Kequan Ding

University of Illlinois

ABSTRACT: Let G be a semisimple Lie group and B a Borel subgroup of G. The quotient space of B\G is a general flag manifold. Hilberts 15th problem(1900) asks for the foundation of Schubert calculus, that leads to the computation of cohomology of the flag manifold B\G. Along this line, one of the major progresses in the 20th century is Chevalley's work on Chevalley-Bruhat order (1958) which characterizes the attachment relationships between two Shubert varieties. We will talk about the lengendary history of Chevalley-Bruhat order, give a new characterization of the order in classical cases and explain how to use chess configurations with rooks and pawns to compute topological invariants.