Insong Choe, Subsheaves of Maximal Rank in a Symplectic and Orthogonal Bundle over a Curve

We first review the known results on the Quot schemes on a smooth algebraic curve. Next we explain how they can be generalized to the Lagrangian Quot scheme, which parametrizes Lagrangian subsheaves on a symplectic vector bundle. Also we discuss the parallel results for orthogonal bundles. This will be an overview of the findings over the past 15 years in collaboration with George H. Hitching and D. Cheong.