Room 638, Institute of Mathematics, Academia Sinica
(中研院數學所 638室)
Quantum Cohomology of the Lagrangian Grassmannian
Hiep Dang (NCTS)
Abstract:
The Lagrangian Grassmannian, denoted by
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, is a homogeneous space of Lagrangian subspaces of a complex symplectic vector space of dimension

. This talk is devoted to the small quantum cohomology ring of
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. More concretely, we shall focus on the quantum structure constants and explain how to compute them. Geometrically, these are

, genus

Gromov-Witten invariants of
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which count the number of rational curves contained in
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intersecting with three Schubert varieties in general position. By the quantum-classical principle of Buch-Kresch- Tamvakis, we show that the quantum structure constants can be computed as intersection numbers on the usual Grassmannian.