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Books/Lecture notes

  1. Motivic integration, the McKay correspondence and wild ramification, in preparation, version:2021-11-11.

  2. A Glimpse into University Math Through Games, Kyoritsu Shuppan (Dec. 2018).

  3. Compoutational Algebraic Geometry with Macaulay2, (English translation of Japanese lecture notes written in Oct. 2012).

  4. Computing Invariant Rings with Macaulay2. (Nov. 2024)

Papers

My papers on Google Scholar

  1. On Igusa's conjectures for weighted homogeneous polynomials with isolated singularities,
    joint work with Kien Huu Nguyen,
    arXiv:2610.12222.

  2. The McKay correspondence and local heights for wild-by-tame split metacyclic groups,
    joint work with Julie Tavernier,
    arXiv:2605.04697.

  3. Exceptional loci of F-blowups and \(G\)-Hilbert schemes,
    joint work with Enrique Chávez-Martínez and Yutaro Kaijima,
    arXiv:2604.23591.

  4. An algorithm for the minimal model program in dimension three,
    arXiv:2603.13703.

  5. On linear \(\alpha_p\)-quotients,
    joint work with Quentin Posva, with an appendix by Linus Rösler,
    arXiv:2603.07152.

  6. Orbifold pseudo-effective cones of toric stacks,
    joint work with Ratko Darda,
    arXiv:2508.20434.

  7. Counting torsors for wild abelian groups,
    joint work with Ratko Darda,
    arXiv:2505.12784.

  8. The Batyrev-Manin conjecture for DM stacks II,
    joint work with Ratko Darda,
    arXiv:2502.07157.

  9. Quotient singularities by permutation actions are canonical,
    Épijournal de Géométrie Algébrique, Volume 9 (2025), Article no. 28, (Dec. 2025).
    DOI: https://doi.org/10.46298/epiga.2025.14300

  10. Motivic versions of mass formulas by Krasner, Serre and Bhargava,
    Forum of Mathematics, Sigma , Volume 13 , 2025 , e148, (Sep. 2025).
    DOI: https://doi.org/10.1017/fms.2025.10099

  11. The Manin conjecture for toric stacks,
    joint work with Ratko Darda,
    arXiv:2311.02012.

  12. Higher Jacobian ideals, contact equivalence and motivic zeta functions,
    joint work with Quy Thuong Lê,
    Revista Matemática Iberoamericana, Volume 41, no. 3, 1057–1080, (Apr. 2025, published online Oct. 2024).
    DOI: https://doi.org/10.4171/rmi/1516

  13. Non-commutative resolutions of linearly reductive quotient singularities,
    joint work with Christian Liedtke,
    The Quarterly Journal of Mathematics, Volume 75, Issue 3, 969–985, (Jun. 2024).
    DOI: https://doi.org/10.1093/qmath/haae033

  14. F-blowups and essential divisors for toric varieties,
    joint work with Enrique Chávez-Martínez and Daniel Duarte,
    Journal of the Mathematical Society of Japan, Vol. 77, No. 4 (Oct. 2025).
    DOI: https://doi.org/10.2969/jmsj/93529352

  15. Log centres of noncommutative crepant resolutions are Kawamata log terminal: remarks on a paper of Stafford and Van den Bergh,
    joint work with Colin Ingalls,
    Contemporary Mathematics 801, Recent Advances in Noncommutative Algebra and Geometry, 143-154, (Jul. 2024).
    Webpage of the entire volume

  16. Quantitative inverse Galois problem for semicommutative finite group schemes,
    joint work with Ratko Darda,
    Journal de théorie des nombres de Bordeaux, Vol. 37, no. 1, 105-123, (Jun. 2025).
    DOI: https://doi.org/10.5802/jtnb.1314

  17. The Batyrev-Manin conjecture for DM stacks,
    joint work with Ratko Darda,
    Journal of the European Mathematical Society, Vol. 28, No. 6, 2351–2400, (Mar. 2026, published online Jul, 2024)
    DOI: https://doi.org/10.4171/jems/1510

