Research

Research Papers including Preprints

[33] Intermediate Jacobians and Burnside invariants
(with A. Kresch and Y. Tschinkel),
to appear in Journal of the Mathematical Society of Japan, (2025),

[32] Homological stability and weak approximation
(with Y. Tschinkel), submitted, (2025),

[31] The spaces of rational curves on del Pezzo surfaces via conic bundles
submitted, (2025),

[30] Homological stability and Manin’s conjecture for rational curves on quartic del Pezzo surfaces (with R. Das, B. Lehmann, and P. Tosteson: an appendix by W. Sawin and M. Shusterman),
submitted, (2025),
the longer version,

[29] Degree two unirational parametrizations over the real field
(with B. Hassett and H. Takagi), submitted, (2025),

[28] Codimension of jumping loci
(with B. Lehmann and E. Riedl),
Journal of Algebraic Geometry, vol. 34, no. 4, 755–814, (2025),
the published version

[27] Campana rational connectedness and weak approximation
(with Q. Chen and B. Lehmann),
to appear in Algebraic Geometry, (2025),

[26] Intermediate Jacobians and linearizability
(with T. Ciurca and Y. Tschinkel),
to appear in Kyoto Journal of Mathematics, (2025),

[25] Campana points on wonderful compactifications
(with D. Chow, D. Loughran, and R. Takloo-Bighash),
Mathematische Annalen, vol. 394, no. 3, article 69, (2026),

[24] On the asymptotic enumerative property for Fano manifolds
(with R. Beheshti, B. Lehmann, C. Lian, E. Riedl, and J. Starr),
Forum of Mathematics, Sigma, vol. 12, e112, (2024),

[23] Non-free curves on Fano varieties
(with B. Lehmann and E. Riedl),
Osaka Journal of Mathematics, vol. 62, no. 1, 19–50, (2025),
the published version, Erratum

[22] Non-free sections of Fano fibrations
(with B. Lehmann and E. Riedl),
to appear in Memoirs of the American Mathematical Society, (2025),

[21] Rational curves on del Pezzo surfaces in positive characteristic
(with R. Beheshti, B. Lehmann, and E. Riedl),
Transactions of the American Mathematical Society, Series B, 10, 407–451, (2023),

[20] The spaces of rational curves on del Pezzo threefolds of degree one
(with N. Shimizu),
European Journal of Mathematics, vol. 8, no. 1, 291–308, (2022),
the published version

[19] Moduli spaces of rational curves on Fano threefolds
(with R. Beheshti, B. Lehmann, and E. Riedl),
Advances in Mathematics, vol. 408 part A, article 108557, (2022),

[18] Classifying sections of del Pezzo fibrations, II
(with B. Lehmann),
Geometry & Topology, 26-6, 2565–2647, (2022),
the published version

[17] Classifying sections of del Pezzo fibrations, I
(with B. Lehmann),
Journal of the European Mathematical Society, vol. 26, no. 1, p. 289–354, (2024),
the published version

[16] Campana points of bounded height on vector group compactifications
(with M. Pieropan, A. Smeets, and A. Varilly-Alvarado),  
Proceedings of the London Mathematical Society, vol. 123, no. 1, 57–101, (2021),

[15] On upper bounds of Manin type
Algebra & Number Theory, 14-3, 731–761, (2020),
the published version

[14] Geometric consistency of Manin’s conjecture
(with B. Lehmann and A. K. Sengupta),
Compositio Mathematica, vol. 158, no. 6, 1375–1427, (2022),

[13] Rational curves on prime Fano threefolds of index 1
(with B. Lehmann),
Journal of Algebraic Geometry, vol. 30 no. 1, 151–188, (2021),
the published version Erratum

[12] Geometric Manin’s conjecture and rational curves
(with B. Lehmann),
Compositio Mathematica, vol. 155, no. 5, 833–862, (2019),
the published version

[11] Zero-loci of Brauer group elements on semi-simple algebraic groups
(with D. Loughran and R. Takloo-Bighash),
Journal of the Institute of Mathematics of Jussieu, vol.19, no.5, 1467–1507, (2020),
the published version

[10] Abelian Calabi-Yau threefolds: Neron models and rational points
(with F. Bogomolov, L. H. Halle, and F. Pazuki),
Mathematical Research Letters, vol. 25, no. 2, 367–392, (2018),
the published version

[9] On the geometry of thin exceptional sets in Manin’s conjecture
(with B. Lehmann),
Duke Mathematical Journal, vol. 166, no. 15, 2815–2869, (2017),
the published version Erratum

