Dr. van Garrel is a researcher in algebraic geometry and mirror symmetry. He specializes in enumerative geometry, in particular log Gromov-Witten theory, in birational geometry, especially with regards to rationality questions and in the Gross-Siebert programme as the mechanism that explains mirror symmetry and constructs mirror families.
Among his most important contributions, Dr. van Garrel initiated new unexpected correspondences of different enumerative theories in different dimensions, relating log, open and local Gromov-Witten invariants, quiver Donaldson-Thomas invariants as well as sheaf counting invariants of local Calabi-Yau fourfolds.
Dr. van Garrel has organized 12 conferences to build on the growing research communities around these themes. Besides an online conference, these took place at Cambridge, Imperial, the Mathematical Research Institute of Oberwolfach and the Korea Institute for Advanced Study. He has given invited talks in 12 countries on 3 continents.