Research

Summary

I work on problems in geometry and topology. I am particularly interested in the symplectic topology of algebraic varieties.

My research is supported by EPSRC Grant EP/W015749/1 "New Frontiers in Symplectic Topology" (a joint grant with YankI Lekili at Imperial College London, running 2022-2026). From 2017-2020, my research was supported by EPSRC Grant EP/P02095X/2 "Singularities and Symplectic Topology" (formerly known as EP/P02095X/1 when I was at UCL).

Papers/books

Lectures on Lagrangian torus fibrations.
a book, arXiv:2110.08643
Symplectic cohomology of compound Du Val singularities.
with Y. Lekili, arXiv:2104.11713
to appear in Annales Henri Lebesgue.
A Lagrangian Klein bottle you can't squeeze.
arXiv:2009.01546
Journal of Fixed Point Theory and Applications Volume 24 (2022) Article number 47, in Symplectic geometry - A Festschrift in honour of Claude Viterbo’s 60th birthday
Constructing local models for Lagrangian torus fibrations.
with M. Mauri, arXiv:1905.09229
Annales Henri Lebesgue, Volume 4 (2021), pp. 537-570.
Antiflips, mutations, and unbounded symplectic embeddings of rational homology balls.
with G. Urzúa, arXiv:1807.06073
Annales de l'Institut Fourier, Volume 71 (2021) no.5 pp. 1807-1843.
Bounds on Wahl singularities from symplectic topology.
with I. Smith, arXiv:1708.02268
Algebraic Geometry, (2020) 1(1) 59-85.
Markov numbers and Lagrangian cell complexes in the complex projective plane.
with I. Smith, arXiv:1606.08656
Geometry & Topology (2018) 22(2):1143-1180.
Generating the Fukaya categories of Hamiltonian G-manifolds.
with Y. Lekili, arXiv:1507.05842
Journal of the American Mathematical Society (2019) 32:119-162.
Exotic spheres and the topology of symplectomorphism groups.
with G. Dimitroglou Rizell, arXiv:1407.3173
Journal of Topology (2015) 8(2):586-602.
Floer cohomology of the Chiang Lagrangian.
with Y. Lekili, arXiv:1401.4073
Selecta Mathematica (2015) 21(4):1361-1404.
Unlinking and unknottedness of Lagrangian submanifolds.
with G. Dimitroglou Rizell, arXiv:1211.6633
Geometry & Topology, (2014) 18:997-1034.
Pseudoholomorphic tori in the Kodaira-Thurston manifold.
with J. Kędra, arXiv:1205.1239
Compositio Mathematica (2015) 151(12) 2212-2250.
Remarks on monotone Lagrangians in Cn.
with J. Kędra, arXiv:1110.0927
Mathematical Research Letters (2014) 6:1241-1255.
The infimum of the Nijenhuis energy.
arXiv:1109.4854
Mathematical Research Letters, (2012) 19(2):383-388.
Quantum cohomology of twistor spaces and their Lagrangian submanifolds.
arXiv:1106.3959
Journal of Differential Geometry, (2014) 96(3)353-397.
Symplectic mapping class groups of some Stein and rational surfaces.
arXiv:0909.5622
Journal of Symplectic Geometry (2011) 9(1):45-82.
Lagrangian spheres in Del Pezzo surfaces.
arXiv:0902.0540
Journal of Topology (2010) 3(1):181-227.

Talks

A Lagrangian Klein bottle you can't squeeze
Western Hemisphere Virtual Symplectic Seminar (September 2020): YouTube version
Symplectic embeddings of rational homology balls
Glasgow Topology Seminar (October 2019): YouTube version
KIAS Lectures on Symplectic aspects of degenerations
Three lectures given at the 2019 ASADCS conference in Seoul: notes
Lagrangian cell complexes and Markov numbers
Institute for Advanced Study (September 2016): video
Exotic spheres and the topology of symplectomorphism groups
Simons Center for Geometry and Physics (August 2014): video and slides
Lectures on symplectic and algebraic geometry
UK-Japan Mathematical Forum (January 2013): notes from Lecture 1, Lecture 2, Lecture 3 and accompanying blog post
The quantum cohomology of twistor spaces
CAST Workshop, Madrid (February 2012), slides
Lagrangian spheres in Del Pezzo surfaces
Lyon, February 2011 and Oxford, April 2010
Symplectic Picard-Lefschetz theory (expository, mostly pictures!)
Slides from a colloquium I gave in Neuchâtel (April 2012).
Luttinger surgery (expository)
ENS Lyon (January 2012) expository notes
Slides/notes from successful job/postdoc talks
Lancaster
UCL
ETH

Research community

PhD students

Postdocs

Collaborators