Publications

  • L. L. Avramov (2018). Homology over trivial extensions of commutative DG algebras. Communications in Algebra. Published, 12/2018.
  • L. L. Avramov (2018). Restricting homology to hypersurfaces. Springer. Published, 11/2018.
  • Srikanth B. Iyengar & Ryo Takahashi (2018). The Jacobian ideal of a commutative ring and annihilators of cohomology. Journal of Algebra. Published, 08/2018.
  • D. Benson & S. B. Iyengar, H. Krause, J. Pevtsova (2018). Stratification for module categories of finite group schemes. J.~Amer.~Math.~Soc.,. Published, 01/2018.
  • D. Benson & S. B. Iyengar, H. Krause, J. Pevtsova (2017). Stratification and $\pi$-cosupport: Finite groups. Math. Z. Published, 12/2017.
  • D. J. Dailey & Srikanth B. Iyengar, Tom Marley (2017). Detecting finite flat dimension of modules via iterates of the Frobenius endomorphism. Journal of Commutative Algebra. Published, 07/2017.
  • D. Benson & S. B. Iyengar, H. Krause, J. Pevtsova (2017). Colocalising subcategories of module over finite group schemes. Ann. K-theory. Published, 06/2017.
  • L. W. Christensen & S. B. Iyengar (2017). Tests for injectivity of modules over commutative rings. Collect. Math. Published, 05/2017.
  • J. F. Carlson & S. B. Iyengar (2017). Hopf algebra structures and tensor products for group algebras. New York J. Math. Published, 01/2017.
  • S. B. Iyengar & R. Takahashi (2016). Annihilation of cohomology and strong generation of module categories. International Math. Res. Notices. Published, 01/2016.
  • Avramov, Luchezar L., Bruns, Winfried & Iyengar, Srikanth B. (2015). To Hans-Bjørn Foxby. Elsevier BV. Published, 2015.
  • BENSON, DAVE, IYENGAR, SRIKANTH B. & KRAUSE, HENNING (2015). A local-global principle for small triangulated categories. Cambridge University Press (CUP). , 1-26. Published, 2015.
  • Iyengar, S. B. & Takahashi, R. (2015). Annihilation of Cohomology and Strong Generation of Module Categories. Oxford University Press (OUP). Published, 2015.
  • A. Conca & S. B. Iyengar, H. Nguyen, T. Roemer (2015). Absolutely Koszul algebras and the Backelin-Roos property. Acta Mathematica Vietnamica. Published, 09/2015.
  • A. Conca & S. B. Iyengar, H. Nguyen, T. Roemer (2015). Absolutely Koszul algebras and the Backelin-Roos property. Acta Mathematica Vietnamica. Published, 09/2015.
  • O.~Celikbas & S. B. Iyengar, G.~Piepmeyer, R.~Wiegand (2015). Criteria for vanishing of Tor over complete intersections. Pacific J. Math. Published, 07/2015.
  • O. Celikbas & S. B. Iyengar, G.~Piepmeyer, R.~Wiegand (2015). Torsion in tensor powers of modules. Nagoya Math. J. Published, 06/2015.
  • S. B. Iyengar & J. Lipman, A. Neeman (2015). Relation between two twisted inverse image pseudofunctors in duality theory. Compositio Math.,. Published, 04/2015.
  • Carlson, Jon F. & Iyengar, Srikanth B. (2014). Thick subcategories of the bounded derived category of a finite group. American Mathematical Society (AMS). , 1. Published, 2014.
  • Iyengar, Srikanth B., Neeman, Amnon & Lipman, Joseph (2014). Relation between two twisted inverse image pseudofunctors in duality theory. Oxford University Press (OUP). , 1-30. Published, 2014.
  • Iyengar, Srikanth B. & Takahashi, Ryo (2014). Annihilation of cohomology and decompositions of derived categories. International Press of Boston. Vol. 16(2), 231-237. Published, 2014.
  • Iyengar, Srikanth B. & Krause, Henning (2013). The Bousfield lattice of a triangulated category and stratification. Springer Science + Business Media. Vol. 273(3-4), 1215-1241. Published, 2013.
  • Benson, Dave, Iyengar, Srikanth B. & Krause, Henning (2013). Module categories for group algebras over commutative rings. Cambridge University Press (CUP). Vol. 11(02), 297-329. Published, 2013.
  • Avramov, Luchezar L. & Iyengar, Srikanth B. (2013). Bass numbers over local rings via stable cohomology. Rocky Mountain Mathematics Consortium. Vol. 5(1), 5-15. Published, 2013.
  • Dwyer, W. G., Greenlees, J. P. C. & Iyengar, S. B. (2013). DG algebras with exterior homology. Oxford University Press (OUP). Vol. 45(6), 1235-1245. Published, 2013.
  • Avramov, Luchezar L., Hochster, Melvin, Iyengar, Srikanth B. & Yao, Yongwei (2012). Homological invariants of modules over contracting endomorphisms. Springer Science + Business Media. Vol. 353(2), 275-291. Published, 2012.
  • Iyengar, Srikanth B., Benson, David J. & Krause, Henning (2012). Colocalizing subcategories and cosupport. Walter de Gruyter GmbH. Vol. 2012(673). Published, 2012.
