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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.
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.
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arXiv (Cornell University) (2023)
SELECTA MATHEMATICA-NEW SERIESno. 4 (2021)
arxiv(2020)
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