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

Preprints

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

Let M be a Weinstein four-manifold mirror to Y\D for (Y,D) a log Calabi--Yau surface; intuitively, this is typically the Milnor fibre of a smoothing of a cusp singularity. We introduce two families of symplectomorphisms of M: Lagrangian translations, which we prove are mirror to tensors with line bundles; and nodal slide recombinations, which we prove are mirror to automorphisms of (Y,D). The proof uses a detailed compatibility between the homological and SYZ view-points on mirror symmetry. Together with spherical twists, these symplectomorphisms are expected to generate all autoequivalences of the wrapped Fukaya category of M which are compactly supported in a categorical sense. A range of applications is given. 

Articles

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

Compositio Math, accepted.

• 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