Book Projects

  1. Multifunctorial Equivariant Algebraic K-Theory [version: April 3, 2024]
  2. Boardman-Vogt Resolutions of Generalized Props
    [with Mark W. Johnson; version: August 8, 2017]

Books

  1. Homotopy Theory of Enriched Mackey Functors. Joint work with Niles Johnson.
    LMS Lecture Note Series, Cambridge University Press, 2025.  Arxiv version.
  2. Bimonoidal Categories, En-Monoidal Categories, and Algebraic K-Theory
    AMS Mathematical Surveys and Monographs Volumes 283–285, 2024.

  3. Grothendieck Construction of Bipermutative-Indexed Categories.
    Chapman and Hall/CRC, 2024.  Arxiv version.
  4. Infinity Operads and Monoidal Categories with Group Equivariance.
    World Scientific, 2022.  Arxiv version.
  5. 2-Dimensional Categories.  Joint work with Niles Johnson.
    Oxford University Press, 2021.  Known errata.
  6. Involutive Category Theory.  Springer Lecture Notes in Mathematics 2279, 2020.
  7. Homotopical Quantum Field Theory  World Scientific, 2020.  Arxiv version.
  8. Operads of Wiring Diagrams.  Springer Lecture Notes in Mathematics 2192, 2018.  Arxiv version.
  9. Colored Operads.  AMS Graduate Studies in Mathematics 170, 2016.  Known errata.
  10. Infinity Properads and Infinity Wheeled Properads.  Joint work with Marcy Robertson and Philip Hackney.  Springer Lecture Notes in Mathematics 2147, 2015.  Arxiv version.
  11. A Foundation for PROPs, Algebras, and Modules.  Joint work with Mark W. Johnson.  AMS Mathematical Surveys and Monographs 203, 2015.  An older version.
  12. A First Course in Analysis.  World Scientific, 2013.
  13. Lambda-Rings.  World Scientific, 2010.

