Department of Mathematics and Statistics
University of Melbourne
Parkville VIC 3010 Australia
Office: 174 Richard Berry
Phone: +61 3 8344 6953
Fax: +61 3 8344 4599
Date and Place of Birth: Las Cruces, New Mexico, USA, October 4, 1966
B.S. in Mathematics, Massachusetts Insitute of Technology, 1987
Ph.D. in Mathematics, University of California, San Diego, 1991
National Science Foundation Postdoctoral Fellow, MIT, 1991-1992
Van Vleck Assistant Professor, University of Wisconsin, Madison, 1992-1995
Assistant Professor, Princeton University, 1995-99
Associate Professor, University of Wisconsin, Madison, 1999-2003
Professor, University of Wisconsin, Madison, 2003-2010
Professor, University of Melbourne, 2007--
ARC Senior Research Fellow, University of Sydney, 1995-1996
Postdoctoral Fellow, Mathematical Sciences Research Institute, Berkeley, Jan. 1997-June 1997
Research fellow, Isaac Newton Institute for the Mathematical Sciences, Cambridge, England, January-June 2001
Research fellow, Max-Planck Institut fur Mathematik, Bonn, Germany, February-July 2005
Program Organizer, Mathematical Sciences Research Institute, Berkeley, Jan. 2008-May 2008
Research fellow, Isaac Newton Institute for the Mathematical Sciences, Cambridge, England, January-March 2009
Research fellow, Hausdorff Research Institute for Mathematics, Bonn, Germany, January-February 2011
Research fellow, Institute for Computational and Experimental Research in Mathematics (ICERM),
Providence, USA, January-June 2013
Australian Research Council Discovery Grant "Tantalizer algebras and generalised lattice models" (with Z. Daugherty), 2013-2015.
Australian Research Council Discovery Grant "Coset spaces and Hecke algebra actions" (with A. Ghitza), 2012-2014.
Australian Research Council Discovery Grant "Representation Theory: Path models and decompositions", 2009-2011.
Australian Research Council Discovery Grant "Macdonald polynomials: Combinatorics and Representations" (with O. Warnaar), 2008-2010.
NSF Grant "Representation Theory and Combinatorics", May 2004-May 2009.
Vilas Associates Award, University of Wisconsin, Madison, July 2004-June 2006.
NSF Grant "Representation Theory and Combinatorics", May 2001-May 2004.
NSA Grant "Representation Theory and Combinatorics", Oct. 2000-Oct. 2002.
NSF Grant "Representation Theory and Combinatorics", Sept. 1996-Aug. 2000.
A Frobenius formula for the Characters of the Hecke algebras,
Matrix units for centralizer algebras
(with H. Wenzl),
J. of Algebra
145 (1992), 378-395.
Weyl group symmetric functions and the representation theory of Lie
Proceedings of the 4th conference ``Formal Power Series
and Algebraic Combinatorics",
Publ. LACIM 11 (1992), 327-342.
Characters of Brauer's centralizer algebras,
Pacific Journal of Math.
Characters of algebras containing a Jones basic construction:
The Temperley-Lieb, Okada, Brauer, and Birman-Wenzl algebras
(with T. Halverson),
Advances in Math. 116 (1995) 263-321.
Standard Lyndon bases of Lie algebras and enveloping algebras
(with P. Lalonde),
Trans. of the Amer. Math. Soc.
Combinatorics of the q-basis of symmetric functions
(with J. Remmel and S.T. Whitehead),
J. Combinatorial Theory Ser. A.
Murnaghan-Nakayama rules for characters
of Iwahori-Hecke algebras of classical Type
(with T. Halverson),
Trans. of Amer. Math. Soc.
348 (1996), 3967-3995.
Applications of the Frobenius formulas for the characters of the
symmetric group and the Hecke algebras of type A
(with J. Remmel),
J. of Algebraic Combinatorics
6 (1997), 59-87.
A ribbon Hopf algebra approach to the irreducible representations
of centralizer algebras:
The Brauer, Birman-Wenzl, and Type A Iwahori-Hecke algebras
(with R. Leduc),
Advances in Math.
125 (1997), 1-94.
