My research is partially supported by NSF grants DMS-1201439 and DMS-1601065.
Theta functions on varieties with effective anti-canonical class, with Mark Gross, Sean Keel, and Bernd Siebert, preprint arXiv:1601.07081, 115pp., pdf.
Canonical bases for cluster algebras, with Mark Gross, Sean Keel, and Maxim Kontsevich, preprint arXiv:1411.1394, 136pp., pdf.
Flipping surfaces, with Jenia Tevelev and Giancarlo Urzua, 65 pp., to appear in J. Algebraic Geom., pdf.
Birational geometry of cluster algebras, with Mark Gross and Sean Keel, Algebr. Geom. 2 (2015), no. 2, 137--175., pdf.
Compact moduli spaces of surfaces and exceptional vector bundles, 31 pp., to appear in "Compactifying moduli spaces", Advanced Courses in Mathematics -- CRM Barcelona, Springer, pdf.
Moduli of surfaces with an anti-canonical cycle, with Mark Gross and Sean Keel, Compos. Math. 151 (2015), no. 2, 265--291, pdf.
Exceptional bundles associated to degenerations of surfaces, Duke Math. J. 162 (2013), no. 6, 1171--1202, pdf.
Mirror symmetry for log Calabi-Yau surfaces I, with Mark Gross and Sean Keel, Publ. Math. Inst. Hautes Études Sci. 122 (2015), 65--168, pdf.
Compact moduli of surfaces of general type, Contemp. Math. 564 (2012), 1--18, pdf.
Smoothable del Pezzo surfaces with quotient singularities,
with Yuri Prokhorov, Compositio Math. 146 (2010), no. 1, 169--192, pdf.
Lectures on flips and minimal models,
with Alessio Corti, János Kollár, Robert Lazarsfeld, and Mircea Mustaţă, in Analytic and Algebraic Geometry: Common Problems, Different Methods, IAS/Park City Math. Ser. 17 (2010), p.557--582,
Stable pair, tropical, and log canonical compactifications of moduli spaces of del Pezzo surfaces,
with Sean Keel and Jenia Tevelev, Invent. Math. 178 (2009), no. 1, 173--227, pdf.
Canonical singularities of orders over surfaces,
with Daniel Chan and Colin Ingalls, Proc. Lond. Math. Soc. (3) 98 (2009), no. 1, 83--115,
The moduli space of curves is rigid, Algebra and Number Theory 2 (2008), no. 7, 809--818,