Associate Professor in Geometry
The Roger Penrose Fellow and Tutor in Mathematics, Wadham College
+44 1865 273556
University of Oxford
Andrew Wiles Building
Radcliffe Observatory Quarter
Invariance of symplectic cohomology and twisted cotangent bundles over surfaces
(5 July 2018) Full text available
The monotone wrapped Fukaya category and the open-closed string map
Selecta Mathematica issue 1 volume 23 page 533-642 (9 January 2017)
Circle-actions, quantum cohomology, and the Fukaya category of Fano toric varieties
Geometry and Topology issue 4 volume 20 page 1941–2052- (15 September 2016)
Floer theory for negative line bundles via Gromov-Witten invariants
Advances in Mathematics volume 262 page 1035-1106 (10 September 2014)
Topological quantum field theory structure on symplectic cohomology
Journal of Topology issue 2 volume 6 page 391-489 (17 January 2013)
Deformations of symplectic cohomology and exact Lagrangians in ALE spaces
Geometric and Functional Analysis issue 3 volume 20 page 779-816 (1 September 2010)
Novikov-symplectic cohomology and exact Lagrangian embeddings
Geometry and Topology issue 2 volume 13 page 943-978 (8 January 2009)
Symplectic topology, Floer theory, Fukaya categories, Homological mirror symmetry.
Oxford OX1 3PN,
HT2020: C2.6 Introduction to Schemes
MT2019: C3.1 Algebraic Topology
MT2018: C3.4 Algebraic Geometry
MT2018: B3.2 Geometry of Surfaces
MT2017: C3.4 Algebraic Geometry
MT2017: B3.2 Geometry of Surfaces
MT2016: C3.4 Algebraic Geometry
MT2016: B3a Geometry of Surfaces
MT2015: C3.4 Algebraic Geometry
MT2015: B3a Geometry of Surfaces
HT2015: C3.4b Lie Groups
MT2014: B3a Geometry of Surfaces
Summer 2014: Lectures on Geometry, Topology, and Penrose Tilings (Oxford Masterclasses)
HT2014: C3.4b Lie Groups
MT2013: Graduate Course, Morse Homology
HT2013: C3.4b Lie Groups
Prizes, awards, and scholarships:
2009-2013 Junior Research Fellow, Trinity College, Cambridge.
2019 Co-Investigator on the EPSRC standard grant EP/T012749/1: 3-year grant, £643K, PI: Dominic Joyce, Co-Investigator: Jason Lotay.
Major / recent publications:
Novikov-symplectic cohomology and exact Lagrangian embeddings, Geometry & Topology 2009.
Deformations of symplectic cohomology and exact Lagrangians in ALE spaces, GAFA 2010.
Topological quantum field theory structure on symplectic cohomology, Journal of Topology 2013.
Floer theory for negative line bundles via Gromov-Witten invariants, Advances in Mathematics 2014.
Circle-actions, quantum cohomology, and the Fukaya category of Fano toric varieties, Geometry and Topology 2016.
The monotone wrapped Fukaya category and the open-closed string map, Selecta Mathematica 2017 (joint work with Ivan Smith).
The McKay correspondence via Floer theory, arXiv:1802.01534, 2018 (joint work with Mark McLean)
Invariance of symplectic cohomology and twisted cotangent bundles over surfaces, arXiv:1807.02086, 2018 (joint work with Gabriele Benedetti)