Seminormal representations of Weyl groups and Iwahori-Hecke algebras,
Proceedings of the London Math. Soc. (3)
75 (1997), 99-133.
Iwahori-Hecke algebras of type A, bitraces and symmetric
functions (with T. Halverson and R. Leduc),
Int. Math. Research Notices (1997)
No. 9, 401-416.
A ``second orthogonality relation'' for
characters of Brauer algebras,
European J. of Combinatorics,
18 (1997), 685-706.
(14) A survey of quantum groups: background, motivation,
and results, in
``Geometric analysis and Lie theory in mathematics
and physics'', A. Carey and M. Murray eds.,
Australian Math. Soc. Lecture Notes Series,
Cambridge University Press, 1997, pp. 20-104.
An elementary proof of Roichman's rule for irreducible characters of
Iwahori-Hecke algebras of type A, in
Mathematical essays in honor of Gian-Carlo Rota B. Sagan and R. Stanley ed., Birkhauser, Boston 1998, pp. 335-342.
Murnaghan-Nakayama rules for ``Hecke algebras'' of the
complex reflection groups G(r,p,n) (with T. Halverson),
Canadian Journal of Mathematics.
50 (1998), 167-192.
(17) Tensor product representations for orthosymplectic Lie superalgebras
(with G. Benkart and C.-Y. Lee Shader),
J. Pure and Applied Algebra
130 (1998), 1-48.
(18) Bitraces for GL_n(F_q) and the Iwahori-Hecke algebra of type A
(with T. Halverson), Indag. Mathem., N.S.
10 (1999), 247-268.
(19) Explicit irreducible representations of the Iwahori-Hecke algebra of
type F_4 (with D. Taylor),
manuscripta mathematica 99 (1999), 13-37.
(20) A review of Young tableaux: With applications to representation theory and geometry, by William Fulton, Cambridge University Press, New York, 1997. Bulletin American Math. Soc.
36 (1999), 251-259.
A Pieri-Chevalley formula in the K-theory of a G/B-bundle (with H. Pittie),
Electronic Research Announcements, 5 (1999), 102--107.
Combinatorial Representation Theory (with H. Barcelo),
in New perspectives in algebraic combinatorics
(Berkeley, CA, 1996--97) , 23--90,
Math. Sci. Res. Inst. Publ., 38 ,
Cambridge Univ. Press, Cambridge, 1999, pp. 23--90.
Analysis of systematic scan Metropolis algorithms using Iwahori-Hecke
algebra techniques (with P. Diaconis),
Michigan Mathematical Journal, 48 (2000), 157--190.
q-rook monoid algebras, Hecke algebras and Schur-Weyl duality
(with T. Halverson),
Zapiski Nauchanyh Seminarov POMI 283 (2001),
Journal of Mathematical Sciences 121 No. 3 (2004),
Representations of graded Hecke algebras
(with C. Kriloff), Representation Theory
6 (2002), 31--69.
Representations of rank two affine Hecke algebras,
in Advances in Algebra and
Geometry, (University of Hyderabad conference 2001), C. Musili ed.,
Hindustan Book Agency, 2002, 57-91.
Classification of graded Hecke algebras for complex reflection groups
(with A. Shepler), Commentari Mathematici Helvetici,
78 No. 2 (2003), 308-334.
Affine Hecke algebras and generalized standard Young tableaux,
J. Algebra 230, volume in honor
of Robert Steinberg's 80th birthday, (2003), 367--415.
Skew shape representations are irreducible,
in Combinatorial and Geometric representation theory ,
S.-J. Kang and K.-H. Lee eds., Contemp. Math.
325 Amer. Math. Soc. 2003, 161-189.
Affine Hecke algebras, cyclotomic Hecke algebras and Clifford theory
(with J. Ramagge),
in A tribute to C.S. Seshadri: Perspectives in Geometry and
Representation theory, V. Lakshimibai et al eds.,
Hindustan Book Agency, New Delhi (2003), 428--466.
Kostka-Foulkes polynomials and Macdonald spherical functions
(with K. Nelsen), in
Surveys in Combinatorics 2003 , C. Wensley ed.,
London Math. Soc. Lect. Notes 307 ,
Cambridge University Press, 2003, 325--370.