Papers

2021–present
  1. Smith Ideals of Operadic Algebras in Monoidal Model Categories (with David White), Algebraic & Geometric Topology 24 (2024), 341-392.
  2. Right Bousfield Localization and Eilenberg-Moore Categories (with David White), Higher Structures 7(1): 22-39, 2023.
  3. Multicategories Model All Connective Spectra (with Niles Johnson), Homology, Homotopy and Applications 25 (2023), 147-172.
  4. Multifunctorial Inverse K-Theory (with Niles Johnson), Annals of K-Theory 7 (2022), 507-548.
  5. Multifunctorial K-theory is an equivalence of homotopy theories (with Niles Johnson), Journal of Homotopy and Related Structures 17 (2022), 569-592.
  6. Homotopy Equivalent Algebraic Structures in Multicategories and Permutative Categories (with Niles Johnson), Theory and Applications of Categories, Vol. 38, 2022, No. 30, pp 1156-1208.
2011–2020
  1. Right Bousfield localization and operadic algebras (with David White), Tbilisi Mathematical Journal, Special issue (Homotopy Theory, Spectra and Structured Ring Spectra – 2020), 71-118.
  2. Modular operads and the nerve theorem (with Marcy Robertson and Philip Hackney), Advances in Mathematics 370 (2020), 107206.
  4. Arrow categories of monoidal model categories (with David White), Mathematica Scandinavica 125 (2019), 185-198.
  5. Homotopical adjoint lifting theorem (with David White), Applied Categorical Structures 27 (2019), 385-426.
  6. Higher cyclic operads (with Marcy Robertson and Philip Hackney), Algebraic & Geometric Topology 19 (2019), 863-940.
  7. On factorizations of graphical maps (with Marcy Robertson and Philip Hackney), Homology, Homotopy and Applications 20 (2018), 217-238.
  8. A simplicial model for infinity properads (with Marcy Robertson and Philip Hackney), Higher Structures 1 (2018), 1-21.
  9. Bousfield Localization and Algebras over Colored Operads (with David White), Applied Categorical Structures 26 (2018) 153-203.
  10. Shrinkability, relative left properness, and derived base change (with Marcy Robertson and Philip Hackney), New York Journal of Mathematics 23 (2017) 83-117.
  11. Relative left properness of colored operads (with Marcy Robertson and Philip Hackney), Algebraic & Geometric Topology 16 (2016) 2691-2714.
  12. The classical Hom-Yang-Baxter Equation and Hom-Lie bialgebras, International Electronic Journal of Algebra 17 (2015) 11-45.
  13. Rota-Baxter Hom-Lie-admissible algebras (with Abdenacer Makhlouf), Communications in Algebra 42 (2014), 1231-1257.
  14. Hom-quantum groups: I. Quasi-triangular Hom-bialgebras, Journal of Physics A 45 (2012) 065203.
  15. Hom-Maltsev, Hom-alternative, and Hom-Jordan algebras, International Electronic Journal of Algebra 11 (2012) 177-217.
  16. On n-ary Hom-Nambu and Hom-Nambu-Lie algebras, Journal of Geometry and Physics 62 (2012) 506-522.
  17. Operations on the Hopf-Hochschild complex for module-algebras, Homology, Homotopy and Applications 13 (2011) 259-272.
  18. The Hom-Yang-Baxter equation and Hom-Lie algebras, Journal of Mathematical Physics 52 (2011) 053502.
  19. Hom-Novikov algebras, Journal of Physics A 44 (2011) 085202.
2001–2010
  1. Hom-bialgebras and comodule Hom-algebras, International Electronic Journal of Algebra 8 (2010) 45-64.
  2. On homotopy invariance for algebras over colored PROPs (with Mark W. Johnson), Journal of Homotopy and Related Structures 4 (2009) 275-315.
  3. The L∞-deformation complex of diagrams of algebras (with Yael Fregier and Martin Markl), New York Journal of Mathematics 15 (2009) 353-392.
  4. Hom-algebras and homology Journal of Lie Theory 19 (2009) 409-421.
  5. The Hom-Yang-Baxter equation, Hom-Lie algebras, and quasi-triangular bialgebras, Journal of Physics A 42 (2009) 165202.
  6. Cohomology with coefficients for operadic coalgebras (with Anita Majumdar), Proceedings Mathematical Sciences 119 (2009) 431-452.
  7. Cohomology and duality for coalgebras over a quadratic operad (with Anita Majumdar), Journal of Generalized Lie Theory and Applications 3 (2009) 131-148.
  8. Enveloping algebras of Hom-Lie algebras, Journal of Generalized Lie Theory and Applications 2 (2008) 95-108.
  9. Cohomology for morphisms of Yetter-Drinfel’d and Hopf modules, International Journal of Algebra 2 (2008) 239-252.
  10. Deformation theory of dialgebra morphisms, Algebra Colloquium 15 (2008) 279-292.
  11. Deformation bicomplex of module algebras, Homology, Homotopy and Applications 10 (2008) 97-128.
  12. Deformation of dual Leibniz algebra morphisms, Communications in Algebra 35 (2007) 1369-1378.
  13. Cohomology and deformation of module-algebras, Journal of Pure and Applied Algebra 209 (2007) 781-792.
  14. Gerstenhaber structure and Deligne’s conjecture for Loday algebras, Journal of Pure and Applied Algebra 209 (2007) 739-752.
  15. Deformations of coalgebra morphisms, Journal of Algebra 307 (2007) 106-115.
  16. (Co)homology of triassociative algebras, Int. J. Math. and Math. Sciences 2006 (2006), Article ID 69248, 21 pages.
  17. On λ-rings and topological realization, Int. J. Math. and Math. Sciences 2006 (2006), Article ID 91267, 21 pages.
  18. Deformation of algebras over the Landweber-Novikov algebra, Journal of Algebra 298 (2006) 507-523.
  19. Deformation theory of modules, Communications in Algebra 33 (2005) 2351-2359.
  20. Loop structures on the homotopy type of S3 revisited, Michigan Mathematical Journal 53 (2005) 283-290.
  21. Cohomology of λ-rings, Journal of Algebra 284 (2005) 37-51.
  22. On adic genus and lambda-rings, Transactions of the AMS 357 (2005) 1341-1348.
  23. Moduli space of filtered λ-ring structures over a filtered ring, Int. J. Math. and Math. Sciences 2004 (2004) 2065-2084.
  24. Maps to spaces in the genus of infinite quaternionic projective space, Progress in Mathematics 215 (2004) 293-302.
  25. Unstable K-cohomology algebra is filtered λ-ring, Int. J. Math. and Math. Sciences 2003 (2003) 593-605.
  26. Clapp-Puppe type Lusternik-Schnirelmann (co)category in a model category, Journal of the Korean Math. Society 39 (2002) 163-191.
  27. Possible line sums for a qualitative matrix (with C.R. Johnson and S.A. Lewis), Linear Algebra and Its Applications 327 (2001) 53-60.

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