Department of Mathematics and Statistics
Lederle Graduate Research Tower, Box 34515
University of Massachusetts Amherst
Amherst, MA 01003-9305, USA hacking@math.umass.edu
Former graduate student Huy Le studied vector bundles on rational surfaces.
Former graduate student Anna Kazanova studied degenerations of Godeaux surfaces and exceptional vector bundles. Thesis.
Teaching.
Math 300.2: Fundamental concepts of mathematics. Course website.
Office hours: Mondays 2:00PM--3:00PM and Tuesdays 1:30PM--2:30PM in LGRT 1235H.
Research.
My research is partially supported by NSF grant 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, 136pp., to appear in J. Amer. Math. Soc., 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,
pdf.
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,
pdf.
The moduli space of curves is rigid, Algebra and Number Theory 2 (2008), no. 7, 809--818,
pdf.
Any opinions, findings and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation (NSF).