Kevin McGerty

I am an Associate Professor in the Mathematical Institute at Oxford University.

Office:		N3.16 Mathematical Institute
Postal Address:		Andrew Wiles Building, Radcliffe Observatory Quarter, Woodstock Road, Oxford, OX2 6GG. United Kingdom
Phone:		+44 (0)1865 273541
Email:		mcgerty at maths dot ox dot ac dot uk

Research Interests

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.
My recent work has focused on symplectic resolutions and their quantizations, especially the many examples arising from Hamiltonian reduction.

Publications

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. (N.S.) 20 (2014), no. 2, 675–717.
Categorical Cell Decomposition of Quantized Symplectic Algebraic Varieties, joint with G. Bellamy , Christopher Dodd, T. Nevins, to appear, Geometry & Topology.
Compatibility of t-structures for quantum symplectic resolutions., joint with T. Nevins, Duke Math. J. 165 (2016), no. 13, 2529–2585.

Preprints

arXiv

Notes for a talk on Representations of the Symmetric group and constructible functions on the Steinberg variety.

Teaching

I am Tutor in Pure Mathematics at Christ Church. This Michaelmas I lectured Metric Spaces and Complex Analysis . Previously, I have taught courses on such things as Lie Algebras, Rings and Modules, Groups and Representation Theory (Imperial) and the Classical Groups (Chicago).