  • Avramov, Luchezar L. & Iyengar, Srikanth B. (2012). Detecting flatness over smooth bases. American Mathematical Society (AMS). Vol. 22(1), 35-47. Published, 2012.
  • Benson, D., Iyengar, S. B. & Krause, H. (2011). Stratifying triangulated categories. Oxford University Press (OUP). Vol. 4(3), 641-666. Published, 2011.
  • Benson, David, Krause, Henning & Iyengar, Srikanth (2011). Stratifying modular representations of finite groups. Annals of Mathematics, Princeton U. Vol. 174(3), 1643-1684. Published, 2011.
  • Iyengar, Srikanth, Lipman, Joseph & Avramov, Luchezar (2011). Reflexivity and rigidity for complexes, II: Schemes. Mathematical Sciences Publishers. Vol. 5(3), 379-429. Published, 2011.
  • Greenlees, J. P. C., Iyengar, S. B. & Dwyer, W. G. (2011). Gross-Hopkins duality and the Gorenstein condition. Cambridge University Press (CUP). Vol. 8(01), 107-133. Published, 2011.
  • Benson, Dave, Krause, Henning & Iyengar, Srikanth B. (2011). Localising subcategories for cochains on the classifying space of a finite group. Elsevier BV. Vol. 349(17-18), 953-956. Published, 2011.
  • Chen, Xiao-Wu & Iyengar, Srikanth B. (2010). Support and injective resolutions of complexes over commutative rings. International Press of Boston. Vol. 12(1), 39-44. Published, 2010.
  • Avramov, Luchezar L., Iyengar, Srikanth B. & Sega, Liana M. (2010). Short Koszul modules. Rocky Mountain Mathematics Consortium. Vol. 2(3), 249-279. Published, 2010.
  • Avramov, Luchezar L., Buchweitz, Ragnar-Olaf, Iyengar, Srikanth B. & Miller, Claudia (2010). Homology of perfect complexes. Elsevier BV. Vol. 223(5), 1731-1781. Published, 2010.
  • Iyengar, Srikanth, Avramov, Luchezar & Lipman, Joseph (2010). Reflexivity and rigidity for complexes, I: Commutative rings. Mathematical Sciences Publishers. Vol. 4(1), 47-86. Published, 2010.
  • Avramov, Luchezar L., Iyengar, Srikanth B., Lipman, Joseph & Nayak, Suresh (2010). Reduction of derived Hochschild functors over commutative algebras and schemes. Elsevier BV. Vol. 223(2), 735-772. Published, 2010.
  • Bergh, Petter Andreas, Iyengar, Srikanth B., Krause, Henning & Oppermann, Steffen (2010). Dimensions of triangulated categories via Koszul objects. Springer Science + Business Media. Vol. 265(4), 849-864. Published, 2010.
  • Avramov, Luchezar L., Conca, Aldo & Iyengar, Srikanth B. (2010). Free resolutions over commutative Koszul algebras. International Press of Boston. Vol. 17(2), 197-210. Published, 2010.
  • Iacob, Alina & Iyengar, Srikanth B. (2009). Homological dimensions and regular rings. Elsevier BV. Vol. 322(10), 3451-3458. Published, 2009.
  • Herbig, Hans-Christian, Iyengar, Srikanth B. & Pflaum, Markus J. (2009). On the Existence of Star Products on Quotient Spaces of Linear Hamiltonian Torus Actions. Springer Science + Business Media. Vol. 89(2), 101-113. Published, 2009.
  • Iyengar, Srikanth B. & Römer, Tim (2009). Linearity defects of modules over commutative rings. Elsevier BV. Vol. 322(9), 3212-3237. Published, 2009.
  • Avramov, L. L., Sega, L. M. & Iyengar, S. B. (2008). Free resolutions over short local rings. Oxford University Press (OUP). Vol. 78(2), 459-476. Published, 2008.
  • Avramov, Luchezar & Iyengar, Srikanth (2008). Gorenstein algebras and Hochschild cohomology. Michigan Mathematical Journal. Vol. 57(0), 17-35. Published, 2008.
  • Puthenpurakal, Tony J. & Iyengar, Srikanth (2007). . American Mathematical Society (AMS). Vol. 135(03), 637-649. Published, 2007.
  • Iyengar, Srikanth & Christensen, Lars Winther (2007). Gorenstein dimension of modules over homomorphisms. Elsevier BV. Vol. 208(1), 177-188. Published, 2007.
  • Avramov, L. L. (Luchezar L.), Miller, Claudia & Iyengar, Srikanth (2006). Homology over local homomorphisms. Johns Hopkins University Press. Vol. 128(1), 23-90. Published, 2006.
  • Iyengar, Srikanth & Bridgeland, Tom (2006). A criterion for regularity of local rings. Elsevier BV. Vol. 342(10), 723-726. Published, 2006.
  • Greenlees, J.P.C., Iyengar, S. & Dwyer, W.G. (2006). Duality in algebra and topology. Elsevier BV. Vol. 200(2), 357-402. Published, 2006.
  • Iyengar, S., Greenlees, John & Dwyer, William (2006). Finiteness in derived categories of local rings. European Mathematical Publishing House. , 383-432. Published, 2006.
  • Avramov, Luchezar L. & Iyengar, Srikanth (2005). Gaps in Hochschild cohomology imply smoothness for commutative algebras. International Press of Boston. Vol. 12(6), 789-804. Published, 2005.
  • Iyengar, Srikanth & Herzog, Jürgen (2005). Koszul Modules. Elsevier BV. Vol. 201(1-3), 154-188. Published, 2005.