  18. Torsors for finite group schemes of bounded height,
    joint work with Ratko Darda,
    Journal of London Mathematical Society, Vol. 108, Issue 3, 1275-1331, (Sep. 2023).
    DOI: https://doi.org/10.1112/jlms.12780

  19. The isomorphism problem of projective schemes and related algorithmic problems,
    International Journal of Algebra and Computation, Vol. 33, No. 5, 893-926, (Jun. 2023).
    DOI: https://doi.org/10.1142/S021819672350039X

  20. Open problems in the wild McKay correspondence and related fields,
    Advanced Studies in Pure Mathematics, Vol. 88 "McKay correspondence, Mutation and related topics," 279-303, (Apr. 2023).
    DOI: https://doi.org/10.2969/aspm/08810279

  21. On the behavior of stringy motives under Galois quasi-étale covers,
    joint work with Javier Carvajal-Rojas,
    Documenta Mathematica, Vol. 30, No. 3, 709–751, (Jun. 2025).
    DOI: https://doi.org/10.4171/dm/1012

  22. The wild McKay correspondence for cyclic groups of prime power order,
    joint work with Mahito Tanno,
    Illinois Journal os Mathematics, 65, 619-654, (Sep. 2021).
    DOI: https://doi.org/10.1215/00192082-9402078

  23. Moduli of formal torsors II,
    joint work with Fabio Tonini,
    Annales l'Institut Fourier, Vo. 73, No. 2, 511-558, (May 2023).
    DOI: https://doi.org/10.5802/aif.3533

  24. Motivic integration over wild Deligne-Mumford stacks,
    Algebraic Geometry, 11(2), 178–255, (Mar. 2024).
    DOI: https://doi.org/10.14231/AG-2024-007

  25. The wild McKay correspondence via motivic integration,
    Sugaku, 70, 159-183 (Apr. 2018)
    (in Japanese. The original Japanese title is モチーフ積分による野性マッカイ対応.)
    DOI: https://doi.org/10.11429/sugaku.0702159, English version in Sugaku Expositions

  26. Notes on the motivic McKay correspondence for the group scheme \(\alpha_p \),
    joint work with Fabio Tonini,
    Singularities — Kagoshima 2017; Proceedings of the 5th Franco-Japanese-Vietnamese Symposium on Singularities, 215-233 (Jul. 2020).
    DOI: https://doi.org/10.1142/9789811206030_0011

  27. Discrepancies of \(p\)-cyclic quotient varieties,
    Journal of Mathematical Sciences, the University of Tokyo, 26, 1-14 (Mar. 2019).
    Journal article page

  28. Moduli of formal torsors,
    joint work with Fabio Tonini,
    Journal of Algebraic Geometry, 29, 753-801 (Jun. 2020).
    DOI: https://doi.org/10.1090/jag/771

  29. Motivic Serre invariants modulo the square of \(\mathbb{L}-1\),
    Proceedings of the American Mathematical Society, 146, 547-554 (Feb. 2018).
    DOI: https://doi.org/10.1090/proc/13780

  30. Vojta’s conjecture, singularities and multiplier-type ideals,
    Kodai Mathematical Journal, 41, 566-578 (Oct. 2018).
    DOI: https://doi.org/10.2996/kmj/1540951254 (this is a shortened version of the preprint "Vojta's conjecture for singular varieties", arXiv:1610.03593).

  31. Mass formulas for local Galois representations and quotient singularities II: dualities and resolution of singularities,
    joint work with Melanie Matchett Wood
    Algebra & Number Theory, 11, 817-840 (Jun. 2017).
    DOI: https://doi.org/10.2140/ant.2017.11.817 (Errata to this paper is available on the ANT website (posted online May 2019). Here are supplementary notes.)

