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Algebra Members

Permanent Faculty

Professor Martin Bridson
Research Interests: 

Geometric Group Theory

Geometry of non-positively curved spaces

Low-dimensional topology

Prizes, Awards and Scholarships: 

Abel Lecturer 2009

EPSRC Senior Fellowship 2007-12

Invited Speaker, International Congress of Mathematicians, Madrid 2006

Royal Society Wolfson Research Merit Award 2006

London Mathematical Society Whitehead Prize 1999

EPSRC Advanced Fellowship 1997-2002

Major/Recent Publications: 

Bridson, Martin R.; Haefliger, André Metric spaces of non-positive curvature. Grundlehren der Mathematischen Wissenschaften  319. Springer-Verlag, Berlin, 1999. xxii+643 pp. ISBN: 3-540-64324- MR1744486 (2000k:53038)

Bridson, Martin R. Non-positive curvature and complexity for finitely presented groups. International Congress of Mathematicians. Vol. II, 961--987, Eur. Math. Soc., Zürich, 2006. MR2275631 (2008a:20071)

Bridson, Martin R.; Grunewald, Fritz J. Grothendieck's problems concerning profinite completions and representations of groups. Ann. of Math. (2) 160 (2004), no. 1, 359--37. MR2119723 (2005k:20069)

Bridson, Martin R.; Howie, James; Miller, Charles F., III; Short, Hamish; Subgroups of direct products of limits groups,  Ann. of Math. (2), 170 (2009), no. 2, in press 

Alonso, Juan M.; Bridson, Martin R. Semihyperbolic groups. Proc. London Math. Soc. (3) 70 (1995), no. 1, 56--114. MR1300841 (95j:20033) 

Bridson, Martin R. Fractional isoperimetric inequalities and subgroup distortion. J. Amer. Math. Soc. 12 (1999), no. 4, 1103--1118.  MR1678924 (2001a:20062)

Bridson, Martin R. Geodesics and curvature in metric simplicial complexes. Group theory from a geometrical viewpoint (Trieste, 1990), 373--463, World Sci. Publ., River Edge, NJ, 1991.  MR1170372 (94c:57040)

Brady, N.; Bridson, M. R. There is only one gap in the isoperimetric spectrum. Geom. Funct. Anal. 10 (2000), no. 5, 1053--1070. MR1800063 (2001j:20046)

Bridson, M. R.; Gersten, S. M. The optimal isoperimetric inequality for torus bundles over the circle. Quart. J. Math. Oxford Ser. (2) 47 (1996), no. 185, 1--23. MR1380947 (97c:20047)


 

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Professor Michael Collins
Research Interests: 
Finite Groups, Representation Theory
Dr Karin Erdmann
Research Interests: 

Representation theory.  Homological algebra: Hochschild cohomology, support varieties and rank varieties for self-injective algebras. Auslander-Reiten theory. Modular Lie powers.

Major/Recent Publications: 

 

  • (with S. Danz) The vertices of a class of Specht modules and simple modules for symmetric groups in characteristic 2. To appear in Algebra Colloquium.
  • (with R. Bryant)  Block components of the Lie module for the symmetric group. To appear in Algebra and Number Theory.
  • (with P. Bergh)  The representation dimension of Hecke algebras and symmetric groups. To appear in Adv. Math.
  • (with J. Bialkowsi and A. Skowronski)  Deformed preprojective algebras of generalized Dynkin type L_n: classification and symmetricity. To appear in J. Algebra.

  • (with S. Danz) Specht modules in the Auslander-Reiten quiver. Submitted.

  • (with M. Johnson)  Lie powers of the natural module for GL(2,K). Submitted.
  • (with L. G. Kovacs) Metabelian Lie powers of the natural module for a general linear group. Submitted. 


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    Dr Anne E Henke
    Research Interests: 
    Representation Theory
    Yakov Kremnitzer
    		 
    Dr Kevin Mcgerty
    Research Interests: 

    Geometric representation theory: quantum groups, algebraic groups, topology of singular varieties, D-modules.

