Hayan Nam

I am a research fellow at the Korea Institute for Advanced Study. I got my Ph.D. at University of California, Irvine with my advisor Nathan Kaplan and I was a postdoctoral scholar at Iowa State University with my mentor Steve Butler. I am interested in Combinatorics and Number Theory. My research focuses on core partitions, integer partitions, numerical semigroups, and their geometric descriptions and applications using Ehrhart theory.

Contact: hnam.math@gmail.com

Office: 7401


Research

  1. Large q convergence of random characteristic polynomials to random permutations and its applications, (with G. Cheong and M. Yu), (2020), submitted. 17pp. (available upon request)

  2. Enumerating parking completions using join and split, (with A. Adeniran, S. Butler, G. Dolparen-Barry, P. Harris, C. Hettle, Q. Liang, J. Martin), Electronic Journal of Combinatorics, Vol 27, (2020), #P2.44

  3. Largest size of an (s,s+1)-core partition with parts of the same parity, (with M. Yu), (2020), International Journal of Number Theory (accepted).

  4. How to determine a partition up to conjugation using multisets of hook lengths, (with M. Yu), Discrete Mathematics, Vol 343, (2020).

  5. A tiling proof of Euler's Pentagonal Number Theorem and generalizations, (with D. Eichhorn and J. Sohn), The Ramanujan Journal (accepted).

  6. On the genus of the quotient of a numerical semigroup, (with A. Adeniran, S. Butler, C. Defant, Y. Gao, P. Harris, C. Hettle, Q. Liang, and A. Volk), Semigroup Forum, Vol 98, (2019), 690--700.

  7. Johnson's bijections and their application to counting simultaneous core partitions, (with J. Baek and M. Yu), European Journal of Combinatorics, Vol 75, (2019), 43--54.

  8. A bijective proof of Amdeberhan's conjecture on the number of (s,s+2)-core partitions with distinct parts, (with J. Baek and M. Yu), Discrete Mathematics, Vol 341, (2018), 1294--1300.

  9. On the asymptotic distribution of cranks and ranks of cubic partitions, (with B. Kim and E. Kim), Journal of Mathematics Analysis and Applications, Vol 443, (2016), 1095--1109.

  10. On a conjecture of Soon-Yi Kang on a certain partition rank difference, (with B.Kim), The Ramanujan Journal, Vol 35, (2014), 467--477.

Teaching and Mentoring

  1. Iowa State University

  • 2020 Spring: Graph Theory

  • 2020 Spring: ISMaRT program - conducted undergraduate research.

  • 2019 Fall: Multivariate Calculus

  1. University of California, Irvine

  • 2018-2019: Peer graduate mentor - served as a mentor for first and second year UCI graduate students.

  • 2014-2019: Volunteer for Math Circle - led and assisted with weekly Math Circles for students ages 10-17 on a variety of topics.

  • 2015-2019: Teaching Assistant for Calculus, Multivariate Calculus, Introduction to linear algebra, Math for economics, Linear algebra, Introduction to abstract mathematics, Introduction to group theory, Combinatorics.

Invited Talks (since 2018)

  1. 2020 KMS Annual Meeting, Seoul, Korea, October 2020.

  2. Yonsei Number Theory seminar 2020, Seoul, Korea, August 2020.

  3. q-Day 2020, Seoul, Korea, July 2020.

  4. Joint Mathematics Meetings, Denver, January 2020.

  5. AMS Sessional Meeting, Gainesville, November 2019.

  6. Palmetto Number Theory Series, Charlotte, September 2019.

  7. KIAS Number Theory Seminar, Seoul, Korea, August 2019.

  8. U. of Minnesota Combinatorics Seminar, Minnesota, June 2019.

  9. USC Combinatorics Seminar, Los Angeles, April 2019.

  10. UIUC Number Theory Seminar, Illinois, March 2019.

  11. Joint Mathematics Meetings, Baltimore, January 2019.

  12. Combinatorics/Partitions Seminar, Penn State University, January 2019.

  13. UCLA Combinatorics Seminar, Los Angeles, January 2019.

  14. KIAS Number Theory Seminar, Seoul, Korea, September 2018.

  15. Number Theory Seminar, Yonsei University, Korea, September 2018.