ANURAG K SINGH portrait
  • Professor, Mathematics

Publications

  • Mel Hochster, Jack Jeffries, Vaibhav Pandey, and Anurag K. Singh, When are the natural embeddings of classical invariant rings pure? Forum of Mathematics, Sigma 11 (2023), paper no. e67, 43 pp. Published, 08/2023.
  • Bhargav Bhatt, Manuel Blickle, Gennady Lyubeznik, Anurag K. Singh, and Wenliang Zhang, Frobenius on the cohomology of thickenings, International Mathematics Research Notices, to appear. Published, 12/2023.
  • Jack Jeffries and Anurag K. Singh, Differential operators on classical invariant rings do not lift modulo p, Advances in Mathematics 432 (2023), paper no. 109276, 53 pp. Published, 08/2023.
  • Annie Giokas and Anurag K. Singh, On an example of Nagarajan, Journal of Algebra 638 (2024), 931-936. Published, 10/2023.
  • Anurag K. Singh and Kei-ichi Watanabe, On Segre products, F-regularity, and finite Frobenius representation type, Acta Mathematica Vietnamica, special volume in honor of Ngo Viet Trung, to appear. Published, 06/2023.
  • Bhargav Bhatt, Manuel Blickle, Gennady Lyubeznik, Anurag K. Singh, and Wenliang Zhang, An asymptotic vanishing theorem for the cohomology of thickenings, Mathematische Annalen 380 (2021), 161-173. Published, 12/01/2021.
  • Linquan Ma, Anurag K. Singh, and Uli Walther, Koszul and local cohomology, and a question of Dutta, Mathematische Zeitschrift 298 (2021), 697-711. Published, 11/01/2021.
  • Anurag K. Singh, Ryo Takahashi, and Kei-ichi Watanabe, Homogeneous prime elements in normal two-dimensional graded rings, Journal of Algebra 571 (2021), 339-349. Published, 12/2021.
  • Anurag K. Singh and Uli Walther, On a conjecture of Lynch, Communications in Algebra 48 (2020), 2681-2682. Published, 01/2020.
  • Bhargav Bhatt, Manuel Blickle, Gennady Lyubeznik, Anurag K. Singh, and Wenliang Zhang, Stabilization of the cohomology of thickenings, American Journal of Mathematics 141 (2019), 531-561. Published, 12/2019.
  • Aldo Conca, Maral Mostafazadehfard, Anurag K. Singh, and Matteo Varbaro, Hankel determinantal rings have rational singularities, Advances in Mathematics 335, (2018), 111-129. Published, 09/2018.
  • Anurag K. Singh, A polynomial identity via differential operators, in: Homological and computational methods in commutative algebra, Springer INdAM Series 20 (2017), 239-247. Published, 12/2017.
  • Anurag K. Singh, Shusuke Takagi, and Matteo Varbaro, A Gorenstein criterion for strongly F-regular and log terminal singularities, International Mathematics Research Notices 21, (2017), 6484-6522. Published, 12/2017.
  • Gennady Lyubeznik, Anurag K. Singh, and Uli Walther, Local cohomology modules supported at determinantal ideals, Journal of the European Mathematical Society 18 (2016), 2545-2578. Published, 12/2016.
  • Bhargav Bhatt and Anurag K. Singh, The F-pure threshold of a Calabi-Yau hypersurface, Mathematische Annalen 362 (2015), 551-567. Published, 12/2015.
  • Lance E. Miller, Anurag K. Singh, and Matteo Varbaro, The F-pure threshold of a determinantal ideal, Bulletin of the Brazilian Mathematical Society 45 (2014), 767-775. Published, 12/2014.
  • Jun Horiuchi, Lance E. Miller, Karl Schwede, Kazuma Shimomoto, and Anurag K. Singh, Deformation of F-injectivity and local cohomology, Indiana University Mathematics Journal 63 (2014), 1139-1157. Published, 12/2014.
  • Bhargav Bhatt, Manuel Blickle, Gennady Lyubeznik, Anurag K. Singh, and Wenliang Zhang, Local cohomology modules of a smooth Z-algebra have finitely many associated primes, Inventiones Mathematicae 197 (2014), 509-519. Published, 12/2014.
  • Mordechai Katzman, Karl Schwede, Anurag K. Singh, and Wenliang Zhang, Rings of Frobenius operators, Mathematical Proceedings of the Cambridge Philosophical Society 157 (2014), 151-167. Published, 12/2014.
  • Anurag K. Singh and Uli Walther, A note on Bockstein homomorphisms in local cohomology, Advanced Studies in Pure Mathematics 62 (2012), 513-521. Published, 12/2012.
  • Akiyoshi Sannai and Anurag K. Singh, Galois extensions, plus closure, and maps on local cohomology, Advances in Mathematics 229 (2012), 1847-1861. Published, 02/2012.
  • Paul Roberts and Anurag K. Singh, Reconciling Riemann-Roch results, Contemporary Mathematics 555 (2011) 165-172. Published, 05/2011.
  • Anurag K. Singh and Uli Walther, Bockstein homomorphisms in local cohomology, with Uli Walther, Journal für die reine und angewandte Mathematik 655 (2011) 147-164. Published, 06/2011.
  • Anurag K. Singh and Irena Swanson, An algorithm for computing the integral closure, Algebra & Number Theory 3 (2009), 587-595. Published, 12/2009.
