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Leonardo Mihalcea : What is Schubert calculus?

Do you ever wanted to know how many lines in 3−space intersect 4 given random lines ? (Answer: 2.) One way to prove this is to do explicit computations in the cohomology of the Grassmannian of lines in the projective space. But interestingly enough, one can also use Representation Theory, or symmetric functions (Schur polynomials), to answer this question. The aim of this talk is to present the basics of Schubert Calculus, as seen from the cohomological point of view. I will define Schubert varieties in Grassmannians, and discuss about how they intersect. The final goal is to show that 2 = 1+ 1 (and I may also use Knutson�?s puzzles for another proof of this).

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