Nick Sheridan has been awarded an ERC Starting Grant worth over £1 million entitled 'Homological mirror symmetry, Hodge theory and symplectic topology'. Mirror symmetry is a deep relationship between algebraic and symplectic geometry, with origins in string theory. It was originally envisioned as an isomorphism between the Hodge theory of an algebraic variety and the quantum Hodge theory' of a mirror' symplectic manifold, but it was subsequently realized by Kontsevich that the relationship went far deeper. His Homological Mirror Symmetry (HMS) conjecture predicts an equivalence between the derived category of the variety and the Fukaya category of its mirror, and has far-reaching implications for diverse areas of mathematics. In previous work Nick has proved the conjecture in fundamental cases, established its precise relationship with the Hodge-theoretic version of mirror symmetry, and used these results to solve questions in enumerative geometry and symplectic topology. The proposed research centres on HMS, new aspects of its relationship with Hodge theory, and new applications to symplectic topology. https://erc.europa.eu/news/StG-recipients-2019