## Research

### Summary

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

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
- A Lagrangian Klein bottle you can't squeeze.
- arXiv:2009.01546
- to appear in Journal of Fixed Point Theory and Applications (special volume for 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
- to appear in Annales de l'Institut Fourier.
- 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
**C**^{n}. - 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

- Matt Buck
- Patrick Ramsey
- Emily Maw
- Momchil Konstantinov (graduated 2019), Thesis: Symplectic topology of projective space: Lagrangians, local systems and twistors.
- Tobias Sodoge (graduated 2017) Thesis: The geometry and topology of stable coisotropic submanifolds.

#### Postdocs

- Daniel Cavey (Jan 2020 - Dec 2020)
- Jack Smith (2017 - 2019)