    Recent Publications (from MathSciNet): 

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    Teaching: 

    Tutor in Pure Mathematics, Christ Church
    Dr Peter M. Neumann
    Research Interests: 

    Algebra

    History of Algebra

     

    Prizes, Awards and Scholarships: 

    Senior Mathematical and Johnson Prizes, Oxford, 1965

    Lester R. Ford Award, Mathematical Association of America, 1987

    Senior Whitehead Prize, London Mathematical Society, 2003

    Appointed Officer in the Order of the British Empire for services to education, New Year 2008

    Award for "Lifetime Achievement in Teaching", Oxford University, 2008

     
    Recent Publications (from MathSciNet): 

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    Dr Hilary Priestley
    		 
    Professor Raphael Alexis Rouquier
    Research Interests: 

    Homological algebra

    Recent Publications (from MathSciNet): 

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    Professor Dan Segal
    Research Interests: 

    Algebra, number theory

    Prizes, Awards and Scholarships: 

    Adams Prize 1981, Whitehead Prize 1985, Ferran Sunyer i Balaguer Prize 2002

    Major/Recent Publications: 

    Generators and commutators in finite groups; abstract quotients of compact groups (with N. Nikolov),  http://arxiv.org/abs/1102.3037

    Powers in finite groups (with N. Nikolov), Groups Geom. Dyn. 5 (2011), no. 2, 501–507

    On verbal subgroups of adelic groups, J. Algebra 326 (2011), 227-237: doi:10.1016/j.jalgebra.2009.03.024   

    Words: notes on verbal width in groups
    LMS Lect. Notes 361, CUP, 2009. ISBN 978-0-521-74766-0

    Polycyclic groups
    Cambridge Tracts in Math. 82, CUP, Cambridge, 1983; paperback 2005. ISBN 978-0-521-02394-8

    Subgroup growth   (with A. Lubotzky)
    Progress in Math. 212, Birkhauser, Basel, 2003. ISBN 3-7643-6989-2

    Analytic pro-p groups, 2nd ed.  (with J.D. Dixon, M.P.F. du Sautoy and A. Mann)
    Cambridge Studies in Advanced Mathematics 61, CUP, Cambridge 1999; paperback 2003. ISBN 978-0-521-54218-0

    New horizons in pro-p groups  (editor, with M. P. F. du Sautoy and A. Shalev)
    Progress in Math. 184, Birkhauser, Boston 2000. ISBN 0-8176-4171-8, 3-7643-4171-8



     

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    Dr Brian Stewart
    		 

    Research Staff

    Dr David A. Craven
    Research Interests: 

    My research interests centre around the representation theory of finite groups. I study:

    • the representation theory of the symmetric group, and in particular, its combinatorics;
    • the modular representations of finite, and particularly simple groups;
    • infinite groups arising from automata;
    • asymptotics of representation theory, via the concept of representation growth; and
    • fusion systems, particularly representation-theoretic and group-theoretic aspects.
    Major/Recent Publications: 
    1. Symmetric Group Character Degrees and Hook Numbers, Proc. Lond. Math. Soc. 96 (2008), 26-50.
    2. Developing Random Network Theory for Carbon Nanotube Modified Electrode Voltammetry (jt with Andrew Holloway, Lei Xiao, Javier Del Campo, and Gregory Wildgoose), J. Phys. Chem. C 112 (2008) 13729-13738.
    3. Simple Modules for Groups with Abelian Sylow 2-Subgroups are Algebraic, J. Algebra 321 (2009), 1473-1479.
    4. Control of Fusion and Solubility in Fusion Systems, J. Algebra 323 (2010) 2429-2448.
    5. Algebraic Modules and the Auslander-Reiten Quiver, J. Pure Appl. Algebra, to appear.
    6. The Structure of Blocks with Klein Four Defect Group (jt with Charles Eaton, Radha Kessar, and Markus Linckelmann), Math. Z., to appear.
    7. Bounds for Representation Growth and Finite Simple Groups, J. Group Theory, to appear.
    8. Fusion Systems on Small p-Groups (jt with Adam Glesser), submitted.
    9. Normal Subsystems of Fusion Systems, submitted.
    10. On the Unit Conjecture for Group Rings (jt with Peter Pappas), preprint, 2010.
    11. Perverse Equivalences and Broue's Conjecture (jt with Raphael Rouquier), preprint, 2010.
    Recent Publications (from MathSciNet): 

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    Teaching: 

    C2.2a, Finite Group Theory
    Olivier Dudas
    		 
    Dr Christopher Hollings
    Research Interests: 

    Semigroup theory: the partial actions of semigroups on sets; the properties of left restriction semigroups, a class of semigroups arising from the study of partial transformations.