  32. Manin's conjecture vs. Malle's conjecture,
    arXiv:1505.04555.

  33. The wild McKay correspondence and \(p\)-adic measures,
    Journal of the European Mathematical Society, 19, 3709-3734 (Nov. 2017). DOI: https://doi.org/10.4171/jems/751

  34. Densities of rational points and number fields,
    arXiv:1408.3912.

  35. Wilder McKay correspondences,
    Nagoya Mathematical Journal, 221, 111-164 (Mar. 2016).
    DOI: https://doi.org/10.1017/nmj.2016.3

  36. Mass formulas for local Galois representations and quotient singularities I: a comparison of counting functions,
    joint work with Melanie Matchett Wood,
    International Mathematics Research Notices, 2015, 12590–12619 (Jan. 2015).
    DOI: https://doi.org/10.1093/imrn/rnv074

  37. Toward motivic integration over wild Deligne-Mumford stacks,
    Higher dimensional algebraic geometry, Advanced Studies in Pure Mathematics, 74, 407-437 (2017).
    DOI: https://doi.org/10.2969/aspm/07410407

  38. Higher Semple-Nash blowups and F-blowups,
    Clay Mathematics Proceedings, Vol. 20, 327-340 (Jan., 2014). PDF of the entire volueme

  39. The p-cyclic McKay correspondence via motivic integration,
    Compositio Mathematica, 150, 1125-1168 (Jul., 2014).
    DOI: https://doi.org/10.1112/S0010437X13007781
    Corrigendum: Compositio Mathematica, 162, 1885-1886 (Aug., 2026).
    DOI: https://doi.org/10.1017/S0010437X26103534

  40. Pure subrings of regular local rings, endomorphism rings and Frobenius morphisms,
    Journal of Algebra, 370, 15-31 (Nov., 2012).
    DOI: https://doi.org/10.1016/j.jalgebra.2012.07.027

  41. F-blowups of normal surface singularities,
    joint work with Nobuo Hara and Tadakazu Sawada,
    Algebra & Number Theory 7-3, 733--763 (Aug., 2013).
    DOI: http://dx.doi.org/10.2140/ant.2013.7.733

  42. Frobenius morphisms of noncommutative blowups,
    Singularities in Geometry and Topology, Strasbourg 2009 (IRMA Lectures in Mathematics and Theoretical Physics 20), 269-283 (Dec., 2012).
    DOI: https://doi.org/10.4171/118-1/14

  43. Universal flattening of Frobenius,
    American Journal of Mathematics, 134, 349-378 (Apr., 2012).
    DOI: https://doi.org/10.1353/ajm.2012.0014, JSTOR article page

  44. Noncommutative resolution, F-blowups and D-modules,
    joint work with Yukinobu Toda,
    Advances in Mathematics, 222, 318-330 (Sep., 2009).
    DOI: https://doi.org/10.1016/j.aim.2009.04.004

  45. On monotonicity of F-blowup sequences,
    Illinois Journal of Mathematics, 53, 101-110 (May, 2009).
    DOI: https://doi.org/10.1215/ijm/1264170841

  46. Non-adic formal schemes,
    International Mathematics Research Notices, 2009, 2417-2475 (Feb., 2009).
    DOI: https://doi.org/10.1093/imrn/rnp021

  47. Flag higher Nash blowups,
    Communications in Algebra, 37, 1001-1015 (Mar., 2009).
    DOI: https://doi.org/10.1080/00927870802279022

  48. Higher Nash blowups,
    Compositio Mathematica, 143, 1493-1510 (Nov., 2007).
    DOI: https://doi.org/10.1112/S0010437X0700276X

  49. Motivic integration over Deligne-Mumford stacks,
    Advances in Mathematics, 207, 707-761 (Dec., 2006).
    DOI: https://doi.org/10.1016/j.aim.2006.01.004

  50. Jet schemes, log discrepancies and inversion of adjunction,
    joint work with L. Ein and M. Mustata,
    Inventiones Mathematicae, 153, 519-535, (Sep., 2003).
    DOI: https://doi.org/10.1007/s00222-003-0298-3

  51. Dimensions of jet schemes of log singularities,
    American Journal of Mathematics, 125, 1137-1145 (Oct., 2003).
    DOI: https://doi.org/10.1353/ajm.2003.0037, JSTOR article page

  52. Twisted jets, motivic measures and orbifold cohomology,
    Compositio Mathematica, 140, 396-422 (Mar., 2004).
    DOI: https://doi.org/10.1112/S0010437X03000368