Jae-Ho Lee | Home

Jae-Ho Lee

Research

Areas of Interest

  • Algebraic combinatorics, Representation Theory, Special functions, Distance-regular graphs.


    • Research Interests

    My research concerns two mathematical objects; the first one is a combinatorial object known as a $Q$-polynomial distance-regular graph and the second is an algebraic object known as the double affine Hecke algebra(DAHA). $Q$-polynomial distance-regular graphs can be thought of a discrete analogue of rank 1 symmetric space. The $Q$-polynomial property appears in other areas in mathematics, such as Lie theory, quantum algebras and orthogonal polynomials. The DAHA was introduced by Cherednik in the beginning of 1990. Since then, the theory of DAHA has been receiving great attention and connected to many other areas, such as integrable systems, algebraic geometry, quantum algebras and orthogonal polynomials. I constructed a relationship between $Q$-polynomial distance-regular graphs and the double affine Hecke algebra of rank one (2013). This provides a new approach to study of $Q$-polynomial distance-regular graphs and the DAHA. Using this approach, I am currently exploring the connections between $Q$-polynomial distance-regular graphs and non-symmetric (or Laurent) case of the terminating branch of the Askey-scheme of orthogonal polynomials.


    Papers

    1. J.-H. Lee, Nonsymmetric Askey-Wilson polynomials and $Q$-polynomial distance-regular graphs, Accepted to the Journal of Combinatorial Theory Series A, arXiv:1509.04433, 38 pages.
    2. (non-refereed) J.-H. Lee, Nonsymmetric Askey-Wilson polynomials and Q-polynomial distance-regular graphs, RIMS kôkyûroku, 1965 (2014), 101–111.
    3. J.-H. Lee, $Q$-polynomial distance-regular graphs and a double affine Hecke algebra of rank one, Linear Algebra Appl. 439 (2013), 3184--3240 (arXiv:1307.5297, 79 pages)
    4. S.M. Cioaba, E.R. van Dam, J.H. Koolen and J.-H. Lee, A lower bound for the spectral radius of graphs with fixed diameter, European J. Combin. 31 (2010), 1560--1566
    5. S.M. Cioaba, E.R. van Dam, J.H. Koolen and J.-H. Lee, Asymptotic results on the spectral radius and the diameter of graphs, Linear Algebra Appl. 432 (2010), 722--737


    Selected Presentations (Conference/ Workshop/ Seminar)

    1. (Invited talk) Positivity in Algebraic Combinatorics, KIAS, Seoul, Korea, June 2016
    2. University of Wisconsin-Madison, Combinatorics Seminar, Madison, WI, April 2016
    3. The 14th Korea-Japan Workshop on Algebra and Combinatorics, Pusan National University, Pusan, Korea, January 2016
    4. Joint Mathematics Meetings: AMS Contributed Paper Session on Ordinary Differential Equations and Special Functions II, Seattle, WA, January 2016
    5. 10th KIAS Combinatorics Workshop, KIAS, Seoul, Korea, December 2015
    6. Binghamton University–SUNY, Combinatorics Seminar, Binghamton, NY, November 2015
    7. University of Rochester, Combinatorics Seminar, Rochester, NY, November 2015
    8. North Dakota State University, Combinatorics Seminar, Fargo, ND, November 2015
    9. 8th Slovenian Conference on Graph Theory: Special Session on Association Schemes, Kranjska Gora, Slovenia, June 2015
    10. Workshop on Algebraic Combinatorics, Tilburg, Netherlands, June 2015
    11. UW-Madison Combinatorics Seminar, Madison, WI, February 2015
    12. The 13th Japan-Korea Workshop on Algebra and Combinatorics, Kyushu Institute of Technology, Kitakyushu, Japan, January 2015
    13. RIMS Workshop: "Research on Finite Groups and Their Representations, Vertex Operator Algebras, and Algebraic Combinatorics”, Kyoto University, Japan, December 2014
    14. Algebraic Combinatorics Workshop, USTC, China, November 2014
    15. Combinatorics Seminar, Graduate School of Information Sciences, Tohoku University, Japan, October 2014
    16. UW-Madison Combinatorics Seminar, Madison, WI, January 2014
    17. Joint Mathematics Meeting: MAA General Contributed Paper Session on Research in Graph Theory and Combinatorics I, Baltimore, MD, January 2014
    18. Combinatorics and Algebraic Geometry Seminar, University of Pennsylvania, PA, November 2013
    19. Algebra-Geometry-Combinatorics Seminar, University of Illinois, Urbana, IL, October 2013
    20. AMS Spring 2013 Central Sectional Meeting: Special Session on Algebraic and Geometric Combinatorics, Iowa State University, Ames, IA, April 2013
    21. UW-Madison Combinatorics Seminar, Madison, WI, April 2013
    22. Joint Mathematics Meeting: AMS Special Session on $q$-series in Mathematical Physics and Combinatorics, San Diego, CA, January 2013
    23. Discrete Math Seminar, Rutgers University, New Brunswick, NJ, November 2012
    24. Mathematical Sciences Department Seminar, WPI, Worcester, MA, November 2012
    25. Minnesota Combinatorics Seminar, University of Minnesota, Minneapolis, MN, November 2012
    26. Shanghai Conference on Algebraic Combinatorics, Shanghai Jiao Tong University, Shanghai, China, August 2012
    27. UW-Madison Combinatorics Seminar, Madison, WI, May 2012
    28. 8th Annual Graduate Student Combinatorics Conference, University of Illinois at Urbana-Champaign, Urbana, IL, April 2012
    29. AMS Fall 2011 Central Section Meeting: Special Session on Association Schemes and Related Topics, University of Nebraska-Lincoln, Lincoln, Nebraska, October 2011
    30. Geometric and Algebraic Combinatorics 5, Oisterwijk, The Netherlands, August 2011
    31. GAC Seminar, POSTECH, Pohang, Korea, June 2011
    32. Workshop on Algebraic Graph Theory, Banff, Canada, April 2011
    33. UW-Madison Combinatorics Seminar, Madison, WI, April 2011
    34. The 4th Korea-Japan Workshop on Algebra and Combinatorics; The Mini-Workshop on Algebraic Combinatorics, POSTECH, Pohang, Korea, February 2008
    35. The 3rd Japan-Korea Workshop on Algebra and Combinatorics; Young Seminar on Algebra and Combinatorics, Kyushu University, Fukuoka, Japan, September 2007