Research Statement

My research home is commutative algebra and much of my work has focussed on homological aspects of the subject, especially on the structure and invariants connected with various triangulated categories that arise in that field. On the other hand, a significant part my research has also involved applying ideas developed in commutative algebra to solve problems in various areas, notably: algebraic topology; the modular representation theory of finite groups and group schemes; and, more recently, algebraic number theory, especially on modularity of Galois representations.

 

Grants, Contracts & Research Gifts

  • Commutative algebra: homological and homotopical aspects (1503044). PI: Srikanth B Iyengar. National Science Foundation, 2014 - 05/31/2017. Total project budget to date: $183,123.00
  • Commutative algebra: homological and homotopical aspects (1201889). PI: Srikanth B Iyengar. National Science Foundation, 2012 - 11/30/2014. Total project budget to date: $177,084.00
  • Pan American Advanced Studies Institute: Commutative Algebra and Its Interactions with Algebraic Geometry, Representation Theory, and Physics; Guanajuato, Mexico; May 14-25, 2012 (1123059). PI: Iyengar, Srikanth. National Science Foundation, 2012 - 12/31/2013. Total project budget to date: $99,970.00
  • Derived categories of complete intersections and Hochschild cohomology (0903493). PI: Iyengar, Srikanth. National Science Foundation, 2009 - 07/31/2013. Total project budget to date: $210,528.00
  • Derived invariants of commutative rings (0602498). PI: Iyengar, Srikanth. National Science Foundation, 2006 - 05/31/2009. Total project budget to date: $139,043.00
  • Homological Invariants of Modules Over Commutative Rings (0442242). PI: Iyengar, Srikanth. National Science Foundation, 2004 - 05/31/2006. Total project budget to date: $62,243.00
  • LOCAL ALGEBRA. PI: IYENGAR,SRIKANTH. NATIONAL SCIENCE FOUNDATION, 07/01/2020 - 06/30/2025. Total project budget to date: $153,656.00