    History of mathematics: the development of semigroup theory and other areas of abstract algebra during the twentieth century in general and the Cold War in particular.

    Recent Publications (from MathSciNet): 

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    Teaching: 

    Class tutor for B9a Galois Theory, Michaelmas Term 2010

    Class tutor for B2b Group Theory, Hilary Term 2010

    Teaching assistant for O1 History of Mathematics, Michaelmas Term 2011
    Dr Aditi Kar
    Research Interests: 

    Geometric Group Theory

    High-dimensional topology

    Combinatorial group theory

    Prizes, Awards and Scholarships: 

    EPSRC post doctoral fellowship 2011-2014

    Research fellowship in Sciences (non-stipendiary), Wolfson College, Oxford.

    Major/Recent Publications: 

    Discrete Groups and CAT(0) Asymptotic Cones, Doctoral dissertation from The Ohio State University, December 2008; Adviser: Indira Chatterji.

    Asymptotically CAT(0) Groups, Publicacions Matematiques 55(1) 2011. 

    On Property (FA) for wreath products, with Y Cornulier, J. of Group Theory 14(1) 2011. 

    Relative ends, L2 Invariants and Property (T), with G.A. Niblo, J. Algebra 2011. 

    Some non-amenable groups, with G. A.. Niblo, Publicacions Matematiques. 

    Topological superrigidity, with G.A. Niblo, Submitted.

     
    Dr Justin McInroy
    		 
    Dr David I. Stewart
    Research Interests: 

    Algebraic groups: subgroup structure, modular representation theory, non-abelian cohomology.

    I am working towards a classification of all Zariski closed, connected, reductive subgroups of the exceptional algebraic groups, i.e. those with root systems G_2, F_4, E_6, E_7 or E_8. The question become interesting where the groups are defined over fields of positive characteristic, due partly to the existence of (following Serre) 'non-G-cr' subgroups. Finding these involves calculations of non-abelian cohomology of groups with coefficients in unipotent groups (i.e. p-groups).

    I am also investigating the extent to which one can bound the dimensions of usual (Hochschild) cohomology groups of algebraic groups with coefficients in simple modules, related to a conjecture of Guralnick: there is a universal bound on the dimension of H^1(G,L) where G is any finite simple group and L is any absolutely irreducible representation for G. (The highest known is currently 3.)

    Major/Recent Publications: 

    G-complete reducibility and the exceptional algebraic groups (PhD Thesis, Imperial College; supervisor: Martin W. Liebeck)

    Unbounding Ext, J. Algebra (revised and resubmitted)

    The second cohomology of simple SL2-modules, Proc. Amer. Math. Soc.,  138,  427--434  (2010)

    The second cohomology of simple SL3-modules, Comm. Alg. (to appear)

    Restriction maps on 1-cohomology of (algebraic) groups, (submitted)

    The reductive subgroups of G2, J. Group Theory, 13, 117--130  (2010)

    The reductive subgroups of F4, Mem. Amer. Math. Soc., (to appear)

    Recent Publications (from MathSciNet): 

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    Teaching: 

    Representation Theory 2a, class.

    Group Theory 2b, class.

    Further Details: 

    New College page

    Personal webpage

    Oxmunch restaurant reviews

    Visitors

    Kabalan Gaspard
    Research Interests: 

    Algebraic Number Theory

    Cyclotomic Fields

    Quadratic Number Fields

    Representation Theory & links to Particle Physics

    Quantum Theory

    Major/Recent Publications: 

    On the Applications of Cyclotomic Fields in Introductory Number Theory, http://arxiv.org/abs/1110.4445. [Under review by the Berkeley Scientific Journal]

    A Simpler Solution to Feynman's "Riddle on Handedness", [short] [to be published soon]
    Professor J.A. Green FRS
    Research Interests: 
    Representation theory
    Prizes, Awards and Scholarships: 

    Senior Berwick Prize, London Mathematical Society, 1984.
    Fellow of the Royal Society, 1987.
    de Morgan Medal, London Mathematical Society, 2001.

