I am an Associate Professor at the University of Sydney, where I am a member of the Algebra Group and the Associate Head (Research) at the School of Mathematics and Statistics. My interests are in algebraic and geometric aspects of representation theory, invariant theory, algebraic combinatorics, and categorification.
I am an Associate Editor at the Journal of the Australian Mathematics Society. Please submit your papers by following this link.
Contact Information
Department of Mathematics & StatisticsUniversity of Sydney NSW 2006
Australia
Office: Carslaw 724
e-mail: [email protected]
Phone: +61-2-9351-5460
Past Teaching
- 2014, 2023 - MATH3962 - third year advanced course on Rings, Fields and Galois Theory.
- 2018-21 - Math 3066, a third year course on Algebra and Logic.
- 2018-22 - OLEO1624/1625, an online course titled Reading and Writing Mathematics.
- 2017-18, 2022 - MATH1907 - a Special Studies Programme for advanced first year students on the Euler characteristic.
- 2015-16 - MPH2 - I taught the Honours course commutative algebra.
- 2014 - MATH2916 - a second year TSP course on knot theory.
- 2013-14, 2018, 2022-23 - MATH1004/1904 - a first year discrete mathematics course - University of Sydney
- 2013 - Math 224 - a second semester course in linear algebra - University of Toronto
- 2013 - Math 223 - a first semester course linear algebra - University of Toronto
- 2012 - Math 195 - second semester calculus course in Engineering Sciences - University of Toronto
- 2011 - Math 188 - linear algbera for engineers - University of Toronto
- 2010, 2011 - Math 133 - a year long financial calculus sequence - University of Toronto
- 2008 - Math 20C - calculus for life science - UC San Diego
My papers and preprints
| Title | Joint with | Status | arXiv |
|---|---|---|---|
| 4-Strand Burau is Unfaithful Modulo 5 | J. Gibson and G. Williamson | submitted | 2310.02403 |
| On the action of the Weyl group on canonical bases | F. Gossow | submitted | 2306.08857 |
| Lie algebra actions on module categories for truncated shifted Yangians | J. Kamnitzer, B. Webster and A. Weekes | Forum Math. Sigma (2024) Vol. 12, 1-69 | 2203.12429 |
| On the action of the long cycle on the Kazhdan-Lusztig basis | F. Gossow | FPSAC proceedings (2022) | 2111.09510 |
| On Schützenberger modules of the cactus group | J. Lim | Algebraic Combinatorics, Vol. 6, no.3 (2023), 773-788 | 2109.09312 |
| Categorical braid group actions and cactus groups | I. Halacheva, A. Licata, I. Losev | Advances in Math., Vol. 429 (2023) | 2101.05931 |
| On a conjecture of Pappas and Rapoport about the standard local model for GL_d | D. Muthiah and A. Weekes | Journal für die Reine und Angewandte Mathematik 772 (2021), 175-185 | 1912.06822 |
| On Category O for affine Grassmannian slices and categorified tensor products | J. Kamnitzer, P. Tingley, B. Webster and A. Weekes | Proceedings of the LMS, (3), 119, 1179-1233, (2019) | 1806.07519 |
| The equations defining affine Grassmannians in type A and a conjecture of Kreiman, Lakshmibai, Magyar, and Weyman | D. Muthiah and A. Weekes | IMRN, iss. 3, 1922-1972 (2022) | 1708.06076 |
| Reducedness of affine Grassmannian slices in type A | J. Kamnitzer, D. Muthiah and A. Weekes | Proceedings of the AMS, 146, No. 2, 861-874, (2018) | 1611.06775 |
| A quantum Mirkovic-Vybornov isomorphism | B. Webster and A. Weekes | Representation Theory, 24 (2020), 38-84 | 1706.03841 |
| An equivalence between truncations of categorified quantum groups and Heisenberg categories | H. Queffelec, A. Savage | Journal de l'École Polytechnique, Tome 5 (2018), 197-238 | 1701.08654 |
| Highest weights for truncated shifted Yangians and product monomial crystals | J. Kamnitzer, P. Tingley, B. Webster and A. Weekes | Journal of Combinatorial Algebra, 3, (2019), no. 3, 237-303 | 1511.09131 |
| A note on categorification and spherical harmonics | A. Arunasalam, J. Ciappara, D. M. H. Nguyen, S. J. Tan | Algebras and Representation Theory (2019) | - |
| Quantum polynomial functors | J. Hong | Journal of Algebra (479) 2017, pp. 326-367 | 1504.01171 |
| Categorification and Heisenberg doubles arising from towers of algebras | A. Savage | J. Comb. Th. Series A 129 (2015), 19-56. | 1309.2513 |
| Yangians and quantizations of slices in the affine Grassmannian | J. Kamnizter, B. Webster, A. Weekes | Algebra and Number Theory 8-4 (2014), 857-893. | 1209.0349 |
| Polynomial functors and categorification of Fock space II | J. Hong | Advances in Math. Volume 237, 360-403 (2013) | 1111.5335 |
| Polynomial functors and categorification of Fock space | J. Hong, A. Touze | Symmetry: Representation Theory and its Applications in honor of Nolan Wallach, Progress in Mathematics, Birkauser, (2015) | 1111.5317 |
| Polynomial representations and categorification of Fock space | J. Hong | Algebras and Representation Theory 16 (2013), no. 5, 1273-1311 | 1101.2456 |
| A quantum analogue of Kostant's theorem for the general linear group | A. Aizenbud | Journal of Algebra 343 (2011), pp. 183-194 | 1007.0133 |
| A basis for the symplectic group branching algebra | S. Kim | Journal of Algebraic Combinatorics (2011) | 1005.2320 |
| An anlaysis of the multiplicity spaces in branching of symplectic groups | - | Selecta Math N.S., Volume 16, Issue 4, (2010) | 0907.3247 |
| A multiplicity formula for tensor products of SL2 modules and an explicit Sp2n to Sp2n-2x Sp2 branching formula. |
N. Wallach | Contemp. Math. 490 | - |
Local Seminars
Past Events
- A public lecture I gave at the International Day of Mathematics (2023) about Galois:
- A seminar about the action of the Weyl group on canonical bases I gave at Northeastern University in March, '22:
Current PhD Students
- Chris Hone (Associate supervisor)
- Eloise Little (Associate supervisor)
Past PhD Students
- Gaston Burrull (Associate supervisor, completed in 2022)
- Joshua Ciappara (Associate supervisor, completed in 2023)
- Joel Gibson (Primary supervisor, completed in 2020)
- Giulian Wiggins (Primary supervisor, completed in 2023)
Honours Students
- Oliver Alexander (2017)
- Joshua Ciappara* (2015)
- Michael Crawford (2015)
- Fern Gossow* (2021)
- Nikola Grujic (2022)
- Angus Johnson (2018-19)
- Jongmin Lim* (2020)
- Giulian Wiggins (2016)
- Michael Zhao (2020)
* Recipient of University Medal and Joye Prize for Most Outstanding Honours Student.