The University of Southampton
Mathematical Sciences
Phone:
(023) 8059 3674
Email:
G.A.Niblo@soton.ac.uk

Professor Graham Niblo

Professor of Mathematics

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Professor Graham Niblo is Professor of Mathematics at the University of Southampton.

• MsC Pure Mathematics (Distinction), University of London, 1985
• PhD Pure Mathematics, University of Liverpool, 1988
• Research Assistant, University of Michigan, 1988
• SERC Postdoctoral Fellow, Sussex, 1988-1990
• SERC Postdoctoral Research Assistant, London, 1990-1992
• Lecturer University of Southampton, 1992-2000
• Visiting Professor, Rutgers, 1998
• Senior Lecturer Southampton University, 2000-2005
• Professor of Mathematics, University of Southampton, 2005-
• Head of Pure Mathematics, University of Southampton, 2006-2011
• Leverhulme Research Fellow, 2011-2012
• Visiting Researcher, University of Oxford, 2011
• Head of Mathematics, University of Southampton, 2012-2015

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Research interests

My principle research interests lie at the intersection of geometry, topology, analysis and group theory. Recent projects include new homological characterisations of amenability and of property A generalising results of Johnson and Block and Weinberger. These results exposed an unexpected relationship between the classical results for amenability and led to new characterisations of generalisations such as the notion of a topologically amenable action on a compact space, or C* exactness for a group. This work does have a functional analytic flavour, arising from the need to construct invariant means as limits. For example the integers are known to admit an invariant mean but no-one has ever seen one in the wild; they are observed to exist as weak limits of geometrically defined subsets known as Folner sets. There has been a lot of interest recently in the use of ideas from geometric group theory to construct such approximations to a mean and this is an ideal area for further exploration, allowing us to use geometry for constructions of objects discovered via analytic methods.

While much of geometric group theory arose from ideas in low dimensional topology (study of the mapping class group, the JSJ decomposition and Stallings' theorem all played a fundamental role) there is increasing interest in tackling problems in high dimensional topology. Given the remarkable recent proof of the Farrell-Jones conjecture for CAT(0) groups (by Bartels and Lueck), there is likely to be scope for a lot more interaction between these areas. In this direction my recent work with our Postdoc Aditi Kar shows that the classical sphere and torus theorems have a generalisation for even dimensional manifolds of real rank at least 2 and for quaternionic manifolds of dimension at least 8. Broadly speaking we show that any $\pi_1$-injective map of such a manifold to an aspherical manifold of dimension 1 higher is homotopic to a finite cover of an embedding. This may be viewed as a topological analogue of the celebrated geometric superrigidity theorem, at least in even dimensions, and we continue to explore the odd dimensional case.

I am also interested in applications of coarse geometry and graph theory to real world problems. My paper with Jim Anderson on construction of universal footprinting templates in DNA is currently being converted to a practical algorithm by an undergraduate Nuffield scholar with plans for the resulting protein assay templates to be built by our collaborator Keith Fox in the new Life Sciences Institute. More recently I have become involved in a project to model catastrophic failure in the the National Grid with the hope of developing new methods to prevent cascading blackouts. Tools from analytic graph theory are being used to detect optimal network decompositions during a crisis. this is joint work with Jacek Brodzki, Ruben Sanchez, Nick Wright and our student Max Fennelly at Southampton, together with engineers and mathematicians from Durham and Edinburgh.

Research projects
1. Topological super-rigidity - a generalisation of the sphere and torus theorems and the JSJ decomposition to high dimensional topology.
2. Topologically amenable actions - generalisations of amenability to a wide variety of geometric and topological contexts. Funded by EPSRC grant
3. Applications of coarse geometry and analytic graph theory - protective islanding of energy networks, homological methods in data analysis. Funded by EPSRC grant

Pure Mathematics

Article(s)

