Orthogonal polynomials are classical objects arising from the study of continued fractions. They have become an important subject in many areas of mathematics including analysis, probability, mathematical physics, random matrix theory, and combinatorics to name a few. In these lectures, we will learn fascinating combinatorial properties of orthogonal polynomials.
Lectures
November 29(Fri)
Lecture 1. Introduction to orthogonal polynomials, 10:00 – 11:30
Lecture 2. The moment functional, orthogonality, and existence of OPS, 14:00 – 15:30
Lecture 3. The fundamental recurrence, 16:00 – 17:30
November 30(Sat)
Lecture 4. Formal power series and generating functions, 10:00 – 11:30
Lecture 5. Dyck paths and Motzkin paths, 14:00 – 15:30
December 27(Fri)
Lecture 6. Set partitions, matchings, and permutations, 10:00 – 11:30
Lecture 7. Combinatorial models for OPS, 14:00 – 15:30
Lecture 8. Moments of classical orthogonal polynomials, 16:00 – 17:30