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01月03日.ROOM-H.15.0.Haibao Duan
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Schubert calculus in Lie groups, 段海豹 (Haibao Duan) 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, despite contributions by many mathematicians in about one century, the integral cohomology of Lie groups remained incomplete. On the other hand, Schubert calculus began with the enumerative geometry 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 problem to the determination of the intersection theory of flag manifolds. In this talk we 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 rings of all compact and simply-connected Lie groups.
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