[Colloquium] Jang Soo Kim, Combinatorics of orthogonal polynomials

Orthogonal polynomials are a family of polynomials which are orthogonal with respect to certain inner product. The n-th moment of orthogonal polynomials is an important quantity, which is given as an integral. In 1983 Viennot found a combinatorial expression for moments using lattice paths. In this talk we will compute the moments of several important orthogonal polynomials using Viennot’s theory. We will also see their connections with continued fractions, matchings, set partitions, and permutations.