The following files are all in pdf format.

Selected Reprints (and accepted papers)

• (with Michel Brion) Equivariant intersection cohomology of semi-stable points , 595-610, American J. Math, vol 118, No.3, (1996).

• The derived category and intersection cohomology of algebraic stacks, in Algebraic K-theory and Algebraic Topology, NATO ASI Series, S\ eries C: Mathematical and Physical Sciences- vol 407 (1993), 91-145.

• Modules over convolution algebras from equivariant derived categories-I, Journal of Algebra, (1997), volume 203, 385-446.

• Equivariant Riemann-Roch for G-quasi-projective varieties, K-theory, volume 17, no. 1 (1999), 1-35.

• Algebraic K-theory and Motivic Cohomology of Linear varieties, Math. Proc. Cambridge. Phil. Soc, (2001) vol 130, no. 1, 37-60

• (with Michel Brion) Vanishing of odd dimensional intersection cohomology:II, Mathematische Annalen, (2001), vol 321, no. 2, 399-437

• Derived functors for maps of simplicial spaces, Journal of Pure and Applied Algebra, vol 171, (2-3), (2002), 219-248

• Riemann-Roch for algebraic stacks:I, Compositio Mathematica, 136(2), (2003), 117-169.

• Intersection Theory on Algebraic Stacks:I, K-Theory, 27, no.2, (2002), 134-195.

• Intersection Theory on Algebraic Stacks:II, K-Theory, 27, no.3, (2002), 197-244.

• (with Reza Akthar) Kunneth decompositions for quotient varieties, Indagationes Math, 17(3), 319-344, (2006)

• Intersection Cohomology of reductive varieties, (joint with Michel Brion): The Journal of the European Math Society, 6, 465-481, (2004)

• Bredon-style homology, cohomology and Riemann-Roch for algebraic stacks, Advances in Mathematics, 209, 1-68, (2007)

• Lefschetz decomposition for quotient varieties, Journal of K-theory, (2009), 3, 547-560 (joint with Reza Akhtar)

• Equivariant Chow ring and Chern classes of wonderful symme\ tric varieties of minimal rank: Transformation Groups, (2008), 13, 471-493, joint with Michel Brion

• Implementation of Stanley's Algorithm for projective group imbeddings: The Journal of Symbolic computation, (2009), 44, 655-672, joint with Shaun van Ault

• You will obtain here a tar file of all the files necessary to run an implementation of the above algorithm written in GAP with calls to LiE and Polymake along with all the examples we have so far worked out.

• Go here for a sample session running this program.

• You will obtain here a tar file of all the files necessary to run Sage implementation of the above algorithm together with various functions to deal with spherical varieties that are group imbeddings. This is written by Shaun van Ault based on the above GAP package. (Caution: one needs to use sage-4.6 for the package to work properly.)

• Here you will find examples of functions in the above package that can be used to deal with spherical varieties that are group imbeddings. This written by Shaun van Ault.

• Toric residue codes:I joint with Reza Akhtar, Finite Fields and Applications, 17, (2011), 15-50.

• K-theory and G-theory of dg-stacks, in Regulators, Contemporary Mathematics, vol. 571, Amer. Math. Soc., Providence, RI, 2012, pp. 175-217.

• Notions of Purity and the Cohomology of Quiver moduli\ , joint with Michel Brion, International Journal of Mathematics, 23 (2012), no. 9, 30 pages.

• Higher K-theory of Toric stacks, joint with Amalendu Krishna, in Annali della Scoula Normale Superiore di Pisa, Vol XIV. (2015), 1-41

• Comparison of cohomology operations in mod$-l$ motivic and \'etale cohomology, joint with Patrick Brosnan, Contemp. Math Series, (Feynman Amplitudes, Periods and Motives), Vol 648, American Math Soc., (2015), 29-55.

• Explicit Chow-Lefschetz Decompsoitions for Kummer manifolds, joint with Reza Akhtar, in {\it K-Theory}, Proceedings of the International Colloquium on K-Theory, Tata Institute, Mumbai, (2018), 155-195

• Brauer groups of schemes associated to symmetric powers of projective smooth curves, joint with J. Iyer, Journal of Pure and Applied Algebra, 224, (2020), 1009-1022.

• Higher Grassmann codes, joint with Mahir Can and Ravindra Girivaru, Finite Fields and Applications, vol 76, (2021), 1-22.

