Faculty Colloquium

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Speaker: Lino Amorim Title: Counting curves via categories Abstract: Counting algebraic curves is a classical problem in geometry. Mirror symmetry revealed that some of these counts, known as Gromov-Witten invariants, can be computed from unrelated complex-geometric data in a different space. Later, Kontsevich’s Homological Mirror Symmetry conjecture suggested that these invariants can be recovered from certain categories. More ambitiously, it should be possible to define analogues of Gromov-Witten invariants for categories equipped with additional structures. I will briefly describe Gromov-Witten theory and give a sample computation. Then I will introduce Categorical Enumerative Invariants, which are a conjectural solution to the problem of assigning curve counts to categories, and explain how this construction aims to connect homological mirror symmetry with enumerative geometry.