**Abstract:** |
The Lagrangian Grassmannian, denoted by $LG(n)$, is a homogeneous space of Lagrangian subspaces of a complex symplectic vector space of dimension $2n$. This talk is devoted to the small quantum cohomology ring of $LG(n)$. More concretely, we shall focus on the quantum structure constants and explain how to compute them. Geometrically, these are $3$-point, genus $0$ Gromov-Witten invariants of $LG(n)$ which count the number of rational curves contained in $LG(n)$ 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. |