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Alg. Topology


Schubert calculus in Lie groups

Prelegent: Haibao Duan

2024-01-24 10:30

The problem of computing the cohomology of Lie groups was raised by É. Cartan in 1929. It is a focus of algebraic topology owing to the fundamental role of Lie groups playing in geometry and topology. However, apart from contributions by many mathematicians in about one century, the integral cohomology rings of Lie groups remains incomplete. On the other hand, Schubert calculus is the intersection of the 19th century. Making this calculus rigorous was stated by Hilbert as his 15th problem. In the course of securing the foundation of algebraic geometry, Van der Waerden and A. Weil related the calculus to the determination of the cohomology rings of flag manifolds.
In this talk I will bring a connection between these two topics both with distinguished backgrounds and illustrate how Schubert calculus in flag manifolds can be extended to obtain an explicit and unified construction of the integral cohomology of the compact and simply connected Lie groups.