Visit my blog, "Geometry-free Schubert calculus," at gfschubertcalculus.blogspot.com!
I'm an algebraic combinatorialist with a specialization in Schubert calculus. I got my PhD in math in 2014. My dissertation (read it here) is about the curious Hopf algebroid structure on the torus-equivariant cohomology ring of a generalized flag variety (though the main result was leveraging the properties of this algebroid to give a Leibniz formula for divided difference operators arising from Coxeter groups). In a sense the equivariant cohomology ring is more fundamental than the cohomology ring because the structure constants arise in an elementary way from a Coxeter group's action on a polynomial ring.
I am also a coauthor of K-theory of minuscule varieties where a K-theoretic analog of Knuth equivalence (aptly named K-Knuth equivalence) is introduced. I had to prove that the "combinatorialist" belongs there, because my dissertation is just algebra!
If you want to collaborate with me academically you can contact me by posting a comment on one of my posts.