KNU Mathematics Intensitve Lecture Series

Introduction to Orthogonal Polynomials

Prof. Jang Soo Kim (Sungkyunkwan University)

November 29–December 7, 2024

Abstract

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)

1. Lecture 1. Introduction to orthogonal polynomials, 10:00 – 11:30
2. Lecture 2. The moment functional, orthogonality, and existence of OPS, 14:00 – 15:30
3. Lecture 3. The fundamental recurrence, 16:00 – 17:30

November 30(Sat)

4. Lecture 4. Formal power series and generating functions, 10:00 – 11:30
5. Lecture 5. Dyck paths and Motzkin paths, 14:00 – 15:30

December 6(Fri)

7. Lecture 6. Set partitions, matchings, and permutations, 10:00 – 11:30
8. Lecture 7. Combinatorial models for OPS, 14:00 – 15:30
9. Lecture 8. Moments of classical orthogonal polynomials, 16:00 – 17:30

December 7(Sat)

9. Lecture 9. Continued fractions, 10:00 – 11:30
10. Lecture 10. Linearization coefficients, 14:00 – 15:30

Venue

• #102, College of Natural Sciences, Kyungpook National University, Daegu, Korea

Accommodation Suggestion

• Hotel Inter-Burgo Exco (호텔 인터불고 엑스코)
• Standard double room rate is about KRW120,000 – KRW150,000 as of Feb. 2024.
• Breakfast is not included.
• Distance from Venue : 40min. by walk (map), 30min. by bus and walk

• Laonzena (호텔 라온제나)
• Standard double room rate is about KRW100,000 – KRW150,000 as of Feb. 2024.
• Breakfast is not included.
• Distance from Venue : 40min. by bus and walk, 20min. drive

• Browndot-KNU (브라운도트-경북대점)
• Standard double room rate is about KRW80,000 – KRW120,000 as of Feb. 2024.
• Breakfast is not included.
• Distance from Venue : 15min. walk (map)

Contact

• Byung Hee An (anbyhee_at_knu.ac.kr)

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