I'm interested in symplectic topology and homological mirror symmetry, and connections to singularity theory, algebraic geometry, and geometric group theory. 

Preprints

• Homological mirror symmetry for projective K3 surfaces, with Paul Hacking

We prove the homological mirror symmetry conjecture of Kontsevich for K3 surfaces in the following form: The Fukaya category of a projective K3 surface is equivalent to the derived category of coherent sheaves on the mirror, which is a K3 surface of Picard rank 19 over the field C((q)) of formal Laurent series. This builds on prior work of Seidel, who proved the theorem in the case of the quartic surface, Sheridan, Lekili--Ueda, and Ganatra--Pardon--Shende. 

Articles

• A universal mirror to (P^2,Ω) as a birational object, with Abigail Ward

JEMS, accepted

• Symplectomorphisms of mirrors to log Calabi-Yau surfaces, with Paul Hacking

Geometry and Topology, accepted

• Symplectomorphisms and spherical objects in the conifold smoothing, with Ivan Smith

Compositio Math, 160 (2024), no 11, 2738-2773 

• On the order of Dehn twists, with Oscar Randal-Williams

NYJM,  volume 29 (2023), 203-212

• Homological mirror symmetry for log Calabi-Yau surfaces, with Paul Hacking 

Geometry and Topology, 26-8 (2022), 3747--3833

Oberwolfach report: here.

• On symplectic stabilisations and mapping classes

  Bulletin of the LMS, 54 (2) (2022), 718-736

• Families of monotone Lagrangians in Brieskorn--Pham hypersurfaces

Math. Annalen,  380(3) (2021), 975-1035 

• Symplectomorphisms of exotic discs, with Roger Casals and Ivan Smith; appendix by Sylvain Courte.

J. Éc. Polytech. Math. 5 (2018), 289–316 

• Homological mirror symmetry for hypersurface cusp singularities 

Selecta Math. (N.S.) 24 (2018), no. 2, 1411–1452 

• Lagrangian tori in four-dimensional Milnor fibres 

Geom. Funct. Anal. 25 (2015), no. 6, 1822–1901 

• Dehn twists and free subgroups of symplectic mapping class groups 

Journal of Topology 7 (2014), no. 2, 436–474