# Mathematics Colloquia and Seminars

Buch and Fulton defined quiver polynomials in a geometric context, and proved that these polynomials can be expressed as integer sums of products of Schur functions in differences of alphabets. Motivated by the fact that Littlewood-Richardson numbers are (very) special cases of the integer quiver coefficients' appearing in these sums, Buch and Fulton conjectured that all quiver coefficients are positive, and moreover described certain factor sequenes' of Young tableaux that they should count. After indicating in an elementary way how quiver polynomials are defined via geometry, I will discuss combinatorial formulae for them that arise on the way to a solution of the Buch-Fulton conjecture. I will define everything from scratch, although previous familiarity with Schur functions will help in understanding the combinatorial motivations. This talk oncerns joint work with Allen Knutson and Mark Shimozono.