Oded Yacobi

I am a senior lecturer 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 Information

Department of Mathematics & Statistics
University of Sydney NSW 2006
Office: Carslaw 724
e-mail: oded.yacobi@sydney.edu.au
Phone: +61-2-9351-5460

Current Teaching - Semester II 2018

Past Teaching

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 the highest weight theory of these algebras.

Title Joint with Status arXiv
On Category O for affine Grassmannian slices and categorified tensor products J. Kamnitzer, P. Tingley, B. Webster and A. Weekes submitted 1806.07519
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 Proceedings of the AMS, 146, No. 2, 861-874, (2018) 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.

Title Joint with Status arXiv
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, 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.

Title Joint with Status arXiv
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.

We are currently running a reading group on the Geometric Satake Correspondence.

Local algebra students might also be interested in the Student Algebra Seminar, organised by Joel Gibson.

In December 2018 we are organising a MATRIX workshop on Geometric and Categorical Representation Theory. This will feature a series of lectures by Luca Migliorini.

PhD Students

Joel Gibson

Giulian Wiggins

Honours Students

Joshua Ciappara (2015)

Michael Crawford (2015)

Giulian Wiggins (2016)

Oliver Alexander (2017)

Angus Johnson (2018)