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Dr David A. Craven
DPhil, MSci
- Junior Research Fellow at Christ Church.
Personal Web Page
eMail:
David [dot] Craven [-at-] maths [dot] ox [dot] ac [dot] uk
Contact Form
Phone Number(s):
Reception/Secretary: +44 1865 273525
Direct: +44 1865 273553
Office:
SGT10
Departmental Address:
Mathematical Institute
24-29 St Giles'
Oxford
OX1 3LB
England
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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;
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the modular representations of finite, and particularly simple groups;
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infinite groups arising from automata;
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asymptotics of representation theory, via the concept of representation growth; and
- fusion systems, particularly representation-theoretic and group-theoretic aspects.
Major/Recent Publications:
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Symmetric Group Character Degrees and Hook Numbers, Proc. Lond. Math. Soc. 96 (2008), 26-50.
- 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.
- Simple Modules for Groups with Abelian Sylow 2-Subgroups are Algebraic, J. Algebra 321 (2009), 1473-1479.
- Control of Fusion and Solubility in Fusion Systems, J. Algebra 323 (2010) 2429-2448.
- Algebraic Modules and the Auslander-Reiten Quiver, J. Pure Appl. Algebra, to appear.
- The Structure of Blocks with Klein Four Defect Group (jt with Charles Eaton, Radha Kessar, and Markus Linckelmann), Math. Z., to appear.
- Bounds for Representation Growth and Finite Simple Groups, J. Group Theory, to appear.
- Fusion Systems on Small p-Groups (jt with Adam Glesser), submitted.
- Normal Subsystems of Fusion Systems, submitted.
- On the Unit Conjecture for Group Rings (jt with Peter Pappas), preprint, 2010.
- Perverse Equivalences and Broue's Conjecture (jt with Raphael Rouquier), preprint, 2010.
Recent Publications (from MathSciNet):
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MR2819694 Craven, David A. Normal subsystems of fusion systems.
J. Lond. Math. Soc. (2) 84 (2011), no. 1, 137–158. (Reviewer: Justin Lynd), 20D20 (20C20 55R35)
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MR2808319 Craven, David A. The theory of fusion systems.
An algebraic approach.
Cambridge Studies in Advanced Mathematics, 131. Cambridge University Press, Cambridge, 2011. xii+371 pp. ISBN: 978-1-107-00596-9 (Reviewer: Nadia P. Mazza), 20C20 (20D20 20D30)
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MR2805443 Craven, David A.; Eaton, Charles W.; Kessar, Radha; Linckelmann, Markus The structure of blocks with a Klein four defect group.
Math. Z. 268 (2011), no. 1-2, 441–476. (Reviewer: Jeffrey M. Riedl), 20C20
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MR2729217 (2011k:20013) Craven, David A. Algebraic modules and the Auslander-Reiten quiver.
J. Pure Appl. Algebra 215 (2011), no. 3, 221–231. (Reviewer: Andrei Marcus), 20C20 (16G70)
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MR2736162 (2012b:20010) Craven, David A. Lower bounds for representation growth.
J. Group Theory 13 (2010), no. 6, 873–890. (Reviewer: Benjamin Klopsch), 20C15 (20C30 20E18 20E26 20F69)
More publications
Teaching:
C2.2a, Finite Group Theory
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