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
, 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
. More concretely, we shall focus on the quantum structure constants and explain how to compute them. Geometrically, these are
, genus
Gromov-Witten invariants of
which count the number of rational curves contained in
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.