of powerful level, J. Eur. Math. Soc., to appear.
  • 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.