Oded Yacobi

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 Information

Department of Mathematics & Statistics
Carslaw Building
University of Sydney NSW 2006
Office: Carslaw 724
e-mail: oded.yacobi@sydney.edu.au

Current Teaching - Semester I 2016


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 (conjectural) quantisations of them using quotients of shifted Yangians. Currently we are studying the highest weight theory of these algebras using monomial crystals.

Title Joint with Status arXiv
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.

Title Joint with Status arXiv
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.

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 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 focus on W-algebras, vertex algebras, and related topics. Further details will be posted here

Andrew Mathas and I co-organised Representation Theory Day in August 2015.

In the past, I've also been involved with...

Fall 2012

Spring 2012

Fall 2011

Spring 2011

Fall 2010

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.