Research
These papers are organized in reverse chronological order.
Iitaka dimension for cycles submitted 

Positivity of the diagonal (joint with J.C. Ottem) submitted 

Geometric Manin's Conjecture and rational curves (joint with S. Tanimoto) submitted 

Correspondences between convex geometry and complex geometry (joint with J. Xiao) EpiGA 1 (2017), Art. 6 

On the geometry of thin exceptional sets in Manin's Conjecture (joint with S. Tanimoto) to appear in Duke Math. J. 

Positivity functions for curves on algebraic varieties (joint with J. Xiao) submitted 

Convexity and Zariski decomposition structure (joint with J. Xiao) Geom. Funct. Anal. 26 (2016), no. 4, 11351189 

Volume and Hilbert function of Rdivisors (joint with M. Fulger and J. Kollár) Mich. Math. J. 65 (2016), no. 2, 371387 

Balanced line bundles on Fano varieties (joint with S. Tanimoto and Y. Tschinkel) to appear in J. Reine Angew. Math. 

Positive cones of dual cycle classes (joint with M. Fulger) Alg. Geom. 4 (2017), no. 1, 128 

Morphisms and faces of pseudoeffective cones (joint with M. Fulger) Proc. Lon. Math. Soc. 112 (2016), no. 4, 651676 

Kernels of numerical pushforwards (joint with M. Fulger) to appear in Adv. Geom. 

Zariski decompositions of numerical cycle classes (joint with M. Fulger) J. Alg. Geom. 26 (2017), no. 1, 43106 

Asymptotic behavior of the dimension of the Chow variety Adv. Math. 308 (2017), 815835 

Volumetype functions for numerical cycle classes Duke Math. J. 165 (2016), no. 16, 31473187 

The movable cone via intersections 

Numerical triviality and pullbacks J. Pure Appl. Algebra 219 (2015), no. 12, 56375649 

Algebraic bounds on analytic multiplier ideals Ann. Inst. Fourier 64 (2014), no. 3, 10771108 

On Eckl's pseudoeffective reduction map Trans. Amer. Math. Soc. 366 (2014), 15251549 

Comparing numerical dimensions Algebra Number Theory 7 (2013), no. 5, 10651100 Update 2015: there is a mistake in the proof of Proposition 5.3 which affects the main theorem. The error is identified in a paper by Eckl. 

Reduction maps and minimal model theory (joint with Y. Gongyo) Compos. Math. 149 (2013), no. 2, 295308 

A cone theorem for nef curves J. of Alg. Geom. 21 (2012), no. 3, 473493 
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, 132 

An introduction to volume functions for algebraic cycles 
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) 

Volumetype functions for numerical cycle classes 
Here are some older expository papers that may be helpful.