These papers are organized in reverse chronological order.

 Rational curves on del Pezzo surfaces in positive characteristic (joint with R. Beheshti, E. Riedl, S. Tanimoto)submitted pdf arxiv Classifying sections of del Pezzo fibrations, II (joint with S. Tanimoto)to appear in Geom. & Top. pdf arxiv Restricted tangent bundles for general free rational curves (joint with E. Riedl)to appear in IMRN pdf arxiv Moduli spaces of rational curves on Fano threefolds (joint with R. Beheshti, E. Riedl, S. Tanimoto)Adv. Math. 408 (2022), Paper No. 108557 pdf arxiv Classifying sections of del Pezzo fibrations, I (joint with S. Tanimoto)submitted pdf arxiv Rational curves on prime Fano threefolds of index 1 (joint with S. Tanimoto)J. Alg. Geom. 30 (2021), no. 1, 151-188 pdf arxiv On exceptional sets in Manin’s Conjecture (joint with S. Tanimoto)Res. Math. Sci. 6 (2019), no. 1, Paper No. 12, 41 pp. pdf arxiv Geometric consistency of Manin’s Conjecture (joint with A.K. Sengupta, S. Tanimoto)to appear in Compos. Math. pdf arxiv Iitaka dimension for cycles Trans. Amer. Math. Soc. 371 (2019), no. 7, 4815-4835 pdf arxiv Positivity of the diagonal (joint with J.C. Ottem)Adv. Math. 335 (2018), 664-695 pdf arxiv Geometric Manin’s Conjecture and rational curves (joint with S. Tanimoto)Compos. Math. 155 (2019), no. 5, 833-862 Errata: The formulation of Geometric Manin’s Conjecture is not quite correct. The definition of the \alpha-constant in the paper is incorrect; the (well-known) typical definition should be used instead. Also, Conjecture 6.5 is incorrect; it should be modified by looking at algebraic instead of numerical equivalence. pdf arxiv Correspondences between convex geometry and complex geometry (joint with J. Xiao)EpiGA 1 (2017), Art. 6 pdf arxiv On the geometry of thin exceptional sets in Manin’s Conjecture (joint with S. Tanimoto)Duke Math. J. 166 (2017), no. 15, 2815-2869 Errata: the proof of Proposition 7.2 is not complete. In the erratum we prove a slightly weaker statement which suffices for all applications in the paper. pdf arxiv Positivity functions for curves on algebraic varieties (joint with J. Xiao)Algebra Number Theory 13 (2019), no. 6, 1243-1279 pdf arxiv Convexity and Zariski decomposition structure (joint with J. Xiao)Geom. Funct. Anal. 26 (2016), no. 4, 1135-1189 pdf arxiv Volume and Hilbert function of R-divisors (joint with M. Fulger and J. Kollár)Mich. Math. J. 65 (2016), no. 2, 371-387 pdf arxiv Balanced line bundles on Fano varieties (joint with S. Tanimoto and Y. Tschinkel)J. Reine Angew. Math. 743 (2018), 91-131 pdf arxiv Positive cones of dual cycle classes (joint with M. Fulger)Alg. Geom. 4 (2017), no. 1, 1-28 pdf arxiv Morphisms and faces of pseudo-effective cones (joint with M. Fulger)Proc. Lon. Math. Soc. 112 (2016), no. 4, 651-676 pdf arxiv Kernels of numerical pushforwards (joint with M. Fulger)Adv. Geom. 17 (2017), no. 3, 373-378 pdf arxiv Zariski decompositions of numerical cycle classes (joint with M. Fulger)J. Alg. Geom. 26 (2017), no. 1, 43-106Errata: Angela Gibney has informed me there are some mistakes in the calculations for symmetrized M_0,7. See this paper by Han-Bom Moon for some correct calculations. pdf arxiv Asymptotic behavior of the dimension of the Chow variety Adv. Math. 308 (2017), 815-835 Errata: When publishing the paper I was completely unaware that the calculation of the dimension of the Chow variety of P^n was done previously by Pablo Azcue in his 1992 thesis “On the dimension of Chow varieties” under Joe Harris at Harvard. I would like to sincerely apologize for the inadvertent failure to credit Azcue for this result. pdf arxiv Volume-type functions for numerical cycle classes Duke Math. J. 165 (2016), no. 16, 3147-3187 pdf arxiv The movable cone via intersections pdf arxiv Numerical triviality and pullbacks J. Pure Appl. Algebra 219 (2015), no. 12, 5637-5649 pdf arxiv Algebraic bounds on analytic multiplier ideals Ann. Inst. Fourier 64 (2014), no. 3, 1077-1108Errata: In the statement of Theorem 1.4 this paper inherits the ambiguity about the definition of abundance from “On Eckl’s pseudo-effective reduction map”. See the errata of that paper for a discussion of which definition must be used. pdf arxiv On Eckl’s pseudo-effective reduction map Trans. Amer. Math. Soc. 366 (2014), 1525-1549Errata: Due to the errors in “Comparing numerical dimensions”, one must be careful about which numerical dimension is used in this paper. See here for a careful discussion. pdf arxiv Comparing numerical dimensions Algebra Number Theory 7 (2013), no. 5, 1065-1100Errata: As demonstrated by this paper by John Lesieutre, the statement of the main theorem is incorrect. There is a mistake in the proof of Proposition 5.3 which invalidates one step in the long chain of inequalities used to prove the main theorem. This error was first pointed out to me by Thomas Eckl. To the best of my knowledge all other parts of the paper are correct: the paper establishes new inequalities between various definitions of the numerical dimension. The corrected statements can be found here or in Lesieutre’s paper. pdf arxiv Reduction maps and minimal model theory (joint with Y. Gongyo)Compos. Math. 149 (2013), no. 2, 295-308Errata: In the proof of Theorem 4.3, we use a result of Noboru Nakayama. Osamu Fujino has informed me that the proof in the citation is incomplete, but it is fixed in this note by Fujino. Due to the error in “Comparing numerical dimensions”, one must be careful about which version of the numerical dimension is used. In this paper we are using kappa_sigma as defined by Nakayama. As explained in the errata to “On Eckl’s pseudo-effective reduction map”, the main results of that paper are compatible with this definition. pdf arxiv A cone theorem for nef curves J. of Alg. Geom. 21 (2012), no. 3, 473-493 pdf arxiv

Expository papers: here are a couple survey papers related to different areas of my research.

 A snapshot of the Minimal Model Program Proc. of Symp. in Pure Math. 95 (2017), AMS, 1-32 pdf An introduction to volume functions for algebraic cycles pdf On exceptional sets in Manin’s Conjecture (joint with S. Tanimoto)Res. Math. Sci. 6 (2019), no. 1, Paper No. 12, 41 pp. pdf arxiv

Long versions: here are longer versions of a couple papers. Warning: there may be errors in these papers that are not in the published versions.

 Zariski decomposition of curves on algebraic varieties (joint with J. Xiao) pdf Volume-type functions for numerical cycle classes pdf