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Cluster dualities and superpotentials for Grassmannian

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KA2W03 - Mathematical physics: algebraic cycles, strings and amplitudes

Marsh-Rietsch described a Landau-Ginzburg model for Grassmannians consisting of the complement of a particular anti-canonical divisor in a Langlands dual Grassmannian together with a superpotential expressed in terms of Plücker coordinates. On the other hand, Grassmannians carry cluster structure which we can write down a superpotential from the work of Gross-Hacking-Keel-Kontsevich. A natural question is — are the two potentials the same or not? Together with Bossinger, Magee, and Najera-Chavez, we identified the cluster structures of the two sides of the mirror Grassmannians and identified the Marsh-Rietsch and the Gross-Hacking-Keel-Kontsevich potentials. As a consequence, we identified the two mirror constructions.

This talk is part of the Isaac Newton Institute Seminar Series series.

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