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.
My CV is available upon request.
Contact InformationDepartment of Mathematics & Statistics
University of Sydney NSW 2006
Office: Carslaw 724
Current Teaching - Semester I 2016
- I am not currently teaching.
- Tuesdays 3-4pm
- Or by appointment...
- 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.
|A proof of the reducedness conjecture in type A||J. Kamnitzer, D. Muthiah and A. Weekes||in preparation||-|
|A quantum Mirkovic-Vybornov isomorphism||B. Webster and A. Weekes||in preparation||-|
|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. Polynomial functors, categorification, and quantum algebra
Description coming soon.
|Categorifying a principal embedding of the Heisenberg algebra (provisional title)||H. Queffelec, A. Savage||in preparation||-|
|Quantum polynomial functors||Jiuzu Hong||submitted||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 main Algebra Seminar meets every Friday at noon.
We are co-organising with Peter MacNamara and Arun Ram a week-long workshop (Nov 28 - Dec 2) at the University of Melbourne. It will be led by Tomoyuki Arakawa and Anne Moreau and focus on W-algebras, vertex algebras, and related topics. Further details will be posted here
Tony Licata and I are organizing the Representation Theory Session at this year's AustMS meeting in Canberra.
Andrew Mathas and I co-organised Representation Theory Day in August 2015.
In the past, I've also been involved with...
- a learning seminar on aspects of higher representation theory and categorification
- the geometric representation theory seminar
- a learning seminar on modular tensor categories
- the geometric representation theory seminar
In May 2012 I co-organized with Chris Dodd and Alex Hoffnung a three day workshop hosted by the Fields Institute on Higher Algebraic and Geometric Structures in Representation Theory.