• Equivariant Derived Categories for Torodial Group Imebddings, Transformation Groups, (2022), vol 27, issue 1, 113-162.

• Equivariant Perverse sheaves and Quasi-Hereditary algebras, Journal of Algebra, vol 591, (2022), 289-341.

• Approximating absolute Galois groups, joint with Gunnar Carlsson, Journal of Pure and Applied Algebra, vol 226, (2022), 1-11.

• The Motivic Segal-Becker theorem, joint with Pablo Pelaez, Annals of K-Theory, vol 7, no. 1, (2022), 191-221.

• Higher Grassmann codes: II, joint with Mahir Can and Ravindra Girivaru, Finite Fields and Applications, vol 89, (2023), 1-21.

• Defects of codes from Higher dimensional algebraic varieties, joint with Mahir Can and Ravindra Girivaru, Design, Codes and Cryptography, https://doi.org/10.1007/s10623-023-01317-2, vol 429, October, (2023), 1-18.

• Additivity of the motivic trace and the motivic Euler characteristic, joint with Pablo Pelaez, Advances in Mathematics, vol 429, (2023), 1-21.

• Equivariant algebraic K-theory, G-theory and derived completion, joint with Gunnar Carlsson, Advances in Mathematics, vol 430, (2023), 1-72.

Selected Preprints

• Brauer groups of smooth split toric schemes and their fans, joint with J. Lee.

• Brauer groups of algebraic stacks and GIT quotients:I, joint with A. Dhillon and J. Iyer.

• Equivariant motivic homotopy theory, joint with Gunnar Carlsson , 2011.

• Motivic Spanier-Whitehead duality and the motivic Becker-Gottlieb transfer, joint with Gunnar Carlsson, 2011.

• Riemann-Roch for algebraic stacks III: Virtual structure sheaves and virtual fundamental classes, 2010.

• Generalized $t$-structures: version of 2014

• Vanishing of odd dimensional intersection cohomology for spherical varieties in positive characteristics, Preprint, September, 2000.

• Generalized multiplicity formulae for modules over convolution algebras, preprint (1999).

• The motivic DGA, Preprint, version of 2012.

• Applications of the Strong Kunneth Decomposition of the diagonal: Talk at the summer school on algebraic cycles, Grenoble, France. (July 3, 2001)

• Grothendieck-Verdier duality in enriched symmetric monoidal $t$-categories.

The following file is a postscript version of the same pdf file as the one just above.

• Grothendieck-Verdier duality in enriched symmetric monoidal $t$-categories.

Software

• Functions for computing intersection numbers of projective Toric varities using Macaulay 2 , (2018)

• A sample session in Macaulay 2 using the above functions along with the package "NormalToricVarieties", (2018)

• Examples of quantum codes produced using the above Macaualy2 functions and based on the recent preprint: "Quantum Stabilizer and Subsystem codes from Algebro-Geometric Toric codes" written jointly with R. Girivaru , (2018).

Transparencies and/or Videos of Selected talks

• Equivariant Intersection Cohomology, talk at Luminy conference on D-modules, April 14-18th, 1997.

• Higher Intersection Theory on Algebraic Stacks: Talk at the MSRI Workshop on Intersection Theory on Algebraic Stacks, March 15, 2002.

• Kunneth decomposition for quotient varieties: Talk at the first joint Indian Math Society-AMS meeting, Bangalore, India, December 17, 2003.

• Isovariant \'Etale descent and Riemann-Roch for algebraic stacks: Talk at the Oberwolfach program on Algebraic K-theory, August 4-10, 2002.

• K-Theory and G-Theory of algebraic stacks: Talk in the seminar on Geometric Representation theory, IAS, Princeton, January 26, 2004.

• Mod$-l$ Topological G-theory for algebraic stacks: Talk in the seminar on Geometric Representation theory, IAS, Princeton, February 2, 2004.

• Intersection Cohomology of reductive varieties: Talk in the University of Michigan-Ohio State workshop on algebraic geometry, November 20, 2004, Ann Arbor, Michigan

• K theory and G-theory of algebraic and dg-stacks, Talk at the Banff workshop on algebraic stacks, March 29, 2012

• Algebraic cycles and motives: a bird's eye-view, Colloquium Talk at various places

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