Research

Research Interests

• Algebraic geometry: Moduli theory, stability, algebraic curves, bundles
• Computer science: Computational complexity, computer vision

Publications

• Conjugacy classes of commuting nilpotents (with William Haboush), Transactions of the American Mathematical Society 372 (2019), no. 6, 4293–4311.
• Note on the decomposition of states (with Jaekwang Kim), Bulletin of the Korean Mathematical Society 55 (2018), no. 4, 1221–1230.
• Grothendieck-Plücker images of Hilbert schemes are degenerate (with Hyoungju Park), Proceedings of the Edinburgh Mathematical Society (2) 62 (2019), no. 1, 47–60.
• Castelnuovo-Mumford regularity and Bridgeland stability for points in the projective plane (with Izzet Coskun and Junyoung Park), Proceedings of the American Mathematical Society, 145 (2017), no. 11, 4573- 4583.
• An outline of the log minimal model program for the moduli space of curves, Experimental Mathematics 26 (2017), no.1, 114-124.
• Generic semistability for reductive group actions (with Dao Phuong Bac), Proceedings of the American Mathematical Society (2016), 144, no.10, 4115-4124.
• State polytope decomposition formula (with Jaekwang Kim), Proceedings of the Edinburgh Mathematical Society (2016), no. 59, 759-776.
• Birational contraction of genus two tails in the moduli space of genus four curves I (with Yongnam Lee), International Mathematical Research Notices (2014), no.13, 3735-3757.
• Log minimal model program for the moduli space of curves: The first flip (with Brendan Hassett), Annals of Mathematics 177 (2013), no.3, 911-968.
• Log minimal model program for the moduli space of stable curves of genus three (with Yongnam Lee), Mathematical Research Letters 17 (2010), no.4, 625-636.
• Stability of tails and 4-canonical models (with Ian Morrison), Mathematical Research Letters 17 (2010), no.4, 721-729.
• A new look at the moduli space of hyperelliptic curves (with Yongnam Lee), Mathematische Zeitschrift 264 (2010), no.2, 317-326.
• Stability computation via Gröbner basis (with Brendan Hassett and Yongnam Lee), Journal of Korean Mathematical Society 47 (2010), 41-62.
• Stability of bicanonical curves of genus three (with Yongnam Lee), Journal of Pure and Applied Algebra 213 (2009), no.10, 1991-2000.
• A log canonical model for the moduli space of curves: The first divisorial contraction (with Brendan Hassett), Transactions of the American Mathematical Society 361 (2009), 4471-4489.
• Stability of tri-canonical curves of genus two (with Yongnam Lee), Mathematische Annalen (2007), no. 2, 337:479–488.
• Note on the stability of principal bundles (with D. Murphy), Proceedings of the American Mathematical Society 132 (2004), no. 8, 2205–2213.
• Principal bundles over a projective scheme, Transactions of the American Mathematical Society 354 (2002), no. 5, 1899–1908.
• Higgs bundles, spectral curves and étale covering, International Journal of Mathematics 12 (2001), no. 4, 393–402.
• Direct images of stable triples, International Journal of Mathematics 11 (2000), no. 9, 1231–124.