Algebra Members
Permanent Faculty
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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. 955. MR2590896 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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Research Interests:
Finite Groups, Representation Theory
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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:
Recent Publications (from MathSciNet):
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Research Interests:
Representation Theory
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Research Interests:
Geometric representation theory: quantum groups, algebraic groups, topology of singular varieties, D-modules. Recent Publications (from MathSciNet):
Teaching:
Tutor in Pure Mathematics, Christ Church |
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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):
Teaching:
Section C course 'Infinite Groups' in HT 2013. |
Emeritus
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Research Interests:
Representation theory
Prizes, Awards and Scholarships:
Senior Berwick Prize, London Mathematical Society, 1984.
Recent Publications (from MathSciNet):
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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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Recent Publications (from MathSciNet):
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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:
Recent Publications (from MathSciNet):
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Affiliate Faculty
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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:
Words: notes on verbal width in groups
Recent Publications (from MathSciNet):
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Research Fellows
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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
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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):
Teaching:
Representation Theory 2a, class. Group Theory 2b, class. Further Details:
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Research Students
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Research Interests:
Homotopical algebraic geometry and its applications to the chromatic picture in stable homotopy theory; Arithmetic geometry |
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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. |
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Research Interests:
Group Theory: groups acting on rooted trees, profinite groups. |
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Research Interests:
Geometric Representation Theory Prizes, Awards and Scholarships:
EPSRC Scholarship Teaching:
TA for B9a Galois Theory and C2.1a Lie Algebras MT12. |
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Teaching:
Teaching Assisstant for B2b Groups and Characters HT 2012 and HT 2013 Teaching Assistant for B9a Galois Theory MT 2012 |
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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 |
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Research Interests:
Group theory, profinite groups, words |
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Research Interests:
I am working under the supervision of Raphael Rouquier on Soergel bimodules and their 2-representation theory. |
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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) |
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Research Interests:
Homotopy type theory, homological algebra, representation theory. |





J.
groups (Birkhaüser, 2000).
-generator soluble subgroups. Bull. London Math. Soc., to appear.





