Anthony Henderson
I am an Associate Professor in the
School of Mathematics and Statistics at the
University of Sydney.
Here is my curriculum vitae (pdf, 8 pages).
Postal address: 
A/Prof Anthony Henderson
School of Mathematics and Statistics F07
University of Sydney NSW 2006
Australia

Office: 
Room 805 Carslaw Building

Email: 
anthony.henderson[at]sydney.edu.au

 
Research
I am a member of the
Algebra research group.
Broadly speaking, I am interested in geometric and combinatorial aspects of representation theory.
The papers and talks listed below can be categorized into three
main themes.

I have a longstanding interest in the geometry of nilpotent varieties and Springer fibres, and their generalizations such as
orbit closures in Hilbert nullcones and Nakajima's quiver varieties. It is often the case that the (intersection) cohomology of these varieties controls decomposition numbers in representation theory. See preprints 14, research publications 1,3,10,13,1518,20,2224 and talks 13.
Current funding for research in this area: In November 2011, I was awarded a fouryear Future Fellowship by the Australian Research Council for the project `Springer fibres, nilpotent cones, and representation theory'.

I have also worked in more combinatorial
areas related to hyperplane arrangements and wonderful compactifications. My interest has been in computing the characters of the
representations of symmetric groups and wreath products on the
cohomology of various varieties on which they act. See
research publications 58,11,12,14,19,21.

The subject of my PhD thesis and subsequent research was the extension
of Lusztig's results on
reductive groups over a finite field
to the case of symmetric spaces. See research publications 2,4,9.
In 2012, I was one of two recipients of the Australian Mathematical Society Medal, awarded annually to a member of the Society under the age of 40 for distinguished research in the mathematical sciences. I thereby became a Fellow of the Australian Mathematical Society.
In 2011, I was the inaugural winner of the Christopher Heyde Medal of the Australian Academy of Science.
I am currently the Elected VicePresident of the Australian Mathematical Society and an Associate Editor of the Journal of the Australian Mathematical Society.
Preprints
 with Pramod N. Achar and Simon Riche:
Geometric Satake, Springer correspondence, and small representations II, available at arXiv:1205.5089 or here (version 3, 73 pages).
 with Pramod N. Achar, Daniel Juteau and Simon Riche:
Modular generalized Springer correspondence I: the general linear group, to appear in J. Eur. Math. Soc., available at arXiv:1307.2702 or here (version 3, 29 pages).
 with Pramod N. Achar, Daniel Juteau and Simon Riche:
Modular generalized Springer correspondence II: classical groups, to appear in J. Eur. Math. Soc., available at arXiv:1404.1096 or here (version 3, 52 pages).

Singularities of nilpotent orbit closures, to appear in Proceedings of the 5th JapaneseAustralian Workshop on Real and Complex Singularities, available at arXiv:1408.3888 or here (version 2, 30 pages).
Research Publications

Fourier transform, parabolic induction, and nilpotent orbits,
Transform. Groups 6 (2001), no. 4, 353370.

Spherical functions of the symmetric space
G(F_{q²})/G(F_{q}),
Represent. Theory 5 (2001), 581614.

Tworow nilpotent orbits of cyclic quivers,
Math. Z. 243 (2003), no. 1, 127143.

Symmetric subgroup invariants in irreducible representations
of G^{F}, when G=GL_{n},
J. Algebra 261 (2003), no. 1, 102144.

Representations of wreath products on cohomology of De ConciniProcesi
compactifications,
Int. Math. Res. Not. 2004 (2004), no. 20,
9831021.

Species over a finite field,
J. Algebraic Combin. 21 (2005), no. 2, 147161.

Bases for certain cohomology representations of the symmetric group,
J. Algebraic Combin. 24 (2006), no. 4, 361390.

Plethysm for wreath products and homology of subposets of Dowling lattices,
Electron. J. Combin. 13 (2006), no. 1, Research Paper 87, 25 pp.

Induced characters of the projective general linear group
over a finite field,
J. Algebra 307 (2007), no. 1, 116135.

Nilpotent orbits of linear and cyclic quivers and KazhdanLusztig
polynomials of type A,
Represent. Theory 11 (2007), 95121.
 with Eric Rains:
The cohomology of real De ConciniProcesi models of Coxeter type,
Int. Math. Res. Not. 2008 (2008), rnn001, 29 pp.

The symmetric group representation on cohomology of the
regular elements of a maximal torus of the special linear group,
J. Aust. Math. Soc.
84 (2008), no. 1, 8598.
 with Pramod N. Achar:
Orbit closures in the enhanced nilpotent cone,
Adv. Math.
219 (2008), no. 1, 2762. Note the corrigendum.
 with Gus Lehrer:
The equivariant Euler characteristic of real Coxeter toric varieties,
Bull. London Math. Soc. 41 (2009), no. 3, 515523.

Exterior powers of the reflection representation in the cohomology of Springer fibres, C. R. Math. Acad. Sci. Paris
348 (2010), no. 1920, 10551058.
 with Pramod N. Achar and Eric Sommers:
Pieces of nilpotent cones for classical groups,
Represent. Theory 15 (2011), 584616.
 with Pramod N. Achar and Benjamin F. Jones:
Normality of orbit closures in the enhanced nilpotent cone, Nagoya Math. J. 203 (2011), 145.

