About Associate Professor Anthony Henderson

My research is in representation theory and related areas of combinatorics and geometry.

I have a long-standing interest 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. A further strand of my research is in more combinatorial areas related to hyperplane arrangements and their 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.

I won the 2011 Christopher Heyde Medal of the Australian Academy of Science, for excellence in research in the mathematical sciences by a researcher under the age of 40 working in Australia.

Selected publications

1. Henderson A and Wachs ML. Unimodality of Eulerian quasisymmetric functions, J. Combin. Theory Ser. A 119 (2012).
2. Achar PN, Henderson A and Jones BF. Normality of orbit closures in the enhanced nilpotent cone. Nagoya Math. J. 203 (2011).
3. Achar PN, Henderson A and Sommers E. Pieces of nilpotent cones for classical groups. Represent. Theory 15 (2011). MR2833469
4. Henderson A and Lehrer GI. The equivariant Euler characteristic of real Coxeter toric varieties. Bull. Lond. Math. Soc. 41 (2009). MR2506835
5. Achar PN and Henderson A. Orbit closures in the enhanced nilpotent cone, Adv. Math. 219 (2008). MR2435419
6. Henderson A and Rains E. The cohomology of real De Concini-Procesi models of Coxeter type, Int. Math. Res. Not. 2008 (2008). MR2428302
7. Henderson A. Nilpotent orbits of linear and cyclic quivers and Kazhdan-Lusztig polynomials of type A, Represent. Theory 11 (2007). MR2320806
8. Henderson A. Plethysm for wreath products and homology of sub-posets of Dowling lattices, Electron. J. Combin. 13 (2006). MR2255429
9. Henderson A. Bases for certain cohomology representations of the symmetric group, J. Algebraic Combin. 24 (2006). MR2266359
10. Henderson A. Representations of wreath products on cohomology of De Concini-Procesi compactifications, Int. Math. Res. Not. 2004 (2004) . MR2036424