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 Prize Lecturer 2009

EPSRC Senior Fellowship 2007-12

Invited Speaker, International Congress of Mathematicians, Madrid 2006

Clay Senior Scholar in Residence, PCMI, 2012

Royal Society Wolfson Research Merit Award 2012

Britton Lectures 2012

Erwin Schrodinger Lecture 2011

Marker Lectures 2009

London Mathematical Society Whitehead Prize 1999

Forder Lecturer 2005

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. 3, 1447–1467. MR2600879

Bridson, Martin R.; Groves, Daniel. The quadratic isoperimetric inequality for mapping tori of free group automorphisms. Mem. Amer. Math. Soc. 203 (2010), no. 955MR2590896

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)

 

Recent Publications (from MathSciNet): 

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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.  Algebra and Number Theory 6(2012), 781-795.
  • (with S. Danz) Specht modules in the Auslander-Reiten quiver. Submitted.
  • (with K. J. Lim and K. M. Tan) The complexity of the Lie module. To appear in Proc. Edinburgh Math. Soc.
  • (with M. Johnson)  Lie powers of the natural module for GL(2,K).  To appear in Quart. J. Math.
  • On Hochschild cohomology for selfinjective special biserial algebras. Submitted.
  • (with K.C. Hannabuss and A.E. Parker)  Dimensions of higher extensions for SL_2. Submitted
  • Recent Publications (from MathSciNet): 

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    Dr Anne E Henke
    Research Interests: 
    Representation Theory
    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 Nikolay Nikolov
    Research Interests: 

    Asymptotic behaviour of invariants of finite or infinite groups, for example expansion, word width, growth of rank or Betti numbers.

    Prizes, Awards and Scholarships: 

    Whitehead prize of the London Mathematical Society, 2007.

    Recent Publications (from MathSciNet): 

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    Teaching: 

    Section C course 'Infinite Groups' in HT 2013.

    Emeritus

    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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    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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    Professor Hilary Priestley
    Recent Publications (from MathSciNet): 

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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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    Affiliate Faculty

    Professor Dan Segal
    Research Interests: 

    Algebra, number theory

    Prizes, Awards and Scholarships: 

    Adams Prize 1981, Whitehead Prize 1985, Ferran Sunyer i Balaguer Prize 2002, Polya Prize 2012

    Major/Recent Publications: 

    The density of representation degrees (with M. Liebeck and A. Shalev), J. Eur. Math. Soc. 14 (2012), 1519–1537

    Generators and commutators in finite groups; abstract quotients of compact groups (with N. Nikolov), Invent. Math. 190 (2012), 513-602; http://www.springerlink.com/openurl.asp?genre=article&id=doi:10.1007/s00...

    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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    Research Fellows

    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: 

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

    Relative ends, L^2 Invariants and Property (T), with G.A. Niblo, J. Algebra 2011. 

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

    A topological splitting theorem for Poincare duality groups and high dimensional manifolds, with G.A. Niblo, accepted Geometry and Topology 2013.

    One relator quotients of Graph products, with Yago Antolin, 2012.

    Rank gradient for Artin Groups and their relatives, with N. Nikolov, 2012.

     

     

     

     

    Teaching: 

    I organise the Advanced Class in Algebra. This term, the theme is Unsolved problems involving Free Groups. Past topics include Profinite Bass Serre theory, L^2 Betti numbers and Stable commutator length. 

    Visitors

    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 165 (2012) 1-11.

    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)

    Non-G-completely reducible subgroups of the exceptional groups, submitted.

    (with B. Parshall and L. Scott) Shifted generic cohomology, submitted.

    (with C. Bendel, D. Nakano, B. Parshall, C. Pillen and L. Scott) Bounding extensions for finite groups and Frobenius kernels, submitted.

    Recent Publications (from MathSciNet): 

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    Teaching: 

    Representation Theory 2a, class.

    Group Theory 2b, class.

    Research Students

     Tobias Barthel
    Research Interests: 

    Homotopical algebraic geometry and its applications to the chromatic picture in stable homotopy theory; Arithmetic geometry

     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.

     Elisabeth Fink
    Research Interests: 

    Group Theory: groups acting on rooted trees, profinite groups.

     Josephine French
    Research Interests: 

    Geometric Representation Theory 

    Prizes, Awards and Scholarships: 

    EPSRC Scholarship
    SET Student of the Year 2012

    Teaching: 

    TA for B9a Galois Theory and C2.1a Lie Algebras MT12.

     Alejandra Garrido Angulo
    Teaching: 

    Teaching Assisstant for B2b Groups and Characters HT 2012 and HT 2013

    Teaching Assistant for B9a Galois Theory MT 2012

     Emanuele Ghedin
    Research Interests: 

    Geometric Representation Theory

    Teaching: 

    Teaching Assistant for B2a Introduction to Representation Theory, MT 2011

    Teaching Assistant for B2b Group Theory and an Introduction to Character Theory, HT 2013

     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

    Representation Theory

    Aspects of Homotopy Theory

    Prizes, Awards and Scholarships: 

    • Engineering and Physical Sciences Research Council Scholarship (University of Oxford, 2009-2013)

    • Joint Honours Scholarship (University of Birmingham, 2008-2009)

     Francisco Simkievich
    Research Interests: 

    Homotopy type theory, homological algebra, representation theory.

    Other Staff