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
![](https://chart.googleapis.com/chart?cht=tx&chl=%24LG(n)%24&chf=bg,s,333333&chco=ffffff)
, is a homogeneous space of Lagrangian subspaces of a complex symplectic vector space of dimension
![](https://chart.googleapis.com/chart?cht=tx&chl=%242n%24&chf=bg,s,333333&chco=ffffff)
. This talk is devoted to the small quantum cohomology ring of
![](https://chart.googleapis.com/chart?cht=tx&chl=%24LG(n)%24&chf=bg,s,333333&chco=ffffff)
. More concretely, we shall focus on the quantum structure constants and explain how to compute them. Geometrically, these are
![](https://chart.googleapis.com/chart?cht=tx&chl=%243%24-point&chf=bg,s,333333&chco=ffffff)
, genus
![](https://chart.googleapis.com/chart?cht=tx&chl=%240%24&chf=bg,s,333333&chco=ffffff)
Gromov-Witten invariants of
![](https://chart.googleapis.com/chart?cht=tx&chl=%24LG(n)%24&chf=bg,s,333333&chco=ffffff)
which count the number of rational curves contained in
![](https://chart.googleapis.com/chart?cht=tx&chl=%24LG(n)%24&chf=bg,s,333333&chco=ffffff)
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.