I am a senior lecturer and an ARC Research Fellow at the University of Sydney, where I am a member of the Algebra Group. Previously I was a postdoctoral fellow at the University of Toronto, working with Joel Kamnitzer, and I also spent a year at Tel Aviv University with Joseph Bernstein. I completed my Ph.D. in 2009 at UC San Diego, where my advisor was Nolan Wallach.
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
Current Teaching - Semester II 2017
- I am currently teaching one module of Math 1907, the Special Studies Programme for advanced first year students. I am giving four lectures on Euler's formula for planar graphs n-e+f=2. We'll prove this formula and give some applications. Hopefully we'll also have some time to discuss the Euler characteristic of surfaces.
- Semester I 2015,2016 - MPH2 - I taught the Honours course commutative algebra.
- Semester I 2014 - MATH3962 - I taught the second half of this third year advanced course on Galois Theory.
- Semester I 2014 - MATH2916 - a second year TSP course on knot theory.
- Semester II 2013,2014 - MATH1004 - a first year discrete mathematics course - University of Sydney
- Spring 2013 - Math 224 - a second semester course in linear algebra - University of Toronto
- Fall 2013 - Math 223 - a first semester course linear algebra - University of Toronto
- Spring 2012 - Math 195 - second semester calculus course in Engineering Sciences - University of Toronto
- Winter 2011 - Math 188 - linear algbera for engineers - University of Toronto
- 2010-11 - Math 133 - a year long financial calculus sequence - University of Toronto
- Spring 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 (conjectural) quantisations of them using quotients of shifted Yangians. Currently we are studying the highest weight theory of these algebras using monomial crystals.
|The equations defining affine Grassmannians in type A and a conjecture of Kreiman, Lakshmibai, Magyar, and Weyman||D. Muthiah and A. Weekes||submitted||1708.06076|
|Reducedness of affine Grassmannian slices in type A||J. Kamnitzer, D. Muthiah and A. Weekes||to appear in PAMS||1611.06775|
|A quantum Mirkovic-Vybornov isomorphism||B. Webster and A. Weekes||submitted||1706.03841|
|Highest weights for truncated shifted Yangians and product monomial crystals||J. Kamnitzer, P. Tingley, B. Webster and A. Weekes||submitted||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.
|An equivalence between truncations of categorified quantum groups and Heisenberg categories||H. Queffelec, A. Savage||submitted||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, June 2012||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||-|
Our Algebra Seminar meets every Friday at noon.
In November 2017 I will be spending the month at HIM in Bonn as part of this Trimester Program.
In December 2017 we are organising a conference Future Directions in Representation Theory at the University of Sydney.
In December 2018 we are organising a MATRIX workshop on Geometric and Categorical Representation Theory.
- Joel Gibson
- Alexander Kerschl (auxiliary supervisor)
- Giulian Wiggins
- Yee Yau (auxiliary supervisor)
- Joshua Ciappara (2015)
- Michael Crawford (2015)
- Giulian Wiggins (2016)
- Oliver Alexander (2017)