Publications

Publications

(With Ivan Smith) Homological mirror symmetry for generalized Greene--Plesser mirrors, Inventiones Mathematicae, to appear, arXiv.

(With Ivan Smith) Lagrangian cobordism and tropical curves, Journal für die reine und angewandte Mathematik (Crelle's Journal), to appear, arXiv.

(With Ivan Smith) Symplectic topology of K3 surfaces via mirror symmetry, Journal of the American Mathematical Society, to appear, arXiv.

(With Ivan Smith) Rational equivalence and Lagrangian tori on K3 surfaces, Commentarii Mathematici Helvetici, to appear, arXiv.

(With Mohammed Abouzaid, Sheel Ganatra and Hiroshi Iritani) The Gamma and Strominger--Yau--Zaslow conjectures: a tropical approach to periods, Geometry & Topology, to appear, arXiv.

Versality of the relative Fukaya category, Geometry & Topology, to appear, arXiv.

Formulae in noncommutative Hodge theory, Journal of Homotopy and Related Structures, 15 (2020), no. 1, 249-299, journal link, doi 10.1007/s40062-019-00251-2, arXiv.

Versality in mirror symmetry, Current Developments in Mathematics, 2017, 37-86, journal link, doi 10.4310/CDM.2017.v2017.n1.a2 arXiv.

On the Fukaya category of a Fano hypersurface in projective space, Publications mathématiques de l'IHÉS, 124 (2016), no. 1, 165-317, journal link, doi 10.1007/s10240-016-0082-8, arXiv.

Homological Mirror Symmetry for Calabi-Yau hypersurfaces in projective space, Inventiones Mathematicae, 199 (2015), no. 1, 1-186, journal link, doi 10.1007/s00222-014-0507-2, arXiv.

On the homological mirror symmetry conjecture for pairs of pants, Journal of Differential Geometry, 89 (2011), no. 2, 271-367, journal link, arXiv.

Preprints

(With Tim Perutz and Sheel Ganatra) Mirror symmetry: from categories to curve counts, 37 pages, arXiv.

(With Tim Perutz) Automatic split-generation for the Fukaya category, 24 pages, arXiv.

(With Tim Perutz) Constructing the relative Fukaya categgory, 43 paes, arXiv.