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Friday, February 24, 2017

**Abstract:** As a deformation of classical cohomology ring, (small) quantum cohomology ring of Grassmannians has a nice description in terms of quantum Schubert classes and it has (3 point, genus 0) Gromov-Witten invariants as its structure constants. In this talk, we will describe how 'quantum corrections' can be made to obtain quantum Schubert calculus from classical Schubert calculus. After studying its structure, we will see that the Gromov-Witten invariants, which define ring structure of quantum cohomology of Grassmannians, are equal to the classical intersection number of two-step flag varieties. If time permits, we will discuss classical and quantum Littlewood-Richardson rule using triangular puzzles.