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 19961997 in Combinatorics at MSRI in Berkeley:
New perspectives in algebraic combinatorics
(Berkeley, CA, 199697),
2390, Math. Sci. Res. Inst. Publ., 38 ,
Cambridge Univ. Press, Cambridge, 1999.
Teaching: Semester II 2024
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.
A paper in tribute to Ian G. Macdonald, presented at
FPSAC 2024 Bochum, Germany.
Joint papers with Aritra Bhattacharya,
Laura Colmenarejo,
Zajj Daugherty,
Weiying Guo
and
Tom Halverson
about Macdonald polynomials:

cfunctions 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.

ClebschGordan coefficients for Macdonald polynomials
(with Aritra Bhattacharya)
arXiv2310.10846.

cfunctions 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

Setvalued 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) 849883 and 885923,
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