Research

My research is in Combinatorial representation theory. H. Barcelo and I have written a survey article about this field, its main questions and the main results:

Combinatorial representation theory, (with H. Barcelo), which appeared in the special volume in conjunction with the special year 1996-1997 in Combinatorics at MSRI in Berkeley: New perspectives in algebraic combinatorics (Berkeley, CA, 1996--97), 23--90, Math. Sci. Res. Inst. Publ., 38 , Cambridge Univ. Press, Cambridge, 1999.

Teaching: Semester II 2024

MAST10006 Calculus 2
         Lecture: Monday 13:00-14:00 PAR133 Glyn Davis B117
         Lecture: Wednesday 13:00-14:00 Glyn Davis B117
         Lecture: Friday 13:00-14:00 Glyn Davis B117
       See the timetable for the practice classes.
I will be taking the Prac Monday 2:15-3:15 in Peter Hall G10 (Practice Class P01_04)

Some recent projects

1. Our students have recently completed a paper which gives an inspring entrée to the world of Macdonald polynomials via usual, quantum and elliptic hook formulas.

Gypsy Akhyar, Yifan Guo and Lihexuan Yuan, Boxes and Polynomials,
The Mathematical Intelligencer (2022) https://doi.org/10.1007/s00283-022-10230-w
arxiv2203.00223.

A paper in tribute to Ian G. Macdonald, presented at FPSAC 2024 Bochum, Germany.

Ian G. Macdonald: Works of Art, Sém. Lothar. Combin. 91B (2024), Art. 0, 26 pp.
arxiv2408.01704.

Joint papers with Aritra Bhattacharya, Laura Colmenarejo, Zajj Daugherty, Weiying Guo and Tom Halverson about Macdonald polynomials:

c-functions and Koornwinder polynomials (with Laura Colmenarejo) In memory of Ian G. Macdonald,
arXiv2410.19957
Lusztig varieties and Macdonald polynomials Dedicated to Peter Littelmann
arXiv:2402.17935.
Clebsch-Gordan coefficients for Macdonald polynomials (with Aritra Bhattacharya)
arXiv2310.10846.
c-functions and Macdonald polynomials (with Laura Colmenarejo) In memory of Georgia Benkart,
J. Algebra 655 (2024), 163–222, MR4756469
arXiv2212.03312
Monk rules for type GL_n Macdonald polynomials (with Tom Halverson) In memory of Georgia Benkart,
J. Algebra 655 (2024), 493–516, MR4756478.
arXiv2212.04032
Set-valued tableaux for Macdonald polynomials (with Zajj Daugherty) In memory of Georgia Benkart,
Sém. Lothar. Combin. 89B (2023), Art. 42, 12 pp., MR4659550.
arXiv2212.04033
Comparing formulas for type GL_n Macdonald polynomials, and Supplement (with Weiying Guo) dedicated to Hélène Barcelo,
Algebraic Combinatorics (ALCO), 5 (2022) 849-883 and 885-923, DOI: 10.5802/alco.227 and DOI: 10.5802/alco.228.
arXiv2104.02942 and arXiv2104.04578.

2. The first of my Math is not broken series is now available.

Limits and topologies, preprint 2019, arXiv????.

3. The following work was performed in Melbourne 31 July 2018. It was presented by THE INSTITUTE FOR ENQUIRING MINDS. Special thanks to Ruth Höflich and Rachel Wilson and the wonderful audience. The transcript of the lecture is available: 'Maybe I Could ...' lecture transcript.

4. The following work was performed in Melbourne 20 July 2017 and (in an improved version) in Basel (11 March 2018) and in Munich (16 March 2018).

Last updated: April 4, 1935