Publications
- Vanishing sequences and Okounkov bodies (with Sébastien Boucksom, Catriona Maclean, and Tomasz Szemberg), arXiv:1306.2181 Mostly supercedes the arXiv submission 1210.3523v2 below, nevertheless the respective contents of the two papers differ considerably.
- Seshadri constants via Okounkov functions and the Segre--Harbourne--Gimigliano--Hirschowitz conjecture (with Marcin Dumnicki, Catriona Maclean, and Tomasz Szemberg), arXiv:1304.0249
- Functions on Okounkov bodies coming from geometric valuations (with an Appendix by Sébastien Boucksom) (with Catriona Maclean and Tomasz Szemberg), arXiv:1210.3523v2
- Okounkov bodies of finitely generated divisors (with Dave Anderson and Victor Lozovanu), arXiv:1206.2499v2, International Mathematics Research Notices, DOI: 10.1093/imrn/rns286.
- Finite generation and geography of models (with Anne-Sophie Kaloghiros and Vladimir Lazić), arXiv:1202.1164, to appear in "Minimal models and extremal rays", Advanced Studies in Pure Mathematics, Mathematical Society of Japan, Tokyo.
- Negative curves on algebraic surfaces (with Th. Bauer, B. Harbourne, A. L. Knutsen, S. Müller-Stach, T. Szemberg), arXiv:1109.1881v2, to appear in Duke Math. J.
- Recent developments and open problems in the theory of linear series (with Thomas Bauer, Christiano Bocci, Susan Cooper, Sandra Di Rocco, Marcin Dumnicki, Brian Harbourne, Kelly Jabbusch, Andreas Leopold Knutsen, Rick Miranda, Joaqim Roé, Hal Schenck, Tomasz Szemberg, Zach Teitler), arXiv:1101.4363, In ''Contributions to Algebraic Geometry'', 93--140, IMPANGA Lecture Notes (Piotr Pragacz , ed.), EMS Series of Congress Reports, edited by the European Mathematical Society Publishing House 2012.
- Positivity on subvarieties and vanishing theorems for higher cohomology, arXiv:1012.1102, Annales de l'Institut Fourier 63 (2013).
- Convex bodies appearing as Okounkov bodies of divisors (with Victor Lozovanu and Catriona Maclean), arXiv:1008.4431, Advances in Mathematics 229 (2012), 2622-2639. .
- Volume functions of linear series (with Victor Lozovanu and Catriona Maclean), arxiv:1008.3986, Mathematische Annalen, DOI: 10.1007/s00208-012-0859-0.
- Zariski decompositions of b-divisors (with Catriona Maclean), arxiv:0807.2809, Mathematische Zeitschrift, DOI: 10.1007/s00209-012-1012-1.
- Higher cohomology of divisors on a projective variety (with Tommaso de Fernex and Robert Lazarsfeld), Mathematische Annalen 337 No. 2. (2007), 443-455.
- A Briancon--Skoda type theorem for graded systems of ideals (with Alexandre Wolfe), Journal of Algebra 307 No. 2. (2007), 795-803.
- Asymptotic cohomological functions on projective varieties, American Journal of Mathematics 128 No. 6. (2006) 1475-1519.
- Asymptotic cohomological functions of toric divisors (with Milena Hering and Sam Payne), Advances in Mathematics 207 No. 2. (2006) 634-645.
- Zariski decompositions, volumes, and stable base loci (with Thomas Bauer and Tomasz Szemberg), Journal für die reine und angewandte Mathematik 576 (2004), 209-233.
- A divisorial valuation with irrational volume, Journal of Algebra 262 (2003), 413-423.
- Computing Levi decompositions in Lie algebras (with Willem de Graaf, Gábor Ivanyos, and Lajos Rónyai), Applicable Algebra in Engineering, Communication and Computing 8 (1997), 291-304.