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, 1135-1189
Volume and Hilbert function of R-divisors (joint with M. Fulger and J. Kollár)
Mich. Math. J. 65 (2016), no. 2, 371-387
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, 1-28
Morphisms and faces of pseudo-effective cones (joint with M. Fulger)
Proc. Lon. Math. Soc. 112 (2016), no. 4, 651-676
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, 43-106
Asymptotic behavior of the dimension of the Chow variety
Adv. Math. 308 (2017), 815-835
Volume-type functions for numerical cycle classes
Duke Math. J. 165 (2016), no. 16, 3147-3187
The movable cone via intersections
Numerical triviality and pullbacks
J. Pure Appl. Algebra 219 (2015), no. 12, 5637-5649
Algebraic bounds on analytic multiplier ideals
Ann. Inst. Fourier 64 (2014), no. 3, 1077-1108
On Eckl's pseudo-effective reduction map
Trans. Amer. Math. Soc. 366 (2014), 1525-1549
Comparing numerical dimensions
Algebra Number Theory 7 (2013), no. 5, 1065-1100
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, 295-308
A cone theorem for nef curves
J. of Alg. Geom. 21 (2012), no. 3, 473-493

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
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)
Volume-type functions for numerical cycle classes

Here are some older expository papers that may be helpful.