Research

Papers Published / Accepted

(For a downloadable list of publications with abstracts, please click here)

[58]   (with S. Kour) Measurings of Hopf algebroids and morphisms in cyclic (co)homology theories, Advances in Mathematics, Vol 442 (2024) 109581, article

[57]   (with S. Das) Heavily separable functors of the second kind and applications, Journal of Algebra, Vol. 643 (2024), 49--75. article

[56]   (with M. Balodi and S. Kour) Comodule theories in Grothendieck categories and relative Hopf objects, Journal of Pure and Applied Algebra, Vol. 228 (2024), No. 6,  107607. article.

[55]   (with S. Kour) Finite duals in Grothendieck categories and coalgebra objects, Higher Structures (accepted). 

[54]   (with M. Balodi and S. Ray) Categories of modules, comodules and contramodules over representations, Forum Math, Vol. 36 (2024), No. 1, 111--152. article.

[53]   Entwined modules over representations of categories, Algebras and Representation Theory, Vol. 26 (2023), No. 6, 3185--3221. article.

[52]   An extension of the Beauville-Laszlo descent theorem, Arch. Math (Basel), Vol. 120 (2023), No. 6, 595--604. article. 

[51]   Galois coverings of enriched categories and an extension of Cohen-Montgomery Theorem, Journal of Algebra, Vol 616 (2023), 155--192. article. 

[50]   Two criteria for locally noetherian Grothendieck categories, Journal of Pure and Applied Algebra, Vol. 227 (2023), No. 3, 107233. article.

[49] (with M. Balodi) Fredholm modules over categories, Connes periodicity and classes in cyclic cohomology, C. R. Math. Acad. Sci. Paris, Vol 361 (2023), 617--652. article.  

[48] (with S. Kour) On measurings of algebras over operads and homology theories, Algebraic & Geometric Topology, Vol. 22 (2022), No. 3, 1113--1158. article.

[47] (with M. Balodi and S. Ray) Entwined modules over linear categories and Galois extensions, Israel Journal of Mathematics, Vol. 241, 623--692 (2021) article.

[46]  On Noetherian schemes over $(\mathcal C,\otimes,1)$ and the category of quasi-coherent sheaves, Indiana University Mathematics Journal, Vol. 70 (2021), 81--119. article.

[45] FI-modules over preadditive categories and torsion theories, Journal of Pure and Applied Algebra, Vol 225 (2021), 106595. article.

[44] (with M. Balodi and A. Naolekar) BV-operators and the secondary Hochschild complex, C. R. Math. Acad. Sci. Paris, Vol. 358 (2020), no. 11-12, pp 1239--1258. article.

[43] (with M. Balodi and S. Ray) Cohomology of modules over H-categories and co-H-categories: Canadian Journal of Mathematics, Vol 72 No. 5, 1352--1385 (2020) article

[42] Spectra as universal objects in categories of supports, Quantum Dynamics proceedings (Banach Center Publications),  Vol. 120,  53--69 (2020) article.

[41] (with S Kour) $(A,\delta)$-modules, Hochschild homology and Higher derivations, Annali di Matematica Pura  ed Applicata, Vol. 198, Issue 5, 1781--1802 (2019).  article

[40] On differential torsion theories and rings with several objects, Canadian Mathematical Bulletin, Vol. 62, Issue 4, 703--714 (2019). article. 

[39]  Completions of monoid objects and descent results,  Journal of Algebra, Vol. 507, 362--399 (2018). article

[38]  Modular Hecke Algebras over Mobius categories, Journal of Geometry and Physics (Special Volume for Alain Connes' 70th Birthday),  Vol. 131 (2018), 23--40. article. 

[37]  Quasimodular Hecke algebras and Hopf actions,  Journal of Noncommutative Geometry, Vol. 12, No. 3 (2018), 1041-1080. article.

[36]  A topological nullstellensatz for tensor triangulated categories, C. R. Math. Acad. Sci. Paris, Vol. 356, No. 4, 365--375 (2018). article. 

[35]  On Auslander's formula and cohereditary torsion pairs,  Communications in Contemporary Mathematics, Vol. 20, No. 6, Paper No. 1750071 (2018).  article.

[34]  Closure operators in abelian categories and spectral spaces,  Theory and Applications of Categories, Vol. 32, No. 20 (2017), 719--735.  article

[33]  Noetherian schemes over abelian symmetric monoidal categories,  International Journal of Mathematics,  Vol. 28, No. 7, Paper No. 1750051, 34 pp. (2017). article

[32] On some spectral spaces associated to tensor triangulated categories,  Arch. Math. (Basel), Vol. 108, No. 6 581--591 (2017). article. 

[31] Monoidal semifilters and arrays of prime ideals,  Fund. Math., Vol. 237, No. 3, 281--296 (2017). article. 

