Anthony Henderson

I am a Lecturer in the School of Mathematics and Statistics at the University of Sydney. Here is my curriculum vitae (pdf, 5 pages).

Postal address:	Dr Anthony Henderson School of Mathematics and Statistics F07 University of Sydney NSW 2006 Australia
Office:	Room 805 Carslaw Building
Email:	`anthonyh[at]maths.usyd.edu.au`
Phone:	+61 2 9351 3881

Research Interests

I am a member of the Algebra research group, and I run the weekly Algebra Seminar. Broadly speaking, I am interested in representations of Lie-theoretic objects and related aspects of combinatorics and geometry. The papers and talks listed below can be categorized into three main themes.

I am very interested in the geometry of the various varieties which generalize the closures of nilpotent orbits, such as orbit closures in exotic nilpotent cones, Nakajima's quiver varieties, and nilpotent orbits for symmetric spaces. The desingularizations and intersection cohomology of these varieties usually have representation-theoretic significance. See papers 1,3,10,13 and talks 9,10,12,16.
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 papers 2,4,9 and talks 1-4.
In the past few years I have started working 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 preprint 1, papers 5-8,11,12, and talks 5-8,11,13-15.

Preprints

with Gus Lehrer: The equivariant Euler characteristic of real Coxeter toric varieties, abstract | pdf (10 pages).

Published Papers

Fourier transform, parabolic induction, and nilpotent orbits, Transform. Groups 6 (2001), pp. 353-370.
Spherical functions of the symmetric space G(F_q²)/G(F_q), Represent. Theory 5 (2001), pp. 581-614.
Two-row nilpotent orbits of cyclic quivers, Math. Z. 243 (2003), pp. 127-143.
Symmetric subgroup invariants in irreducible representations of G^F, when G=GL_n, J. Algebra 261 (2003), no. 1, pp. 102-144.
Representations of wreath products on cohomology of De Concini-Procesi compactifications, Int. Math. Res. Not. 2004:20 (2004), pp. 983-1021.
Species over a finite field, J. Algebraic Combin. 21 (2005), no. 2, pp. 147-161.
Bases for certain cohomology representations of the symmetric group, J. Algebraic Combin. 24 (2006), no. 4, pp. 361-390.
Plethysm for wreath products and homology of sub-posets 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, pp. 116-135.
Nilpotent orbits of linear and cyclic quivers and Kazhdan-Lusztig polynomials of type A, Represent. Theory 11 (2007), pp. 95-121.
with Eric Rains: The cohomology of real De Concini-Procesi 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), pp. 85-98.
with Pramod N. Achar: Orbit closures in the enhanced nilpotent cone, Adv. Math. 219 (2008), no. 1, pp. 27-62.

Selected Talks

Spherical functions of the symmetric space G(F_q²)/G(F_q), MIT Lie Groups Seminar, November 2000, pdf (15 pages).
Spherical functions and character sheaves, University of Sydney Algebra Seminar, August 2001 (a revised version of my thesis defence), pdf (12 pages).
Symmetric subgroup invariants in irreducible representations of G^F, when G=GL_n, Annual Meeting of the Australian Mathematical Society, September 2001, pdf (6 pages).
Fourier transform and Kloosterman sums, University of Sydney Algebra Seminar, October 2002, pdf (14 pages).
Species over a finite field, Australia/New Zealand Mathematics Convention, July 2003, pdf (6 pages, 2 pictures missing).
Polynomial functors and representations of wreath products, University of Sydney Algebra Seminar, August 2003, pdf (14 pages).
Representations of wreath products on cohomology of De Concini-Procesi compactifications, Lie Minisymposium, November 2003, pdf (12 pages, 4 pictures missing).
The symmetric group representation on cohomology of the regular elements of a maximal torus of the special linear group, Annual Meeting of the Australian Mathematical Society, September 2004, pdf (8 pages, 19 counting overlays).
Nilpotent orbits and Kazhdan-Lusztig polynomials of type A, Mathematical Physics and Lie Theory, December 2004, pdf (7 pages).
Equalities of Kazhdan-Lusztig polynomials of type A, University of Sydney Algebra Seminar, March 2005, pdf (14 pages).
Bases for certain cohomologies with local coefficients of a hyperplane complement, Annual Meeting of the Australian Mathematical Society, September 2005, pdf (9 pages, 24 counting overlays).
Quiver varieties and zero weight spaces, AMSI Workshop on Lie Theory, Lattices, and Dynamics, November 2005, pdf (11 pages).
Poset homology and the cohomology of real De Concini-Procesi models, University of Sydney Algebra Seminar, August 2006, pdf (17 pages, 53 counting overlays).
The cohomology of the real De Concini-Procesi model of type B_n, Annual Meeting of the Australian Mathematical Society, September 2006, pdf (8 pages, 20 counting overlays).
The cohomology of real De Concini-Procesi models of Coxeter type, Braids and their Ramifications, Cortona, May 2007, pdf (14 pages, 45 counting overlays).
Orbit closures in the enhanced nilpotent cone, Shuffles, Descents, and Representations, Nice, September 2007, pdf (14 pages, 37 counting overlays).

Teaching

In First Semester 2002, I taught the Pure Mathematics Honours unit Introduction to Lie Theory. I also taught Honours-level courses on Lie Algebras in the 2004 AMSI Summer School, in Pure Mathematics Honours in Second Semester 2005, and in the 2007 AMSI Summer School.

In First Semester 2003 and 2004, I taught the third-year normal-level unit MATH3002 Rings and Fields, which has since been subsumed into MATH3062 Algebra and Number Theory.

In First Semester 2005, 2006, and 2008, I conducted four seminars on regular polytopes in the first-year Special Studies Program unit MATH1906.

In Second Semester 2006--08, I taught the third-year unit MATH3966 Modules and Group Representations (Advanced).

In First Semester 2007--08, I taught half of the first-year unit MATH1901 Differential Calculus (Advanced).

In First Semester 2007--08, I taught half of the second-year unit MATH2069 Discrete Mathematics and Graph Theory (joint with the Advanced version MATH2969).

Since 2006, I run the SUMS Problem Competition for undergraduates from around Australia.

Some Links

School of Mathematics and Statistics external front page
Mathematics ArXiv
Mathematics on the Web
My page in the Mathematics Genealogy Project.
George Lusztig, my thesis advisor at MIT.
Kevin McGerty, my mathematical brother at Imperial College.
Lenny Ng, a friend of mine at Duke University.
Pramod Achar, a friend and collaborator of mine at Louisiana State University.
Tara Holm, a friend of mine at Cornell University.
Programs I have prepared and broadcast for 2MBS-FM 102.5, Sydney's fine music station.