Department
of Mathematics
University of Georgia
Athens GA 30602, USA
Recent papers and preprints
(with Rita Pardini)
On the existence of ramified
abelian covers, Rendiconti del Seminario Matematico Universita e Politecnico di Torino, to appear.
(with Dmitri Orlov)
Derived categories of Burniat surfaces and exceptional collections, Math. Annalen, to appear.
(with Alexander Borisov)
On the log discrepancies in
Mori contractions, Proc. Amer. Math. Soc., to appear.
(with Christopher Hacon)
Non-rational centers of log canonical singularities,
J. Algebra, 369 (2012), 1-15.
(with Ryan
Livingson,
Joe
Tenini, et al.)
Extended
Torelli map to the Igusa blowup in genus 6, 7, and 8.
(long
version here.),
Experimental Mathematics, 21(2), 2012, 193-203.
(with Rita Pardini)
Non-normal
abelian covers,
Compositio Mathematica,
148, no. 4 (2012), 1051-1084.
(with Adrian Brunyate)
Extending Torelli map to toroidal compactifications of Siegel space, Inventiones Mathematicae, 188 (2012), issue 1, 175-196.
(with Angela Gibney
and David
Swinarski)
Conformal
blocks divisors on
M0,n
from sl(2), Proc. Edinburgh Math. Soc., to appear.
(with Rita Pardini)
Explicit
compactifications of moduli spaces of Campedelli and Burniat surfaces:
color
version,
black-and-white version.
(with David Swinarski)
Nef divisors on
M0,n
from GIT, Geometry and Arithmetic, 2012, European Math. Soc., EMS Congress Reports, pp. 1-22.
Weighted grassmannians and stable hyperplane
arrangements
(updated 6/19/08)
Higher-dimensional
analogues of stable curves,
Proceedings of Madrid ICM2006, 2 (2006), 515-536,
Eur. Math. Soc. Pub. House.
(with Michael
Guy)
Moduli of
weighted stable maps and their gravitational descendants,
Journal
of the Institute of Mathematics of Jussieu, 7
(2008), no.3, 425-456.
Limits of stable pairs, Pure and Applied
Math Quaterly, 4 (2008), no.3, 767-783.
(with Christopher Hacon
and Yujiro
Kawamata)
Termination
of (many) 4-dimensional log flips
(successor to "A note on termination of 4-dimensional flips" below)
Inventiones
Mathematicae,
168 (2007), 433-448.
(with
Viacheslav V. Nikulin) Del Pezzo and K3 surfaces,
Memoirs
of the Mathematical Society of Japan, 15
(2006), x+149pp.
(with Allen Knutson)
Complete
moduli of branchvarieties, Jour. f.d. Reine Angew.
Mathematik (Crelle's Journal), 639 (2010), 29-71.
A
report in the Bourbaki Seminar
on my research
(with Michel
Brion)
Stable spherical varieties and their moduli
International Math. Research Papers, vol. 2006 (2006), Article ID
46293, 57 pages.
Compactified
jacobians and Torelli map
Publ.
RIMS, Kyoto Univ.
40 (2004), 1241-1265.
(40-year RIMS anniversary issue)
(Here is a local
copy.)
A note on termination of 4-dimensional flips
(6/8/2004)
(with
Viacheslav V. Nikulin)
Classification of log del Pezzo surfaces of index
<=2
(with Michel
Brion)
Toric degenerations of spherical varieties
Selecta
Mathematica 10 (2004), 1-26.
(with Ludmil Katzarkov)
On K-stability of reductive varieties
Geometric and Functional Analysis GAFA 15:2
(2005), 297-310.
(with Michel
Brion)
Moduli of affine schemes with reductive group
action
Journal of Algebraic Geometry 14 (2005),
83-117.
(with Michel
Brion) Boundedness
of spherical Fano varieties
Proceedings of "The Fano conference" Turin Sept. 2002, pp. 69-80
(2004).
(with Michel
Brion)
Stable reductive varieties I: Affine varieties
Inventiones Math.
157/2 (2004), 224-274.
(with Michel
Brion)
Stable reductive varieties II: Projective case
Advances of Math.
184/2 (2004), 380-408.
Complete moduli in the presence of semiabelian
group action
Annals of Math. 155 (2002), 611-708.
(with Christina
Birkenhake and Klaus
Hulek)
Degenerations of Prym varieties
Jour. f.d. Reine Angew. Mathematik (Crelle's Journal) 553
(2002), 73-116.
(with Shigefumi Mori)
Bounding
singular surfaces of general type
In "Algebra, Arithmetic and Geometry with Applications", ed. by
Christensen et al, Springer-Verlag (2003), 143-174.
(with Iku Nakamura)
On
Mumford's construction of degenerating abelian varieties, Tohoku
Mathematical Journal 51(1999), 399-420.
Books edited
(with Arnaud Beauville, C. Herbert Clemens, Elham Izadi)
Curves and Abelian Varieties: International conference March 30-April
2, 2007, University of Georgia, Athens. Contemporary
Mathematics, American Math. Soc.,
Vol. 465 (2008), 270 pp.
(with Angela Gibney, Elham Izadi, Eduard Looijenga, János
Kollár)
Compact Moduli and Vector Bundles. Proceedings of the 2010
conference at the University of Georgia, Athens.
Contemporary Mathematics, American Math. Soc., 255 pp. to appear.
Some conferences I coorganized
March 30 - April 3, 2007:
Curves
and abelian varieties, University of Georgia, Athens, GA
October 21-24, 2010: Compact
moduli and vector bundles,
University of Georgia,
Athens, GA
May 21 - June 1, 2012:
UGA school and conference on algebraic geometry, Athens, GA
My students
Vitaly Vologodsky, PhD 2003, The extended Jacobi and Prym maps
Tawanda Gwena, PhD 2004, Degenerations of Prym varieties and
Cubic threefold
Michael Guy, PhD 2007, Moduli of Weighted Stable Maps and
Their Gravitational Descendants
Peter Petrov, PhD 2007, Nash problem on spaces of arcs
Joe Rusinko, PhD 2007, Equivalence of
Mirror Families Constructed from Toric Degenerations of Flag Varieties
Jaeho Shin
Xiaoyan (Shannon) Hu
Joe Tenini
Adrian Brunyate
Teaching
Spring 2012:
MATH 2260
"Integral calculus".
MATH 4690/6690
"Graph theory". Textbook:
Agnarsson-Greenlaw, Graph Theory: Modeling, Applications, and Algorithms
I am coorganizing the annual
UGA
Mathematical Competition for High School Students
Recipient of a 2009 Sandy Beaver Excellence in
Teaching Award from the UGA Franklin College of Arts and Sciences.
Mandatory
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