[30] Realizations of pairs and Oka families in tensor triangulated categories, European Journal of Mathematics, Vol. 2, No. 3, 760--797 (2016). article. 

[29] Some remarks on a theorem of Bergman, C. R. Math. Acad. Sci. Paris, Vol. 354, No. 7, 665--670 (2016). article.

[28] Homologie de Hochschild et espaces algébriques, Math. Scand, Vol. 118, No. 1, 33--42 (2016). article 

[27] Schemes over symmetric monoidal categories and torsion theories, Journal of Pure and Applied Algebra. Vol 220, No. 9, 3017--3047 (2016). article 

[26] Une note sur les dérivations localement nilpotentes dans les catégories monoïdales symétriques:  Bulletin of the Belgian Mathematical Society, Vol. 23, No. 1, 151--160 (2016).  article

[25] Schémas sur les catégories abéliennes monoidales symétriques et faisceaux quasi-cohérents: Journal of Algebra. Vol. 423, 148--176 (2015). article

[24] Nearby Cycles and the Dold-Kan correspondence, Communications in Algebra, Vol. 43, No. 12, 5362--5371 (2015). article.

[23] Action de Hopf sur les opérateurs de Hecke modulaires tordus, Journal of Noncommutative Geometry, Vol. 9 No. 4, 1155--1173 (2015). article.

[22] Extensions de la filtration de Saito, C.R. Math. Acad. Sci. Paris. Vol. 352, No. 5, 377--382 (2014). article

[21] Les motifs de Tate et les opérateurs de périodicité de Connes, Ann. Math. Blaise Pascal, Vol. 21, No. 1, 1--23 (2014). article

[20] Localization of monoid objects and Hochschild homology, Communications in Algebra, Vol. 42, No. 10, 4548--4558 (2014). article

[19] On the Lie transformation algebra of monoids in symmetric monoidal categories: Rend. Sem. Mat. Univ. Padova, Vol. 131, 151--157 (2014). article

[18] Bivariant Chow groups and the topology of envelopes: Topology and its Applications, Vol. 160, No. 1, 230--240 (2013). article

[17] Connes-Karoubi long exact sequence for Frechet Sheaves: Munster Journal of Mathematics, Vol. 6, 167--179 (2013). article

[16] Hecke operators on Line bundles over Modular curves: Journal of Number Theory, Vol. 132, No. 4, 714--734 (2012). article (slides). 

[15] Affine Group Schemes over Symmetric Monoidal Categories : Pacific Journal of Mathematics, Vol. 255, No. 1, 25--40 (2012).  article

[14] Centre of Monoids, centralisers and localisation : Communications in Algebra, Vol. 40, No. 11, 3975--3993 (2012). article

[13] Derived Schemes and the Field with one element : Journal de Mathematiques Pures et Appliquees, Vol 97, No. 3, 189--203 (2012). article

[12] Lifting of model structures to Fibred Categories : Homology, Homotopy and Applications,  Vol. 13. No. 2, 1--17 (2011). article  (slides)

[11] Higher Bivariant Chow Groups and Motivic Filtrations: Trans. Amer. Math. Soc. , Vol. 363, No. 11, 5943--5969 (2011). article 

[10] The relative Picard Functor on Schemes over a symmetric monoidal category: Bulletin des Sciences Mathematiques, Vol 135,400--419(2011).article(slides)

[9] Hopf Action and Rankin-Cohen Brackets on an Archimedean Complex: Journal of Noncommutative Geometry. Vol. 5, No. 3, 401--421 (2011).  article

[8] Zeta functions of certain noncommutative algebras : Proc. Japan Acad. Ser. A. Math. Sci. Vol. 87, No. 4, pp 51--55 (2011). article

[7] A note on product structures on Hochschild homology of schemes : Colloquium Mathematicum. Vol. 123. No. 2, 233--238 (2011). article

[6] Higher Derivations and Hochschild Homology:  C. R. Math. Acad. Sci. Soc. R. Can. Vol. 33. No. 2, pp 33-43 (2011). article

[5] Nearby Cycles and Periodicity in Cyclic Homology: Noncommutative Geometry, Arithmetic and related topics (Proceedings of the 21st JAMI Conference, 2009), Johns Hopkins University Press (2011).  

[4] Hopf Cyclic Cohomology and Biderivations: Proc. Amer. Math. Soc., Vol. 138, No. 6, 1929-1939, (2010). article

[3] Cartan Homotopy Formulae and the Bivariant Hochschild Complex: C. R. Math. Acad. Sci. Paris, Vol. 347, No. 17-18, pp 997-1000, (2009). article

[2] A Note on Regularity Properties with respect to Ideals: Communications in Algebra, Vol. 36, No. 3, pp 1067--1077, (2008). article

[1] Unique Factorization and Ring Extensions: International Journal of Pure and Applied Mathematics, Vol. 26, No.4, pp 457--464, (2006). article

Other Publications (As an undergraduate student at Indian Statistical Institute)

Noetherian Rings, Dimension and Chain conditions: American Journal of Undergraduate Research, Vol 4, No. 3 (2005).

