学术报告（桂弢 2025.11.6）

摘要： The Peterson variety is a remarkable subvariety of the flag variety, introduced by Dale Peterson to realize the quantum cohomology rings of all Langlands dual partial flag varieties geometrically. We give an explicit, positive, and type-uniform formula for all equivariant structure constants of the Peterson Schubert calculus in arbitrary Lie types, using only the Cartan matrix of the corresponding root system. As an application, we derive a type-uniform formula for the mixed Eulerian numbers.  As far as we know, this is the first example of an explicit, complete, and type-uniform positive algebraic formula in general Schubert calculus. Joint with Yuqi Jia, Xinkai Yu, Zhexi Zhang, and Yuchen Zhu.