Former graduate student Feifei Xie studied birational geometry of cluster varieties. Thesis.
Former graduate student Huy Le studied vector bundles on rational surfaces. Thesis.
Former graduate student Anna Kazanova studied degenerations of Godeaux surfaces and exceptional vector bundles. Thesis.
MATH 461: Affine and projective geometry.
My research is partially supported by NSF grants DMS-1901970 and DMS-2200875.
Symplectomorphisms of mirrors to log Calabi--Yau surfaces, with Ailsa Keating, preprint arXiv:2112.06797 [math.SG], pdf.
Secondary fan, theta functions, and moduli of log Calabi--Yau pairs, with Sean Keel and Tony Yue Yu, preprint arXiv:2008.02299 [math.AG], 54 pp, pdf.
Homological mirror symmetry for log Calabi--Yau suraces, with Ailsa Keating, to appear in Geometry and Topology, pdf.
The mirror of the cubic surface, with Mark Gross, Sean Keel, and Bernd Siebert, to appear in Proceedings of Miles Reid 70 conference, pdf.
Mirror symmetry and cluster algebras, with Sean Keel, Proceedings of the International Congress of Mathematicians -- Rio de Janeiro 2018, Vol. II: Invited lectures, 671--697, pdf.
Theta functions on varieties with effective anti-canonical class, with Mark Gross and Bernd Siebert, to appear in Mem. Amer. Math. Soc., 123pp., pdf.
Canonical bases for cluster algebras, with Mark Gross, Sean Keel, and Maxim Kontsevich, J. Amer. Math. Soc. 31 (2018), no. 2, 497--608, pdf.
Flipping surfaces, with Jenia Tevelev and Giancarlo Urzua, J. Algebraic Geom. 26 (2017), no. 2, 279--345, pdf.
Compact moduli spaces of surfaces and exceptional vector bundles, in Compactifying moduli spaces, Adv. Courses Math. CRM Barcelona, Birkhäuser/Springer (2016), 41--67, pdf.
Birational geometry of cluster algebras, with Mark Gross and Sean Keel, Algebr. Geom. 2 (2015), no. 2, 137--175., pdf.
Moduli of surfaces with an anti-canonical cycle, with Mark Gross and Sean Keel, Compos. Math. 151 (2015), no. 2, 265--291, 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.
Exceptional bundles associated to degenerations of surfaces, Duke Math. J. 162 (2013), no. 6, 1171--1202, 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), 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,