Research

I am an algebraic geometer, interested in moduli problems and attendant GIT constructions.

Publications and preprints

29. CM minimizers are standard models of del Pezzo fibrations, with Hamid Abban and Igor Krylov, in preparation, 2024.

28. K-moduli of Fano threefolds of rank 4 and degree 24, with Ivan Cheltsov, Kento Fujita, and Anne-Sophie Kaloghiros, in preparation, 2024.

27. Symmetric F-conjecture for $g\leq 35$, preprint on arXiv:2007.13457

26. Stability of fibrations over one-dimensional bases (joint with Hamid Ahmadinezhad and Igor Krylov), arXiv:1912.08779.

25. Associated form morphism (joint with Alexander Isaev), arXiv:1807.02082,

24. VGIT presentation of the second flip of $\overline{M}_{2,1}$ (joint with Matthew Grimes), arXiv:1805.08581,

23. Geometric Invariant Theory of syzygies, with applications to moduli spaces, arXiv:1712.02776

22. Direct sum decomposability of polynomials and factorization of associated forms, arXiv:1705.03452,

A short Macaulay2 package co-written by Z.Fang and J.Kim (supported by Summer 2017 BC URF) determines if a homogeneous polynomial with a nonzero discriminant over the rationals is a direct sum and computes a direct sum decomposition when it exists.

21. Stability of associated forms (joint with Alexander Isaev) on arXiv:1703.00438

20. GIT semistability of Hilbert points of Milnor algebras on arXiv:1508.06991

19. Semiampleness criteria for divisors on $\overline{M}_{0,n}$, submitted, 36pp. An accompanying SAGE worksheet

18. Second flip in the Hassett-Keel program: A local description (joint with Jarod Alper, David Smyth, and Fred van der Wyck)

17. Second flip in the Hassett-Keel program: Existence of good moduli spaces (joint with Jarod Alper and David Smyth)

16. Second flip in the Hassett-Keel program: Projectivity (joint with Jarod Alper and David Smyth),

15. Toward GIT stability of syzygies of canonical curves (joint with Anand Deopurkar and David Swinarski) on arXiv:1401.6101

14. Groebner techniques and ribbons (joint with Anand Deopurkar and David Swinarski),

13. New nef divisors on $\overline{M}_{0,n}$ on arXiv:1308.5993.

12. Singularities with G_m-action and the log minimal model program for $\overline{M}_g$ (joint with Jarod Alper and David Smyth),

11. GIT of genus five canonical curves (joint with David Smyth) on arXiv:1302.4804

10. Moduli spaces of hyperelliptic curves with A and D singularities

9. Finite Hilbert stability of (bi)canonical curves (joint with Jarod Alper and David Smyth)

*The final publication is available at www.springerlink.com

8. Stability of 2nd Hilbert points of canonical curves (joint with David Jensen)

7. The final log canonical model of the moduli space of stable curves of genus four

6. Cyclic covering morphisms on $\overline{M}_{0,n}$ (with an appendix by Anand Deopurkar, 2013); an older version on arXiv:1105.0655

5. Alternate compactifications of moduli spaces of curves (joint with David Smyth) on arXiv:1012.0329

4. Moduli spaces of weighted stable curves and log canonical models of M_{g,n}

3. Ample divisors on moduli spaces of pointed rational curves (joint with David Smyth)

2. Severi varieties and the moduli space of curves (Harvard dissertation) on arXiv:0710.1623

1. Rigidity and polynomial invariants of convex polytopes (joint with Igor Pak)