Exactness, Tor and Flat modules over a Commutative Ring: American Journal of Undergraduate Research, Vol 3, No. 3 (2004).

Short Term Positions / Conferences / Research Visits

Mathematical Sciences Research Institute (MSRI), Berkeley, (Feb 2020) (Scheduled).

Fields Institute, Toronto, Canada, (Nov, 2019). 

Euler Institute of Mathematical Sciences, St. Petersburg Department of Steklov Mathematical Institute, St. Petersburg, Russia (Sep 2019). 

Indian Institute of Science and Educational Research, Kolkata (IISER--K), India, (July 2019). 

International Congress of Mathematicians (ICM), Rio de Janeiro, Brazil (Aug 2018).

Homotopy Theory Summer, Freie Universitat & Technische Universitat, Berlin, Germany (June 2018).

Hausdorff Institute for Mathematics (HIM), Bonn, Germany (Jan - Feb, 2018).

Shanghai Center for Mathematical Sciences, Fudan University, Shanghai, China. (March -- April, 2017)

Stefan Banach Mathematical Center, IMPAN, Warsaw, Poland (October 2016). 

Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing (June 2016). 

Max-Planck Institut fur Mathematik, Bonn, Germany (Dec 2015 - Feb, 2016). 

Institut des Hautes Etudes Scientifiques, Bures sur Yvette, France (May - July, 2015). 

Institute for Advanced Study (IAS), Princeton, NJ, USA (March 2015). 

Hausdorff Institute for Mathematics (HIM), Bonn, Germany (Nov - Dec, 2014).

Institut des Hautes Etudes Scientifiques, Bures sur Yvette, France (Nov, 2013). 

Mathematisches Forschungsinstitut Oberwolfach (MFO), Germany, (Sept, 2013).

Institute of Mathematics of the Romanian Academy (IMAR), Romania (Sept, 2013).

Trinity College, Dublin, Ireland (Aug, 2013).

University of Copenhagen, Denmark, (July, 2013).

Universite de Luxembourg, Luxembourg City, Luxembourg (Higher Algebras and Lie-infinity Homotopy Theory), (June, 2013).

Universite Internationale de Rabat, Rabat, Morocco (June, 2013).

Freie Universitat, Berlin, Germany, (Syzygies in Berlin), (May, 2013).

Isaac Newton Institute for Mathematical Sciences, Cambridge,UK, (Operads and Deformation Theory), (Apr, 2013).

Technion-Israel Institute of Technology, Haifa, Israel, (Feb, 2013).

Centre de Recherches Mathematiques (CRM), Montreal, Quebec, (Sept, 2012). 

Jagiellonian University, Krakow, Poland (6th European Congress of Mathematicians), (July, 2012). 

Oslo University College, Oslo, Norway; (Noncommutative Geometry and Quantum Groups), (June, 2012). 

Institut des Hautes Etudes Scientifiques, Bures sur Yvette, France (June, 2012). 

Centro de Investigacion en Matematicas (CIMAT), Guanajuato, Mexico, (May, 2012). 

Pacific Institute of Mathematical Sciences (PIMS), Vancouver, Canada, (April, 2012). 

Mathematisches Forschungsinstitut Oberwolfach, Germany (Workshop on Noncommutative Geometry)

(Sept, 2011). 

Institut des Hautes Etudes Scientifiques, Bures sur Yvette, France (June-Sept, 2011). 

Istanbul Centre for Mathematical Sciences, Istanbul, Turkey; (Algebraic and Homological

aspects of Noncommutative Geometry) (July, 2011). 

Max-Planck Institut fur Mathematik, Bonn, Germany (March-April, 2011). 

Centro Internazionale per la Ricerca Matematica, Trento, Italy; (School and Workshop

on Minimal Model Programme and Shokurov's ACC conjecture);  (July, 2010)

Institut des Hautes Etudes Scientifiques, Bures sur Yvette, France (June-Sept, 2010).

Centre de Recerca Matematica, Bellaterra, Barcelona, Spain (April, 2010).

Tata Institute of Fundamental Research, Mumbai, India (Aug-Sept, 2009).

Korea Advanced Institute of Science and Technology, Daejeon, South Korea (Jul-Aug, 2009).

Hausdorff Institute of Mathematics, Bonn, Germany, May-July, 2008).

Tata Institute of Fundamental Research, Mumbai, India, (Dec, 2004-Jan, 2005).

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