Publications

(italic: undergraduate students)

  1. (with K.-S. Lee) Derived categories of symmetric products and moduli spaces of vector bundles on a curve. J. Math. Pures Appl, to appear.
  2. (with A. Campbell, F. Dedvukaj, D. McCormick III, and J. Morales) On algebraic space filling curves. preprint.
  3. (with R. Jain and P. Wu) Distribution of the number of zeros of polynomials over a finite field. Involve, to appear.
  4. (with P. Gallardo, J. Martinez-Garcia, and D. Swinarski) Computation of GIT quotients of semisimple groups. preprint.
  5. (with A. Caminata and L. Schaffler) Determinantal varieties from point configurations on hypersurfaces. Int. Math. Res. Not. IMRN, 2023, Issue 22, pp. 19743-19772. DOI: https://doi.org/10.1093/imrn/rnad244.
  6. Tropical geometry and phylogenetic diversity. preprint.
  7. (with K.-S. Lee) Derived category and ACM bundles of moduli space of vector bundles on a curve. Forum. Math, Sigma, Volume 11, 2023, e81, DOI: https://doi.org/10.1017/fms.2023.75.
  8. (with H. Wong) Consequences of the compatibility of cluster algebra and skein algebra on surfaces. New York J. Math. 30 (2024) 1648–1682.
  9. (with F. Azad, Z. Chen, M. Dreyer, and R. Horowitz) Presentations of the Roger-Yang generalized skein algebra. Algebr. Geom. Topol. 21 (2021), no. 6, 3199–3220.
  10. (with A. Caminata, N. Giansiracusa, and L. Schaffler) Point configurations, phylogenetic trees, and dissimilarity vectors. Proc. Natl. Acad. Sci. USA, 2021, 118 (12).
  11. (with H. Wong) The Roger-Yang skein algebra and the decorated Teichmuller space. Quantum Topol., Volume 12, Issue 2, 2021, pp. 265–308.
  12. (with S.-B. Yoo) Finite generation of the algebra of type A conformal blocks via birational geometry II: higher genus. Proc. Lond. Math. Soc., vol.120 (2020), issue 2, 242-264.
  13. (with L. Schaffler)  KSBA compactification of the moduli space of K3 surfaces with purely non-symplectic automorphism of order four. Proc. Edinb. Math. Soc. Volume 64, Issue 1, February 2021, pp. 99-127.
  14. (with A. Caminata, N. Giansiracusa, and L. Schaffler) Equations for point configurations to lie on a rational curve. Adv. Math., Vol. 340, (2018) no. 15, 653-683. Minor correction of the published version.
  15. (with S.-B. Yoo) Finite generation of the algebra of conformal blocks via birational geometry. Int. Math. Res. Not. IMRN, (2021), no. 7, 4941-4974.
  16. (with K. Chung) Birational geometry of the moduli space of pure sheaves on quadric surface. C. R. Math. Acad. Sci. Paris, 355 (2017), no. 10, 1082–1088.
  17. (with K. Chung) Mori’s program for the moduli space of conics in Grassmannian. Taiwanese J. Math., a special issue for Algebraic Geometry in East Asia 2016, Vol. 21, (2017) no. 3, 621-652.
  18. (with D. Swinarski) On the $S_n$-invariant F-conjecture.  J. Algebra. Vol. 517, (2019) no. 1, 439-456. supplementary files on the webpage of the second author.
  19. (with C. Summers, J. von Albade, and R. Xie) Birational contractions of $\bar{M}_{0,n}$ and combinatorics of extremal assignments. J. Algebraic Comb., Vol. 47, (, no. 1, 51–90, supporting codes.
  20. (with K. Chung) Chow ring of the moduli space of stable sheaves supported on quartic curves. Q. J. Math., Vol. 68, (2017), no. 3, 851–887, supporting calculations and codes.
  21. (with K. Chung) Moduli of sheaves, Fourier-Mukai transform, and partial desingularization.  Math. Z., 283 (2016), no. 1-2, 275-299.
  22. (with S.-B. Yoo) Birational geometry of the moduli space of rank 2 parabolic bundles on a rational curve. Int. Math. Res. Not. IMRN, (2016), no. 3, 827–859.
  23. (with D. Swinarski) Effective curves on $\bar{M}_{0,n}$ from group actions. Manuscripta Math., 147 (2015), no. 1-2, 239–268.
  24. Mori’s program for $\bar{M}_{0,7}$ with symmetric divisors. Canad. J. Math., 69 (2017), no. 3, 613-649.
  25. Mori’s program for $\bar{M}_{0,6}$ with symmetric divisors. Math. Nachr., 288 (2015), no. 7, 824-836.
  26. (with A. Gibney, D. Jensen, and D. Swinarski) Veronese quotient models of $\bar{M}_{0,n}$ and conformal blocks. Michgan Math. J., 62 (2013), no. 4, 721-751.
  27. (with N. Giansiracusa and D. Jensen) GIT compactifications of $M_{0,n}$ and flips. Adv. Math., Vol. 248, (2013), 242-278.
  28. A family of divisors on $\bar{M}_{g,n}$ and their log canonical models. J. Pure Appl. Algebra, 219 (2015), no. 10, 4642-4652.
  29. Log canonical models for the moduli space of stable pointed rational curves. Proc. Amer. Math. Soc., 141 (2013), no. 11, 3771-3785.
  30. (with Y.-H. Kiem) Moduli spaces of weighted pointed stable rational curves via GIT. Osaka J. Math., 48 (2011), no. 4, 1115-1140.
  31. (with Y.-H. Kiem) Moduli spaces of stable maps to projective space via GIT. Internat. J. Math., 21 (2010), no. 5, 639-664.
  32. Birational geometry of moduli spaces of curves of genus zero. Thesis, Seoul National University, August 2011.

on arXiv

My ORCID record ORCID logo

Essays

  1. (In Korean) Small mathematical world: Phylogenetic trees, tropical geometry, and point configurations, Horizon webzine.

Posters

  1. Chow ring of the moduli space of stable sheaves supported on quartic curves. Intended to be presented in AMS Summer Institute in Algebraic Geometry, but not be presented.

Unpublished notes

  1. Mori’s program for the moduli space of pointed stable rational curves. (superseded by publication 4.)
  2. (with K.-S. Lee) Positivity of the Poincare bundle on the moduli space of vector bundles and its applications. (superseded by publication 26.)