Research

Here is a list of my preprints and publications. Versions here may be different than arXiv or published versions.

Publications

"A Strange Family of Calabi-Yau 3-folds", with Pat Devlin, in String Math 2014, PSPM vol. 93m AMS, Providence, RI, 2016, pp. 245-262. arXiv:1308.2915.

"A note on the existence of stable vector bundles on Enriques surfaces", Selecta Math., 22(3), 2016, pp. 1117-1156. arXiv: 1406.3328.

"On (2,4) complete intersection threefolds that contain an Enriques surface", with Lev Borisov, Mathematische Zeitschrift, 284, 2016, no. 3-4, 853-876. arXiv: 1210.1903. 

"Projectivity and birational geometry of Bridgeland moduli spaces on an Enriques surface", Proceedings of the London Mathematical Society, (3) 113, 2016, no. 3, pp. 345-386. arXiv: 1406.0908.

"Unirationality of moduli spaces of special cubic fourfolds and K3 surfaces". Rationality problems in algebraic geometry, 161–167, Lecture Notes in Math., 2172, Fond. CIME/CIME Found. Subser., Springer, Cham, 2016. 

"Unirationality of moduli spaces of special cubic fourfolds and K3 surfaces", Algebr. Geom. 4 (2017), no. 3, 281–289. arXiv: 1503.05256.

"Ulrich bundles on Enriques surfaces", with Lev Borisov,  Int. Math. Res. Not. IMRN 2018, no. 13, 4171–4189. arXiv:1606.01459.

"MMP Via Wall-crossing for Moduli Spaces of Stable Sheaves on an Enriques surface", with Kōta Yoshioka, Advances in Mathematics, 372, 2020. arXiv:1901.04848.

"A Refined Derived Torelli Theorem for Enriques Surfaces", with Chunyi Li, Paolo Stellari, and Xiaolei Zhao, Mathematische Annalen, 379, no. 3-4, 2021. arXiv:1912.04332. 

"Stability conditions in families",  with Arend Bayer, Martì Lahoz, Emanuele Macrí, Alex Perry, and Paolo Stellari, Publications Mathématiques de l'IHES, DOI 10.1007/s10240-021-00124-6. arXiv:1902.08184.

"The Cohomology of the general stable sheaf on a K3 surface", with Izzet Coskun and Kōta Yoshioka. To appear in Advances in Math.  Full list of Possible Counterexamples up to rank 20.

Preprints

"Stable sheaves on bielliptic surfaces: from the classical to the modern" . Submitted.

"The Brill-Noether Theory of the Moduli Spaces of Sheaves on Surfaces", with Izzet Coskun and Jack Huizenga.  Submitted.

"The Bogomolov-Gieseker-Koseki Inequality on surfaces with canonical singularities in arbitrary characteristic," with Alan Sorani. Submitted.

"Supporting rank and the Intersection of all Hassett Divisors," with Elad Gal. Submitted.

Work-in-Progress

"Surjectivity of the Donaldson-Mukai morphism in higher rank", with Jun Li, Yinbang Lin, and Xiaolei Zhao, in preparation.

"Projectivity of Bridgeland moduli spaces for stack quotients", in preparation.

Posters

On (2,4) Complete Intersection Threefolds that contain an Enriques Surface, a poster based on work of the same name with Lev Borisov.

Unirationality of moduli spaces of special cubic fourfolds and K3 surfaces, a poster presented at the AMS Summer Institute on Algebraic Geometry, Summer 2015.

Macaulay2 Scripts

Scripts for performing the Macaulay2 computations in my paper, "On (2,4) complete intersection threefolds that contain an Enriques surface" with Lev Borisov.

Scripts for carrying out the Macaulay2 calculations in my paper, "Unirationality of moduli spaces special cubic fourfolds and K3 surfaces."

Slides from Talks

Calabi-Yau's containing Enriques surfaces, from a talk I gave at the Rutgers Algebra Seminar, 11/14/2012.