• The local spectrum of the Dirac operator for the universal cover of SL_2(R) - Brodzki, Jacek, Niblo, Graham A., Plymen, Roger and Wright, Nick
Published:
2016
Publication:
Journal of Functional Analysis
Volume:
270, (3)
Page Range:
957-975
doi:
doi:10.1016/j.jfa.2015.10.010
• Benevolent characteristics promote cooperative behaviour among humans - Capraro, Valerio, Smyth, Conor, Mylona, Kalliopi and Niblo, Graham A.
Published:
2014
Publication:
PLoS ONE
Volume:
9, (8)
Page Range:
1-6
doi:
10.1371/journal.pone.0102881
• The local spectrum of the Dirac operator for the universal cover of SL2(R) - Brodzki, Jacek, Niblo, Graham A., Plymen, Roger and Wright, Nick
Published:
2014
Publication:
Author's Original
Volume:
, (arXiv:1406.0365)
Page Range:
1-17
• Hierarchical spectral clustering of power grids - Sanchez-Garcia, Ruben, Fennelly, Max, Norris, Sean, Wright, Nick, Niblo, Graham, Brodzki, Jacek and Bialek, Janusz
Published:
2014
Publication:
IEEE Transactions on Power Systems
Page Range:
1-9
doi:
10.1109/TPWRS.2014.2306756
• Uniform local amenability - Brodzki, Jacek, Niblo, Graham A., Špakula, Ján, Willett, Rufus and Wright, Nick J.
Published:
2013
Publication:
Journal of Non Commutative Geometry
Volume:
7, (2)
Page Range:
583-603
doi:
10.4171/JNCG/128
• K-theory and exact sequences of partial translation algebras - Brodzki, Jacek, Niblo, Graham A. and Wright, Nick
Published:
2013
Publication:
Advances in Mathematics
Volume:
273
Page Range:
287-323
doi:
10.1016/j.aim.2014.12.023
• A homological characterization of topological amenability - Brodzki, Jacek, Niblo, Graham A., Nowak, Piotr and Wright, N.J.
Published:
2012
Publication:
Algebraic & Geometric Topology
Volume:
12, (3)
Page Range:
1767-1780
• A cohomological characterisation of Yu's Property A for metric spaces - Brodzki, Jacek, Niblo, Graham A. and Wright, Nick
Published:
2012
Publication:
Geometry & Topology
Volume:
16, (1)
Page Range:
391-432
doi:
10.2140/gt.2012.16.391
• Some non-amenable groups - Kar, Aditi and Niblo, Graham A.
Published:
2012
Publication:
Publicacions Matemàtiques
Volume:
56, (1)
Page Range:
255-259
• Complexes and exactness of certain Artin groups - Niblo, Graham A. and Guentner, Erik
Published:
2011
Publication:
Algebraic and Geometric Topology
Volume:
11, (3)
Page Range:
1471-1495
doi:
10.2140/agt.2011.11.1471
• A topological splitting theorem for Poincar\'e duality groups and high dimensional manifolds - Niblo, Graham and Kar, Aditi
Published:
2010
Publication:
Geometry & Topology
Volume:
17
Page Range:
2203-2221
doi:
10.2140/gt.2013.17.2203
• Amenable actions, invariant means and bounded cohomology - Brodzki, Jacek, Niblo, Graham A., Nowak, Piotr and Wright, Nick
Published:
2010
Publication:
Journal of Topology and Analysis
Volume:
4, (321)
Page Range:
321-334
doi:
10.1142/S1793525312500161
• Relative ends, L^2 invariants and Property (T) - Niblo, Graham and Kar, Aditi
Published:
2010
Publication:
Journal of Algebra
Volume:
333, (1)
Page Range:
232-240
doi:
10.1016/j.jalgebra.2011.02.030
• Pairings, duality, amenability and bounded cohomology - Brodzki, Jacek, Niblo, Graham A. and Wright, Nick
Published:
2010
Publication:
Journal of the European Mathematical Society
Volume:
14, (5)
Page Range:
1513-1518
doi:
10.4171/JEMS/338
Published:
2010
Publication:
Pre-print
• Property A and CAT(0) cube complexes - Brodzki, J., Campbell, S.J., Guentner, E., Niblo, G.A. and Wright, N.J.
Published:
2009
Publication:
Journal of Functional Analysis
Volume:
256, (5)
Page Range:
1408-1431
doi:
10.1016/j.jfa.2008.10.018
• Partial translation algebras for trees - Brodzki, Jacek, Niblo, Graham A. and Wright, Nick J.
Published:
2009
Publication:
Journal of Noncommutative Geometry
Volume:
3, (1)
Page Range:
83-98
doi:
10.4171/JNCG/31
Published:
2008
Publication:
54
• Property A and exactness of the uniform Roe algebra - Brodzki, Jacek, Niblo, Graham A. and Wright, Nicholas
Published:
2008
Publication:
L’Enseignement Mathématique (2)
Volume:
54
Page Range:
46-48
• Property A, partial translation structures and uniform embeddings in groups - Brodzki, Jacek, Niblo, Graham A. and Wright, Nick
Published:
2007
Publication:
Journal of the London Mathematical Society
doi:
10.1112/jlms/jdm066
• A characterization of hyperbolic spaces - Chatterji, Indira and Niblo, Graham A.
Published:
2007
Publication:
Groups, Geometry and Dynamics
Volume:
1, (3)
Page Range:
281-299
• A fast algorithm for the construction of universal footprinting templates in DNA - Anderson, James W., Fox, Keith R. and Niblo, Graham A.
Published:
2006
Publication:
Journal of Mathematical Biology
Volume:
52, (3)
Page Range:
307-342
doi:
10.1007/s00285-005-0357-z
• Minimal cubings - Niblo, Graham, Sageev, Michah, Scott, Peter and Swarup, Gadde A.
Published:
2005
Publication:
International Journal of Algebra and Computation
Volume:
15, (2)
Page Range:
343-366
doi:
10.1142/S0218196705002347
• Hilbert space compression and exactness of discrete groups - Campbell, Sarah and Niblo, Graham A.
Published:
2005
Publication:
Journal of Functional Analysis
Volume:
222, (2)
Page Range:
292-305
doi:
10.1016/j.jfa.2005.01.012
• From wall spaces to CAT(0) cube complexes - Chatterji, Indira and Niblo, Graham
Published:
2005
Publication:
International Journal of Algebra and Computation
Volume:
15, (5-6)
Page Range:
875-885
doi:
10.1142/S0218196705002669
• A geometric proof of Stallings' Theorem on groups with more than one end - Niblo, Graham
Published:
2004
Publication:
Geometriae Dedicata
Volume:
105, (1)
Page Range:
61-76
doi:
10.1023/B:GEOM.0000024780.73453.e4
• Coxeter Groups act on CAT(0) cube complexes - Niblo, G.A. and Reeves, L.D.
Published:
2003
Publication:
Journal of Group Theory
Volume:
6, (3)
Page Range:
399-413
doi:
10.1515/jgth.2003.028
• Engulfing in word-hyperbolic groups - Niblo, G.A. and Williams, B.T.
Published:
2002
Publication:
Algebraic and Geometric Topology
Volume:
2
Page Range:
743-755
doi:
10.2140/agt.2002.2.743
• The singularity obstruction for group splittings - Niblo, G.A.
Published:
2002
Publication:
Topology and its Applications
Volume:
119, (1)
Page Range:
17-31
doi:
10.1016/S0166-8641(01)00059-1
• Subgroup separability, knot groups, and graph manifolds - Niblo, Graham A. and Wise, Daniel T.
Published:
2001
Publication:
Proceedings of the American Mathematical Society
Volume:
129, (3)
Page Range:
685-693
• Double coset decompositions of groups - Niblo, Graham A.
Published:
1999
Publication:
Journal of Algebra
Volume:
220, (2)
Page Range:
512-518
doi:
10.1006/jabr.1999.7935
• The geometry of cube complexes and the complexity of their fundamental groups - Niblo, Graham A. and Reeves, Lawrence D.
Published:
1998
Publication:
Topology
Volume:
37, (3)
Page Range:
621-633
doi:
10.1016/S0040-9383(97)00018-9
• Groups acting on CAT(0) cube complexes - Niblo, Graham and Reeves, Lawrence
Published:
1997
Publication:
Geometry and Topology
Volume:
1
Page Range:
1-7
doi:
10.2140/gt.1997.1.1
• Groups acting on cubes and Kazhdan's property (T) - Niblo, Graham A. and Roller, Martin A.
Published:
1996
Publication:
Proceedings of the American Mathematical Society
Volume:
126, (3)
Page Range:
693-699
• Finding splittings of groups and three-manifolds - Niblo, G.A.
Published:
1995
Publication:
Bulletin of the London Mathematical Society
Volume:
27
Page Range:
567-574

