Department of Mathematics
University of Georgia
Athens GA 30602, USA

Algebraic geometry seminar

Recent papers and preprints

(with Michael Guy) Moduli of weighted stable maps and their gravitational descendants, Journal of the Institute of Mathematics of Jussieu, to appear.

Limits of stable pairs, Pure and Applied Math Quaterly, 4 (2008), no.3, 1-15, to appear.

(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

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)

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.

Descriptions of some older papers

My students

Teaching

Fall 2007:
MATH 8310: Schemes, sheaves, and cohomology
MATH 8800: Tropical geometry

Spring 2008:
MATH 3000: Linear algebra
MATH 8800: Tropical geometry

Previously taught courses at UGA.

I am coorganizing the annual UGA Mathematical Competition for High School Students

Conferences, talks, etc

April 11-13, Texas Algebraic Geometry Seminar, Houston

May 28 - June 3, 2008: Kurosh-100 conference, Moscow, Russia

June 13, 2008: Universita di Roma "La Sapienza", Rome, Italy

June 16-28, 2008: Aspects of Moduli (workshop and conference), Scuola Normale, Pisa, Italy

June 30 - July 5, Satellite conference on algebraic geometry for the European Congress of Mathematics, Leiden, Netherlands

July 6-20, 2008: Analytic and algebraic geometry, Park City, Utah

July 21-25, Concluding WAG conference, Warwick, England

September 22-26, Higher dimensional algebraic geometry, Edinburgh, Scotland

(2009)