Enhancing the Jordan canonical form, Austral. Math. Soc. Gaz. 38 (2011), no. 4, 206211.
 with Michelle L. Wachs:
Unimodality of Eulerian quasisymmetric functions, J. Combin. Theory Ser. A 119 (2012), no. 1, 135145.
 with Peter E. Trapa:
The exotic RobinsonSchensted correspondence, J. Algebra 370 (2012), 3245.

Rational cohomology of the real Coxeter toric variety of type A, in Configuration Spaces: Geometry, Combinatorics, and Topology, Publications of the Scuola Normale Superiore, no. 14, A. Björner, F. Cohen, C. De Concini, C. Procesi and M. Salvetti (eds.), Pisa, 2012, 313326, available from SNS and Birkhäuser.
 with Pramod N. Achar:
Geometric Satake, Springer correspondence, and small representations, Selecta Math. (N.S.) 19 (2013), no. 4, 949986.
 with Pramod N. Achar, Daniel Juteau and Simon Riche:
Weyl group actions on the Springer sheaf, Proc. Lond. Math. Soc. 108 (2014), no. 6, 15011528.
 with Anthony Licata:
Diagram automorphisms of quiver varieties, Adv. Math. 267 (2014), 225276.
Selected Recent Talks

Geometric Satake, Springer correspondence, and small representations, Algebraic Groups and Representation Theory, Hong Kong, January 2013.

A partial history of the Schur functor, my plenary lecture at the Australian Mathematical Society Annual Meeting, Sydney, September 2013.

Character sheaves and modular generalized Springer correspondence, the first two parts of a 3lecture series in the Winter School on Geometric Representation Theory, RIMS, Kyoto, January 2015.

Geometric modular representation theory, the introduction to a lecture series I gave at the Centre for Geometry and its Applications, POSTECH, Pohang, February 2015. Here is a YouTube video of an earlier version of this talk, given at the University of Western Sydney, August 2013.
Postdoctoral Supervision
From July 2013 to March 2015, I supervised the University of Sydney Postdoctoral Fellowship of Alan Stapledon.
Postgraduate Supervision
I supervise or have supervised the following postgraduate students.
 Christopher Ryba, PhD (current)
 Harrison Jones, PhD (associate supervisor  current)
 Michael Hendriksen, MSc (associate supervisor  current)
 Andrew Crisp, PhD (candidature suspended)
 Clinton Boys, PhD (associate supervisor  approved Feb 2015)
 Natalie Aisbett, PhD (approved Jun 2013)
 Graham White, MSc (associate supervisor  approved May 2013)
 Ge Li, PhD (associate supervisor  approved Dec 2012)
 Justin Koonin, PhD (associate supervisor  approved Mar 2012)
 Neil Saunders, PhD (associate supervisor  approved Feb 2011)
 Michael Sun, MSc (approved Jan 2010)
I have also supervised seven Honours projects and eight Vacation Scholarships.
For information about available PhD projects, see
my
page in Research Supervisor Connect.
Undergraduate Teaching
In May 2009, I was awarded a Faculty of Science Citation for Excellence in Teaching.
I have lectured the following units of study.
 Semester 1, 200708:
MATH1901 Differential Calculus (Advanced).
 Semester 1, 200506,0810:
Special Studies Program unit MATH1906.
 Semester 1, 200709:
MATH2069 Discrete Mathematics and Graph
Theory (joint with the Advanced version MATH2969).
 Semester 1, 2011 and Semester 2, 2013:
Special Studies Program unit MATH2916/MATH2917.
 Semester 2, 2011:
MATH2968 Algebra (Advanced).
 Semester 2, 200610:
MATH3966 Modules and Group Representations (Advanced).
 Semester 1, 200304:
MATH3002 Rings and Fields.
 Semester 2, 2005, Semester 1, 2011 and Semester 2, 2014: Pure Mathematics Honours unit
Lie Algebras.
 Semester 1, 2002: Pure Mathematics Honours unit
Introduction to Lie Theory.
 Summer 2004 and 2007: Lie Algebras in the
AMSI Summer School.
My lecture notes on Lie algebras have been published as the undergraduate textbook `Representations of Lie Algebras: An Introduction Through gl_{n}', Australian Mathematical Society Lecture Series, no. 22, Cambridge University Press, Cambridge, 2012, available from CUP Australia, CUP America, Amazon, Amazon UK and Book Depository. See the reviews in MathSciNet, zbMATH, Choice (subscriptions required), and the Gazette of the Australian Mathematical Society.
I also run the SUMS Problem Competition
for undergraduates from around Australia.
Some Links
 School of Mathematics and Statistics external front page.
 Mathematics ArXiv.
 My publications in zbMATH.
 My author profile in MathSciNet.
 My page
in the Mathematics Genealogy Project.
 George Lusztig, my
thesis advisor at MIT.
 Kevin McGerty,
a fellow Lusztig student, now at Oxford University.
 Lenny Ng, a fellow MIT graduate student, now at Duke University.
 Tara Holm, a fellow MIT graduate student, now at Cornell University.
 Pramod Achar, a fellow MIT graduate student, now a
collaborator at Louisiana State University.
 Peter Trapa, a fellow MIT graduate student, now a
collaborator at the University of Utah.
 Eric Sommers,
a fellow Lusztig student, now a collaborator at the University of Massachusetts Amherst.
 Daniel Juteau, a collaborator at Université de Caen.
 Simon Riche, a collaborator at Université Blaise Pascal  ClermontFerrand II.
 Tony Licata, a collaborator at the Australian National University.
 Geordie Williamson, a collaborator at MaxPlanckInstitut für Mathematik in Bonn.