讲座内容：

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. Harada and Tymoczko posed the open problem (in type A) of finding a positive formula for the structure constants of the cohomology ring of the Peterson variety. 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 Φ. As an application, we derive a type-uniform formula for the mixed Φ-Eulerian numbers.