||I am a Royal Society University Research Fellow in the Mathematical Institute at Oxford University.
||T2 Mathematical Institute
||24-29 St Giles'
Oxford, OX1 3LB.
||+44 (0)1865 273541
My research is in geometric representation theory- more specifically I am interested in algebraic groups, quantum groups and the geometry and topology of varieties associated to them.
Recently I have been working on quantum groups at a root of unity and their relation to the rational Cherednik algebra and the Hilbert scheme of points in the plane.
Cells in quantum affine sl_n, Int. Math. Res. Not. 2003, no.24, 1341--61.
The Kronecker quiver and bases of quantum affine sl_2, Adv. Math. 197, (2005), no. 2, 411-429.
Generalized q-Schur algebras and Quantum Frobenius, Adv. Math. (2007), no. 1, 116--131.
Langlands duality for representations and quantum groups at a root of unity, Comm. Math. Phys. 296 (2010), no. 1, 89-109.
Hall algebras and Quantum Frobenius, Duke Math. J. 154 (2010), no. 1, 181--206.
On the geometric realization of the inner product and canonical basis for quantum affine sl_n, Algebra Number Theory 6 (2012) no. 6, 1097-1131.
On the center of the cyclotomic Hecke algebra of G(m,1,2), Proc. Edinb. Math. Soc. (2) 55 (2012) no. 2, 497-506.
Microlocal KZ functors and rational Cherednik algebras, Duke Math. J. 161 (2012), no. 9, 1657-1709.
Derived equivalence for quantum symplectic resolutions, joint with T. Nevins, Selecta Math. (available online))
My preprints (and papers in preprint form) are all available on the arXiv.
- Notes for a talk on Representations of the Symmetric group and constructible functions on the Steinberg variety.
I am Tutor in Pure Mathematics at Christ Church. Details for college teaching are here. This term I am also teaching the Part A Algebra II course.
Previously, I have taught courses on such things as Lie algebra and the Classical Groups.
I am organizing a short conference funded by the LMS on the interactions between mirror symmetry and geometric representation theory in the context of symplectic resolutions in July. Go here for more information.
Any resemblances to the webpage of a (former) colleague are entirely uncoincidental.