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, 1995-1999

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

General Areas

Algebra and Combinatorics

Specific Topics

Representation theory
Lie groups and quantum groups
Hecke algebras and centralizer algebras
Symmetric functions

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.

(1) A Frobenius formula for the Characters of the Hecke algebras, Invent. Math. 106 (1991), 461-488.

(2) Matrix units for centralizer algebras (with H. Wenzl), J. of Algebra 145 (1992), 378-395.

(3) Weyl group symmetric functions and the representation theory of Lie algebras, Proceedings of the 4th conference ``Formal Power Series and Algebraic Combinatorics", Publ. LACIM 11 (1992), 327-342.

(4) Characters of Brauer's centralizer algebras, Pacific Journal of Math. 169 (1995) 173-200.

(5) 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.

(6) Standard Lyndon bases of Lie algebras and enveloping algebras (with P. Lalonde), Trans. of the Amer. Math. Soc. 347 (1995), 1821-30.

(7) Combinatorics of the q-basis of symmetric functions (with J. Remmel and S.T. Whitehead), J. Combinatorial Theory Ser. A. 76 (1996) 231-71.

(8) Murnaghan-Nakayama rules for characters of Iwahori-Hecke algebras of classical Type (with T. Halverson), Trans. of Amer. Math. Soc. 348 (1996), 3967-3995.

(9) 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.

(10) 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.

(11) Seminormal representations of Weyl groups and Iwahori-Hecke algebras, Proceedings of the London Math. Soc. (3) 75 (1997), 99-133.

(12) 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.

(13) 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, 11 Cambridge University Press, 1997, pp. 20-104.

(15) 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.

(16) 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.

(21) A Pieri-Chevalley formula in the K-theory of a G/B-bundle (with H. Pittie), Electronic Research Announcements, 5 (1999), 102--107.

(22) 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.

(23) Analysis of systematic scan Metropolis algorithms using Iwahori-Hecke algebra techniques (with P. Diaconis), Michigan Mathematical Journal, 48 (2000), 157--190.

(24) q-rook monoid algebras, Hecke algebras and Schur-Weyl duality (with T. Halverson), Zapiski Nauchanyh Seminarov POMI 283 (2001), 224-250 and Journal of Mathematical Sciences 121 No. 3 (2004), 2419-2436.

(25) Representations of graded Hecke algebras (with C. Kriloff), Representation Theory 6 (2002), 31--69.

(26) 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.

(27) Classification of graded Hecke algebras for complex reflection groups (with A. Shepler), Commentari Mathematici Helvetici, 78 No. 2 (2003), 308-334.

(28) Affine Hecke algebras and generalized standard Young tableaux, J. Algebra 230, volume in honor of Robert Steinberg's 80th birthday, (2003), 367--415.

(29) 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.

(30) 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.

(31) 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.

(32) 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) (2006) 963-1013.

(35) Affine Braids, Markov traces and the Category O (with R. Orellana), Proceedings of the International Colloquium on 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.

(36) 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.

(42) 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) Hopf algebras and Markov chains: Two examples and a theory, (with P. Diaconis and A. Pang), arXiv1206.3620, Journal of Algebraic Combinatorics 39 (2014) 527-585. DOI:10.1007/s10801-013-0456-7

(48) Generalized Schubert Calculus, (with N. Ganter), arXiv1212.5742, J. Ramanujan Math. Soc. 28A (Special Issue-2013), 149-190.

(49) Affine and degenerate affine BMW algebras: The center (with Z. Daugherty and R. Virk), arXiv:1105.4207, Osaka J. Math. 51 (2014) 257-283.

(50) Cyclic representation of the Temperley-Lieb algebra, complex Virasoro representations and stochastic processes (with F.C. Alcaraz and V. Rittenberg), arXiv:1402.5990, J. Phys. A: Math. Theor. 47 (2014) 212003.

(51) MathML for mathematics research articles, preprint 2008.

(52) Alcove walks, buildings, symmetric functions and representations (with J. Parkinson), preprint 2008, arXiv0807.3602.