I am an Associate Professor at the University of Sydney, where I am a member of the Algebra Group. My interests are in algebraic and geometric aspects of representation theory, invariant theory, algebraic combinatorics, and categorification. Here is my CV.
Contact InformationDepartment of Mathematics & Statistics
University of Sydney NSW 2006
Office: Carslaw 724
- Wednesdays, 11-12
- Or by appointment...
- In Semester 1 2021 I am teaching Math 3066, a third year course on Algebra and Logic.
- During the February and July Intensive periods I will be teaching OLEO1624/1625, Reading and Writing Mathematics.
- 2018, 2019, 2020 - Math 3066, a third year course on Algebra and Logic.
- 2018, 2019, 2020 - OLEO1624/1625, an online course titled Reading and Writing Mathematics.
- 2017, 2018 - MATH1907 - a Special Studies Programme for advanced first year students on the Euler characteristic.
- 2015, 2016 - MPH2 - I taught the Honours course commutative algebra.
- 2014 - MATH3962 - I taught the second half of this third year advanced course on Galois Theory.
- 2014 - MATH2916 - a second year TSP course on knot theory.
- 2013, 2014, 2018 - 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
I. Truncated shifted Yangians and slices in the affine Grassmannian
We study slices to Schubert varieties in the affine Grassmannian. These slices are Poisson varieties, and we define quantisations of them using quotients of shifted Yangians. Currently we are studying their representation theory in connection with symplectic duality and the generalised Geometric Satake Correspondence.
|On a conjecture of Pappas and Rapoport about the standard local model for GL_d||D. Muthiah and A. Weekes||to appear in Crelle's Journal||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||to appear in IMRN||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|
|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|
|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|
II. Categorical representation theory and quantum algebra
These are a mix of papers, some of which are closely connected to each other. The papers with Jiuzu Hong and Antoine Touzé concern strict polynomial functors and their role in categorical representation theory. With Alistair Savage and Hoel Queffelec we've studied various guises of Heisenberg categorification, and its relation to the ``standard'' Khovanov-Lauda categorification of affine Lie algebras. With Rami Aizenbud we proved that quantum analog of the classical result that functions on nxn matrices are free over their Poisson center.
|Categorical braid group actions and cactus groups||I. Halacheva, A. Licata, I. Losev||submitted||2101.05931|
|A note on categorification and spherical harmonics||A. Arunasalam, J. Ciappara, D. M. H. Nguyen, S. J. Tan||Algebras and Representation Theory (2019)||-|
|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|
|Quantum polynomial functors||Jiuzu 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|
|Polynomial functors and categorification of Fock space II||Jiuzu Hong||Advances in Math. Volume 237, 360-403 (2013)||1111.5335|
|Polynomial functors and categorification of Fock space||Jiuzu Hong, Antoine 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||Jiuzu 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||Avraham Aizenbud||Journal of Algebra 343 (2011), pp. 183-194||1007.0133|
III. Branching of symplectic group representations
This papers are related to my Ph.D. thesis, where I studied finite dimensional representations of the symplectic group Sp2n, and their restriction to the rank n-1 symplectic subgroup. This restriction is not multiplicity-free, and I showed that by studying the branching algebra one can endow the multiplicity spaces with irreducible actions of a product of n SL2's. This is explained in more detail in my report Multiplicity spaces in symplectic branching.
|A basis for the symplectic group branching algebra||Sangjib 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.
|Nolan Wallach||Contemp. Math. 490||-|
- The Algebra Seminar is on hiatus.
- The Informal Friday Seminar meets every Friday usually at 3pm, and is organised by Anna Romanova and Geordie Williamson.
- Local algebra students will be interested in the Student Algebra Seminar, organised by Josh Ciappara.
- SMRI hosts the Algebra and Geometry Online Seminar.
Current PhD Students
- Joshua Ciappara (co-supervised with Geordie Williamson)
- Chris Hone (co-supervised with Geordie Williamson)
- Giulian Wiggins
Past PhD Students
- Joel Gibson (completed his PhD in 2020)
- Joshua Ciappara (2015)
- Michael Crawford (2015)
- Giulian Wiggins (2016)
- Oliver Alexander (2017)
- Angus Johnson (2018-19)
- Jongmin Lim (2020)
- Michael Zhao (2020)