Book Section(s)

• Approximation properties for discrete groups - Brodzki, Jacek and Niblo, Graham A.. In C*-algebras and Elliptic Theory - Bojarski, B., Mishchenko, A., Troitsky, E. and Weber, A. (eds.)
Published:
2006
Published by:
Basel, Switzerland
Series:
Trends in Mathematics
Page Range:
23-35
• Some free-by-cyclic groups - Leary, I.J., Niblo, G.A. and Wise, D.T.. In Groups St Andrews 1997 in Bath - Campbell, C.M., Robertson, E.F., Ruscuc, N. and Smith, G.C. (eds.)
Published:
1999
Published by:
Cambridge, UK
Series:
London Mathematical Society Lecture Note Series
Page Range:
512-516
doi:
10.2277/0521655765
• The engulfing property for 3-manifold groups - Niblo, Graham A. and Wise, Daniel T.. In The Epstein Birthday Schrift - Rivin, Igor, Rourke, Colin and Series, Caroline (eds.)
Published:
1998
Published by:
Coventry, UK
Series:
Geometry & Topology Monographs
Volume:
1
Page Range:
413-418
doi:
10.2140/gtm.1998.1.413
Professor Graham Niblo
Building 54 Mathematical Sciences University of Southampton Highfield Southampton SO17 1BJ

Room Number: 54/8007

Telephone: (023) 8059 3674
Facsimile: (023) 8059 5147
Email: G.A.Niblo@soton.ac.uk

Professor Graham Niblo's personal home page
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