Kevin McGerty

		I am a Royal Society University Research Fellow in the Mathematical Institute at Oxford University.
		Office:   T2 Mathematical Institute Postal Address: 24-29 St Giles' Oxford, OX1 3LB. United Kingdom Phone: +44 (0)1865 273541 Email: mcgerty@maths.ox.ac.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.
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.

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. to appear, Algebra and Number Theory.
• On the center of the cyclotomic Hecke algebra of G(m,1,2), to appear, Proceedings of the Edinburgh Mathematical Society.
• Microlocal KZ functors and rational Cherednik algebras, accepted, Duke Mathematical Journal.

Preprints

• Derived equivalence for quantum symplectic resolutions, joint with T. Nevins, submitted.
• A Geometric construction of the Quantum Frobenius morphism, preprint.
• Notes for a talk on Representations of the Symmetric group and constructible functions on the Steinberg variety.

Teaching

Conferences

Miscellaneous