Teaching Responsibilities 2020/21:
Term 1: MA951 Graduate Algebra
Term 2: MA106 Linear Algebra
Research Interests: Homotopical methods in algebraic geometry:
algebraic K-theory; A1-homotopy theory; motivic cohomology; homology of classical groups; higher Grothendieck-Witt groups; derived categories
Research supported by :
- EPSRC standard grant EP/M001113/1, 28th Feb 2015 -- 27th Feb 2018
- Leverhulme fellowship: 1st October 2018 -- 30th September 2019
- Euler class groups and the homology of special and elementary linear groups, Adv. Math. 320 (2017), 1-81.
- The homotopy fixed point theorem and the Quillen-Lichtenbaum conjecture in hermitian K-theory; joint with A.J. Berrick, M. Karoubi and P.A. Østvær, Adv. Math. 278 (2015), 34-55.
- The Mayer-Vietoris principle for Grothendieck-Witt groups of schemes, Invent. Math. 179 (2010), no. 2, 349 - 433.
- Cyclic homology, cdh-cohomology and negative K-theory, joint with G. Cortiñas, C. Häsemeyer and C. A. Weibel, Ann. of Math. 167 (2008), 549 - 573.
- A note on K-theory and triangulated categories, Invent. Math. 150 (2002), no. 1, 111 - 116.