Research Interests Papers/Preprints
  1. On liftable and weakly liftable modules
    J. Algebra, 318 (2007), 723-736.
  2. comments

  3. Some observations on local and projective hypersurfaces
    Math. Res. Lett., 15 (2008), 207-219.
  4. comments

  5. On injectivity of maps between Grothendieck groups induced by completion
    Mich. Math. J, 57 (2008), 195-199.
  6. comments

  7. Comparing complexities of pairs of modules (with Oana Veliche)
    J. Algebra, 322 (2009), 3047-3062.
  8. comments

  9. Remarks on non-commutative crepant resolutions over complete intersections
    Advances in Math. 224 (2010), 1021-1030.
  10. comments

  11. On the (non)rigidity of the Frobenius endomorphism over Gorenstein rings (with Jinjia Li and Claudia Miller)
    Algebra and Number Theory, 4:8 (2010), 1039-1053
  12. comments

  13. Asymptotic Behavior of Ext functors for modules of finite complete intersection dimension (with Olgur Celikbas)
    Math. Z., 269 (2011), 1005-1020.
  14. comments

  15. Decent intersection and Tor-rigidity for modules over local hypersurfaces
    Transactions of the AMS, 365 (2013), no. 6, 2803--2821.
  16. comments

  17. Picard groups of punctured spectra of dimension three local hypersurfaces are torsion-free
    Compositio Math, 148 (2012), 145--152.
  18. comments

  19. Vanishing of Ext, cluster-tilting modules and finite global dimension of endomorphism rings (with Craig Huneke)
    American J. Math., 135 (2013), no. 2, 561--578.
  20. comments

  21. Asymptotic behavior of Tor and applications
    preprint.
  22. comments

  23. Necessary conditions for Auslander's depth formula (with Olgur Celikbas)
    J. Pure and Applied Algebra, 218 (2014), no.3 522--530.
  24. comments

  25. Bounds on the Hilbert-Kunz Multiplicity (with Olgur Celikbas, Craig Huneke and Yi Zhang)
    Nagoya Math. Journal, 205 (2012), 149--165.
  26. comments

  27. Bounds on the regularity and projective dimension of ideals associated to graphs (with Craig Huneke and Jay Schweig)
    Journal of Algebraic Combinatorics, 38 (2013), no.1, 37--55.
  28. comments

  29. Projective Dimension, Graph Domination Parameters, and Independence Complex Homology (with Jay Schweig)
    Journal of Combinatorial Theory A, 120 (2013), no. 2, 453--469.
  30. comments

  31. Modules that detect finite homological dimensions (with Olgur Celikbas and Ryo Takahashi)
    Kyoto Journal of Mathematics, 54 (2014), no.2, 295--310.
  32. comments

  33. Some Homological Properties of Modules over a Complete Intersection, with Applications
    Commutative Algebra: Expository Papers Dedicated to David Eisenbud on the Occasion of His 65th Birthday, Springer, 2013.
  34. comments

  35. The radius of a subcategory of modules (with Ryo Takahashi)
    Algebra and Number Theory, 8 (2014), no. 1, 141--172.
  36. comments

  37. The dimension of a subcategory of modules (with Ryo Takahashi)
    Forum Math. Sigma, accepted.
  38. comments

  39. Classification of resolving subcategories and grade consistent functions (with Ryo Takahashi)
    International Math. Res. Notices, (2015), no. 1, 119--149.
  40. comments

  41. Upper bounds for dimensions of singularity categories (with Ryo Takahashi)
    Comptes rendus Mathematique, 353 (2015), no. 4, 297--301.
  42. comments

  43. Non-commutative resolutions and Grothendieck groups (with Osamu Iyama, Ryo Takahashi and Charles Vial)
    Journal of Non-commutative Geometry, 9 (2015), no. 1, 21--34.
  44. comments

  45. Hochster's theta pairing and numerical equivalence (with Kazuhiko Kurano)
    Journal of K-Theory, 14 (2014), no. 3, 495--525.
  46. comments

  47. Bounding Projective Dimensions of square-free Monomial Ideals using domination parameters for clutters (with Jay Schweig)
    Proceedings of AMS, 143 (2015), no. 2, 555--565.
  48. comments

  49. On generalized Hilbert-Kunz function and multiplicity (with Ilya Smirnov)
    submitted.
  50. comments

  51. Noncommutative desingularizations and the global spectrum of a commutative ring (with Eleonore Faber and Colin Ingalls)
    Algebra and Representation Theory, 18 (2015), no. 3, 633--664.
  52. comments

  53. Further applications of clutter domination parameters to projective dimension (with Jay Schweig)
    Journal of Algebra, 432 (2015), 1--11.
  54. comments

  55. Boundary and shape of Cohen-Macaulay cone (with Kazuhiko Kurano)
    Mathematische Annalen, accepted.
  56. comments

  57. On the relationship between depth and cohomological dimension (with Shunsuke Takagi)
    Compositio Math., accepted
  58. comments

  59. Some computations of higher Hilbert-Kunz multiplicities (with Kei-ichi Watanabe)
    Proceedings of AMS, accepted
  60. comments

  61. Representation schemes and rigid maximal Cohen-Macaulay modules (with Ian Shipman)
    Selecta Mathematica, accepted
  62. comments

  63. Cohomological support and the geometric join (with Billy Sanders)
    submitted.
  64. comments

  65. On the associated primes of local cohomology (with Pham Hung Quy)
    submitted.
  66. comments

  67. Finite F-type and F-abundant modules (with Tony Se)
    submitted.
  68. comments

  69. Noncommutative resolutions using syzygies (with Osamu Iyama, Srikanth B. Iyengar, Ryo Takahashi, Michael Wemyss, Yuji Yoshino)
    submitted.
  70. comments

  71. Gorenstein modifications and Q-Gorenstein rings (with Osamu Iyama, Ryo Takahashi, Michael Wemyss)
    submitted.
  72. comments

In preparation (this means that some rough version exists, email me if you are interested. In fact, your email would probably motivate us to finish them sooner (-:):

  1. Asymptotic behavior of system of ideals via K-theoretic methods (with Kazuhiko Kurano)
    in preparation.
  2. comments

  3. A generalization of Lipman-Danilov theorem on class groups (with Scot Pruyn)
    in preparation.
  4. comments

  5. On the module structure of Hom(M,N)
    in preparation.
  6. comments