  • Kazuhiko Kurano, Ei-ichi Sato, Anurag K. Singh, and Kei-ichi Watanabe, Multigraded rings, diagonal subalgebras, and rational singularities, Journal of Algebra, 322 (2009), 3248-3267. Published, 12/2009.
  • Anurag K. Singh, Tight closure: applications and questions, in: Proceedings of the 4th Japan-Vietnam Joint Seminar on Commutative Algebra, February 17-21, 2009, Meiji University (2009), 45-63. Published, 12/2009.
  • Anurag K. Singh and Uli Walther, A connectedness result in positive characteristic, Transactions of the American Mathematical Society 360 (2008) 3107-3119. Published, 06/2008.
  • Anurag K. Singh and Sandra Spiroff, Divisor class groups of graded hypersurfaces, Contemporary Mathematics 448 (2007), 237-243. Published, 12/2007.
  • Anurag K. Singh and Uli Walther, Local cohomology and pure morphisms, Illinois Journal of Mathematics 51 (2007), 287-298. Published, 12/2007.
  • Paul Roberts, Anurag K. Singh, and V. Srinivas, Annihilators of local cohomology in characteristic zero, Illinois Journal of Mathematics 51 (2007), 237-254. Published, 12/2007.
  • Anurag K. Singh and Uli Walther, On the arithmetic rank of certain Segre products, Contemporary Mathematics 390 (2005), 147-155. Published, 12/2005.
  • Anurag K. Singh, The F-signature of an affine semigroup rings, Journal of Pure and Applied Algebra 196 (2005), 313-321. Published, 12/2005.
  • Anurag K. Singh and Irena Swanson, Associated primes of local cohomology modules and of Frobenius powers, International Mathematics Research Notices 33 (2004), 1703-1733. Published, 12/2004.
  • Anurag K. Singh, Associated primes of local cohomology modules, in: Proceedings of the 48th Algebra Symposium, August 4-7, 2003, Nagoya University (2003), 133-145. Published, 12/2003.
  • Anurag K. Singh, Cyclic covers of rings with rational singularities, Transactions of the American Mathematical Society 355 (2003), 1009-1024. Published, 12/2003.
  • Kazuhiko Kurano and Anurag K.Singh, Todd classes of affine cones of Grassmannians, International Mathematics Research Notices 35 (2002), 1841-1855. Published, 12/2002.
  • Anurag K. Singh, p-torsion elements in local cohomology modules II, in: Local Cohomology and its Applications, Marcel Dekker (2002), 155-167. Published, 12/2002.
  • Anurag K. Singh, Relative test elements for tight closure, Journal of Pure and Applied Algebra 158 (2001), 101-109. Published, 12/2001.
  • Anurag K. Singh, p-torsion elements in local cohomology modules, Mathematical Research Letters 7 (2000), 165-176. Published, 12/2000.
  • Claudia M. Miller and Anurag K. Singh, Intersection multiplicities over Gorenstein rings, Mathematische Annalen 317 (2000), 155-171. Published, 12/2000.
  • Anurag K. Singh, Veronese subrings and tight closure, Pacific Journal of Mathematics 192 (2000), 399-413. Published, 12/2000.
  • Anurag K. Singh, Multi-symbolic Rees algebras and strong F-regularity, Mathematische Zeitschrift 235 (2000), 335-344. Published, 12/2000.
  • Anurag K. Singh, Q-Gorenstein splinter rings of characteristic p are F-regular, Mathematical Proceedings of the Cambridge Philosophical Society 127 (1999), 201-205. Published, 12/1999.
  • Anurag K. Singh, Separable integral extensions and plus closure, Manuscripta Mathematica 98 (1999), 497-506. Published, 12/1999.
  • Anurag K. Singh, F-regularity does not deform, American Journal of Mathematics 121 (1999), 919-929. Published, 12/1999.
  • Anurag K. Singh, Deformation of F-purity and F-regularity, Journal of Pure and Applied Algebra 140 (1999), 137-148. Published, 12/1999.
  • Anurag K. Singh, Tight closure in non-equidimensional rings, Communications in Algebra 26 (1998), 3969-3983. Published, 12/1998.
  • Anurag K. Singh, A computation of tight closure in diagonal hypersurfaces, Journal of Algebra 203 (1998), 579-589. Published, 12/1998.
  • Anurag K. Singh, Failure of F-purity and F-regularity in certain rings of invariants, Illinois Journal of Mathematics 42 (1998), 441-448. Published, 12/1998.
  • Srikanth B. Iyengar, Graham Leuschke, Anton Leykin, Claudia Miller, Ezra Miller, Anurag K. Singh, and Uli Walther, Twenty-four hours of local cohomology, AMS Graduate Studies in Mathematics 87, 2007. Published, 12/2007.

Grants, Contracts & Research Gifts

  • Local cohomology, differential operators, and determinantal rings. PI: Anurag K. Singh. NSF, 06/01/2021 - 05/31/2024. Total project budget to date: $270,000.00
  • Determinantal rings, local cohomology, and tight closure. PI: Anurag K. Singh. NSF, 06/01/2018 - 05/31/2021. Total project budget to date: $255,000.00