Anthony Henderson
I am a Professor of Mathematics in the
School of Mathematics and Statistics at the
University of Sydney, and Executive Director of the University of Sydney Mathematical Research Institute, established in 2018.
Here is my curriculum vitae (pdf, 9 pages).
Postal address: 
Prof Anthony Henderson
Sydney Mathematical Research Institute A14
University of Sydney NSW 2006
Australia

Office: 
Room L4.44, Quadrangle A14

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

 
Research
As well as being the Executive Director of the Sydney Mathematical Research Institute, I am a member of the
Pure Mathematics research group within the School of Mathematics and Statistics.
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 research publications 1,3,10,13,1518,20,2232 and talks 14.

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 an Associate Editor of the Journal of the Australian Mathematical Society.
I was one of the organizers of a conference on Future Directions in Representation Theory, held at the University of Sydney, December 48, 2017.
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 retracting one statement. That statement was later proved by Carl Mautner in Proc. Amer. Math. Soc. 145 (2017), no. 4, 13931398.]
 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.
 with Pramod N. Achar and Simon Riche:
Geometric Satake, Springer correspondence, and small representations II, Represent. Theory 19 (2015), 94166.

Singularities of nilpotent orbit closures, Rev. Roumaine Math. Pures Appl. 60 (2015), no. 4, 441469.
 with Pramod N. Achar, Daniel Juteau and Simon Riche:
Modular generalized Springer correspondence I: the general linear group, J. Eur. Math. Soc. (JEMS) 18 (2016), no. 7, 14051436.
 with Pramod N. Achar, Daniel Juteau and Simon Riche:
Constructible sheaves on nilpotent cones in rather good characteristic, Selecta Math. (N.S.) 23 (2017), no. 1, 203243.
 with Pramod N. Achar, Daniel Juteau and Simon Riche:
Modular generalized Springer correspondence II: classical groups, J. Eur. Math. Soc. (JEMS) 19 (2017), no. 4, 10131070.
 with Pramod N. Achar, Daniel Juteau and Simon Riche:
Modular generalized Springer correspondence III: exceptional groups, Math. Ann. 369 (2017), no. 12, 247300.

Involutions on the affine Grassmannian and moduli spaces of principal bundles, Bull. Inst. Math. Acad. Sin. (N.S.) 13 (2018), no. 1, 4397.
 with Pramod N. Achar, Daniel Juteau and Simon Riche:
Modular generalized Springer correspondence: an overview, in Tsinghua Lectures in Mathematics, Adv. Lect. Math., no. 45, L. Ji, Y.S. Poon and S.T. Yau (eds.), International Press, Boston, 2019, 7799, available from International Press and Amazon.
Selected Recent Talks

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.

Geometric representation theory, four lectures on canonical bases of quantized universal enveloping algebras, delivered at the AMSI Winter School on Algebra, Geometry and Physics, Brisbane, July 2015. See here for the preceding lectures given by Masoud Kamgarpour and Tony Licata.

Involutions on the affine Grassmannian and moduli spaces of principal bundles, Nilpotent Orbits and Representation Theory, Pisa, June 2016.
Postdoctoral Supervision
I have been the formal supervisor of the following postdoctoral researchers.
 Thomas Gobet, Research Associate (ARCsupported), January 2018  August 2019.
 Ulrich Thiel, Research Fellow (ARCsupported), April 2017  March 2019.
 Alan Stapledon, University of Sydney Postdoctoral Fellow, July 2013  March 2015.
Postgraduate Supervision
I supervise or have supervised the following postgraduate students.
 Kane Townsend, PhD (current)
 Joshua Ciappara, PhD (auxiliary supervisor  current)
 Joseph Baine, MPhil (auxiliary supervisor  current)
 Mengfan Lyu, PhD (auxiliary supervisor  current)
 Joel Gibson, PhD (auxiliary supervisor  current)
 Alexander Kerschl, PhD (auxiliary supervisor  approved Jul 2019)
 Michael Hendriksen, MSc (associate supervisor  approved Jan 2016)
 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 eleven Honours projects and eight Vacation Scholarships.
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, 2018:
MATH1001 Differential Calculus.
 Semester 1, 200708:
MATH1901 Differential Calculus (Advanced).
 Semester 1, 2016:
MATH1002 Linear Algebra.
 Semester 1, 200506,0810:
Special Studies Program unit MATH1906.
 Semester 2, 2016:
MATH2068 Number Theory and Cryptography (joint with the Advanced version MATH2988).
 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 and 2017:
MATH2968 Algebra (Advanced).
 Semester 2, 200610:
MATH3966 Modules and Group Representations (Advanced).
 Semester 1, 200304:
MATH3002 Rings and Fields.
 Semester 1, 201618: Pure Mathematics Honours unit Representation Theory.
 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 was the Director of the 2017 AMSI Summer School, held at the University of Sydney in JanuaryFebruary 2017.
Some Links
 School of Mathematics and Statistics external front page.
 Mathematics ArXiv.
 My author profile in MathSciNet.
 My publications in zbMATH.
 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 and regular collaborator of mine, now at Louisiana State University.
 Peter Trapa, a fellow MIT graduate student, now at the University of Utah.
 Eric Sommers,
a fellow Lusztig student, now at the University of Massachusetts Amherst.
 Daniel Juteau, a collaborator of mine at Institut de Mathématiques de Jussieu.
 Simon Riche, a collaborator of mine at Université Clermont Auvergne.
 Tony Licata, a collaborator of mine at the Australian National University.