Affine Hecke algebras and the Schubert calculus
(with S. Griffeth), European J. of Combinatorics, special volume in
honor of Alain Lascoux on the occasion of his 60th birthday, 25 no. 8 (2004) 1263-1283.
(33) Partition algebras (with T. Halverson), European J. of Combinatorics, 26 (2005) 869-921.
(34) Alcove walks, Hecke algebras, spherical functions,
crystals and column strict tableaux,
Pure and Applied Mathematics Quarterly 2 no. 4
(Special Issue: In honor of
Robert MacPherson, Part 2 of 3)
(35) Affine Braids, Markov traces and the Category O (with R. Orellana),
Proceedings of the International
Algebraic Groups and Homogeneous Spaces Mumbai 2004,
V.B. Mehta ed., Tata Institute of Fundamental Research, Narosa Publishing
House, Amer. Math. Soc. (2007) 423-473.
Combinatorics in affine flag varieties
(with J. Parkinson and C. Schwer), Journal of Algebra 321 (2009) 3469-3493. doi:10.1016/j.jalgebra.2008.04.015
(37) Commuting families in Hecke and Temperley-Lieb algebras (with T. Halverson and M. Mazzocco), arXiv:0710.0596, Nagoya Math. J. 195 (2009), 125-152.
(38) Universal Verma modules and the Misra-Miwa Fock space (with P. Tingley,) arXiv1002.0558, Int. J. Math. and Math. Sci., special issue on "Categorification in Representation Theory", Volume 2010, Article ID 326247, 19 pages, doi:10.1155/2010/326247.
(39) Homogeneous representations of Khovanov-Lauda algebras (with A. Kleshchev), arXiv0809.0557, J. Eur. Math. Soc. 12 (2010), 1293-1306, DOI 10.4171/JEMS/230.
(40) A combinatorial formula for Macdonald polynomials (with M. Yip), arXiv:0803.1146, Advances in Math. 226 (2011), 309-331, doi:10.1016/j.aim.2010.06.022.
(41) Representations of Khovanov-Lauda-Rouquier Algebras and Combinatorics of Lyndon Words (with A. Kleshchev), arXiv0909.1984, Math. Annalen 349 (2011), 943-975, DOI 10.1007/s00208-010-0543-1.
Millennium Prize: the Hodge Conjecture, published in The Conversation,
http://theconversation.edu.au/millenium-prize-the-hodge-conjecture-4243, 22 November 2011.
(43) A probabilistic interpretation of the Macdonald polynomials
(with P. Diaconis), arXiv1007.4779,
The Annals of Probability 40 (2012) No. 5, 1861-1896, DOI 10.1214/11-AOP674.
(44) Universal Specht modules for cyclotomic Hecke algebras
(with A. Kleshchev and A. Mathas), arXiv1102.3519,
Proc. London Math. Soc. (3) 105 (2012) 1245-1289.
(45) Affine and degenerate affine BMW algebras: Actions on tensor space
(with Z. Daugherty and R. Virk), arXiv:1205.1852,
Selecta Mathematica 19 no. 2 (2013) 611-653.
(46) Symmetry breaking, subgroup embeddings and the Weyl group (with D. George, J. Thompson and R. Volkas), arXiv:1203.1048,
Physical Review D 87
105009 (2013) [14 pages].
(47) Generalized Schubert Calculus, (with N. Ganter),
arXiv1212.5742, J. Ramanujan Math. Soc. 28A
(Special Issue-2013), 149-190.
(48) Hopf algebras and Markov chains: Two examples and a theory,
(with P. Diaconis and A. Pang), arXiv1206.3620,
Journal of Algebraic Combinatorics (2013)
(49) Affine and degenerate affine BMW algebras: The center (with Z. Daugherty and R. Virk), preprint 2011, arXiv:1105.4207, to appear in
Osaka J. Math..
(50) MathML for mathematics research articles, preprint 2008.
(51) Alcove walks, buildings, symmetric functions and representations
(with J. Parkinson),
preprint 2008, arXiv0807.3602.