Dr van Garrel is a researcher in algebraic geometry and mirror symmetry. He specialises 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. Using the Gross-Siebert programme, he developed new instances of mirror symmetry for log Calabi-Yau surfaces with smooth boundary.
Dr van Garrel has organised 13 conferences that 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. In addition, Dr van Garrel is an organiser for the LMS Midlands Regional Meeting 2022 at the University of Birmingham. He has given invited talks in 12 countries on 3 continents. He was an invited speaker at the Algebraic Geometry Session of the British Mathematical Colloquium 2021.