• Date:  2023-12-13 (Wed) 10:00 AM ~ 12:00 PM
• Place:  129-406 (SNU)
• Speaker:  김현문 (University of Toronto)
• Title:  A user’s guide to Schubert calculus of Lagrangian Grassmannians
• Abstract: Understanding the topology of real and complex Lagrangian Grassmannians is a classical question. In varying degrees, the topology of real Lagrangian Grassmannians was investigated by Borel (1951), Arnold (1967), Fuks (1968), Fuchs (2004), and Rabelo (2016), and for complex Lagrangian Grassmannians, by Borel (1951), Bernstein-Gelfand-Gelfand (1973), and Pragacz (1991). One of the tools to understand them has been the Schubert / Arnold / Bruhat cell decomposition. However, the natural inclusion of the real Lagrangian Grassmannian inside the complex Lagrangian Grassmannian, does not induce maps of chain complexes. We will show how to subdivide the complex Schubert cells so that the inclusion map induces a chain map. We will also give an updated user’s guide to understanding the topology the real Lagrangian Grassmannians using shifted Young diagrams of Pragacz.