He studies moduli problems in algebraic geometry, and ‘mirror symmetry’—a phenomenon in pure mathematics predicted by string theory in theoretical physics.

[6] Motivated by homological mirror symmetry, he produced braid group actions on derived categories of coherent sheaves in joint work with Paul Seidel.

[9] With Martijn Kool and Vivek Shende, he used the PT invariants to prove the Göttsche conjecture—a classical algebro-geometric problem going back more than a century.

Much of his work is related to mirror symmetry and Calabi–Yau geometry, and thus has an important bearing on exciting contemporary interactions with mathematical physics.

"[21] In 2010 he also was invited speaker for the algebraic geometry section at the International Congress of Mathematicians in Hyderabad, where he delivered a lecture on mirror symmetry.