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    Professor J S Wilson
    Research Interests: 
    profinite groups, finite and infinite soluble groups, model theory of groups, branch groups, word growth of groups, finitely presented groups, generation problems for finite simple groups.
    Major/Recent Publications: 
    • Profinite groups. London Math. Soc. Monographs, New Series 19 (Clarendon Press, Oxford, 1998).
    • (with C.$ \, $J.$ \, $B. Brookes and J.$ \, $E.Roseblade) Exterior powers of modules for polycyclic groups. J. London Math. Soc. (2) 56 (1997), 231–244.
    • Finitely presented soluble groups. In Geometric and Homological Topics in Group Theory, (Cambridge University Press, 1998), 296–316.
    • (with A. Lucchini and M.$ \, $C. Tamburini) Hurwitz groups of large rank. J. London Math. Soc. (2) 61 (2000), 81–92.
    • On abstract and profinite just infinite groups. Chapter 5 in New horizons in pro-$ p $ groups (Birk­haüser, 2000).
    • (with R.$ \, $M. Guralnick) On the probability of generating a finite soluble group. Proc. London Math. Soc. (3) 81 (2000), 405–427.
    • (with R.$ \, $I. Grigorchuk) A structural property concerning abstract commensurability of subgroups. J. London Math. Soc. (2) 68 (2003), 671–682.
    • (with R.$ \, $I. Grigorchuk) The uniqueness of the actions of certain branch groups on rooted trees. Geom. Dedicata 100 (2003), 103–116.
    • On exponential growth and uniformly exponential growth for groups. Invent. Math. 155 (2004), 287–303.
    • On growth of groups with few relators. Bull. London Math. Soc. 36 (2004), 1–2.
    • Structure theory for branch groups. In Geometric and Homological Topics in Group Theory (Cambridge University Press), to appear.
    • First-order characterization of the radical of a finite group. J. Symbolic Logic, to appear.
    • Linear groups with many $ 2 $-generator soluble subgroups. Bull. London Math. Soc., to appear.
    • Characterization of the soluble radical by a sequence of words. J. Algebra, to appear.
    Popular article The glass bead game. Math. Intelligencer 19 (1997), no. 2, 23–25.
    Recent Publications (from MathSciNet): 

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    Research Students

    Tobias Barthel
    Research Interests: 

    Homotopical algebraic geometry and its applications to the chromatic picture in stable homotopy theory; Arithmetic geometry
    Georgia Christodoulou
    		 
    Nicholas Cooney
    Research Interests: 

    Geometric Representation Theory, Cherednik algebras, Higher Representation Theory. 

    Teaching: 

    Teaching Assistant: Representations of Symmetric Groups, Hilary Term, 2009.

    Teaching Assistant: Introduction to Representation Theory, Michaelmas Term, 2010.
    Leo Dreyfus-schmidt
    		 
    Elisabeth Fink
    Research Interests: 

    Group Theory: groups acting on rooted trees, profinite groups.
    Christopher C. Gill
    		 
    Ainhoa Iniguez
    Research Interests: 

    Group theory, profinite groups, words
    Florian Klein
    Research Interests: 

    I am working under the supervision of Raphael Rouquier on Soergel bimodules and their 2-representation theory.
    Jason Semeraro
    Research Interests: 

    Finite Group Theory

     
    Francisco Simkievich
    Research Interests: 

    Homotopy type theory, homological algebra, representation theory.

    Other Staff

    Dr Susanne Danz
    Major/Recent Publications: 

    • (with J. Müller) Source algebras of blocks, sources of simple modules, and a conjecture of Feit, submitted

    • (with R. Boltje) A ghost ring for the left-free double Burnside ring and an application to fusion systems, submitted

    • (with K. Erdmann) Specht modules in the Auslander--Reiten quiver, submitted

    • (with H. Ellers and J. Murray) The centralizer of a subgroup in a group algebra, to appear in the Proceedings of the Skye Conference on Algebraic Topology, Group Theory and Representation Theory

    • (with K. Erdmann) The vertices of a class of Specht modules and simple modules for symmetric groups in characteristic 2, to appear in Algebra Colloq.

    • (with J. Müller) The vertices and sources of the natural simple module for the alternating group in even characteristic, Comm. Algebra 39 (2011), 1--25

    • (with R. Boltje and B. Külshammer) On the depth of subgroups and group algebra extensions, J. Algebra 335 (2011),  258--281

    • The depth of some twisted group algebra extensions, Comm. Algebra 39 (2011), 1--15

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