[8] Effective bounds for Brauer groups of Kummer surfaces over number fields
(with V. Cantoral-Farfan, Y. Tang, and E. Visse),
Journal of the London Mathematical Society, vol. 97, no. 3, 353–376, (2018),
the published version

[7] Distribution of rational points of bounded height on equivariant compactifications of PGL_2 I (with R. Takloo-Bighash),
Research in Number Theory, vol. 2, Art 6, (2016),

[6] Kodaira dimension of moduli of special cubic fourfolds
(with A. Varilly-Alvarado),
Journal fur die reine und angewandte Mathematik (Crelle), 752, 265–300 (2019),
the published version

[5] Balanced line bundles on Fano varieties
(with B. Lehmann and Y. Tschinkel),
Journal fur die reine und angewandte Mathematik (Crelle), 743, 91–131, (2018),
the published version

[4] The distribution of S-integral points on SL_2 orbit closures of binary forms
(with J. Tanis),
Journal of the London Mathematical Society, vol. 92, no. 3, 760–777, (2015),
the published version

[3] Brauer groups on K3 surfaces and arithmetic applications
(with K. McKinnie, J. Sawon, and A. Varilly-Alvarado),
Progress in Mathematics vol. 320 “Brauer groups and obstruction problems: moduli spaces and arithmetic”, Birkhauser, 177–218, (2017),
the published version

[2] Balanced line bundles and equivariant compactifications of homogeneous spaces
(with B. Hassett and Y. Tschinkel),
International Mathematics Research Notices, vol. 2015, no. 15, 6375–6410, (2015),
the published version

[1] Height zeta functions of equivariant compactifications of semi-direct products of algebraic groups (with Y. Tschinkel),
Contemporary Mathematics, 566, “Zeta functions in Algebra and Geometry”, 119–157, (2012),

Books

[2] Birational Geometry and Manin’s Conjecture
to appear in Cambridge Tracts in Mathematics, (2026),

[1] Proceedings of Kinosaki Algebraic Geometry Symposium 2023
(edited with T. Abe and I. Iwanari), pp. 140, (2024),

Survey Papers and etc

[14] Geometric Manin’s conjecture in characteristic p
(with B. Lehmann), submitted,

[13] Rational curves on Fano threefolds
ZAG handbook of modern algebraic geometry, (2025),

[12] From exceptional sets to non-free sections
RIMS Kokyuroku, 2295, “Algebraic Number Theory and Related Topics 2023”, 111–122, (2024),

[11] Diophantine equations (Japanese)
Lecture notes for public lecture series of Mathematics AGORA, Graduate School of Mathematics, Nagoya University, (2023),

[10] Exceptional sets in Manin’s conjecture and their applications to algebraic geometry (Japanese)
An extended abstract for an invited talk at Algebra section, MSJ Autumn Meeting 2023, (2023),

[9] From exceptional sets to non-free sections
Oberwolfach reports, vol. 20, no. 2, Recent Trends in Algebraic Geometry, (2023),
the published version

[8] On Manin’s conjecture (Japanese)
to appear in Sugaku, (2022),

[7] An introduction to Geometric Manin’s conjecture
Proceedings of Miyako-no-Seihoku Algebraic Geometry Symposium 2021, “Positivity of tangent bundles and related topics”, 102–118 (2021),

[6] Campana points, Height zeta functions, and log Manin’s conjecture
RIMS Kokyuroku 2196, “Problems and Prospects in Analytic Number Theory”, 26–36 (2021),

[5] Book Review: Osamu Fujino, “Foundations of the minimal model program” (Japanese)
Sugaku, vol. 73, no. 3, 323–327 (2021),
the published version

[4] Movable Bend and Break for sections of del Pezzo fibrations
Proceedings of 64th Algebra Symposium 2019, 209–220 (2020),

[3] Unramified Brauer groups and rationality problems of invariant fields (Japanese)
Proceedings of 27th Number Theory Summer School 2019 “Constructive inverse Galois problem and rationality of invariant fields”, 255–266 (2020),

[2] Geometric aspects of Manin’s Conjecture
Proceedings of Kinosaki Algebraic Geometry Symposium 2018, (2019),

[1] On exceptional sets in Manin’s conjecture
(with B. Lehmann),
Research in the Mathematical Sciences, vol. 6, Art 12, (2019),
the published version

[0] Distribution of rational points on algebraic varieties
Ph. D. Thesis, New York University, (2012),