**Books edited **

1. (with J.P.C.Greenlees and R.R.Bruner) Homotopy Methods in Algebraic Topology, Proceedings of the 1999 Conference in Boulder, A. M. S. Cont. Math. Series **271**, 2001.

**Research Papers **

All papers since 2002 are available in preprint form at arxiv.org. Many older papers are also available on one or more of the following archives: the Hopf archive at https://hopf.math.purdue.edu, the K–theory archive at https://faculty.math.illinois.edu/K-theory, or the group cohomology archive at https://homepages.abdn.ac.uk/d.j.benson/pages/html/archive.html.

1. The geometry of the James-Hopf Maps,* Pac. J. Math.* **102** (1982), 397–412.

2. (with S.A.Mitchell and S.B.Priddy) The Whitehead conjecture and splitting *\(B(\mathbb Z/2)^k\), Bull. A. M. S.* **7 **(1982), 255–258.

3. A Kahn-Priddy sequence and a conjecture of G.W.Whitehead, *Math. Proc. Camb. Phil. Soc.* **92 **(1982), 467–483. (Corrigenda, 95(1984), 189–190.)

4. (with F.R.Cohen, R.L.Cohen, and J.L.Neisendorfer) Bundles over configuration spaces, *Pac. J. Math. ***104 **(1983), 47–54.

5. The homology of the James-Hopf maps, *Ill. J. Math.* **27 **(1983), 315–333.

6. Spacelike resolutions of spectra, *Northwestern Homotopy Theory Conference, Proc. Evanston, 1982, A. M. S. Cont. Math. Series ***19** (1983), 153–165.

7. Suspension spectra and homology equivalences, *Trans. A. M. S.* **283** (1984), 303–313.

8. (with an appendix by P.Landrock) The modular Hecke algebra and Steinberg representation of finite Chevalley groups,* J. Algebra ***91 **(1984), 125–141.

9. Extended powers of spectra and a generalized Kahn-Priddy Theorem, *Topology* **23 **(1985), 473–480.

10. Chevalley group theory and the transfer in the homology of symmetric groups, *Topology* **24 **(1985), 247–264.

11. (with S.B.Priddy) The transfer and Whitehead’s conjecture, *Math. Proc. Camb. Phil. Soc.* **98** (1985), 459–480.

12. (with S.A.Mitchell) The multiplicity of the Steinberg representation of \(GL_n(\mathbb F_q)\) in the symmetric algebra,* Proc. A. M. S. ***96**(1986), 1–6. 1

13. Exact sequences of spectra and duality,* Proc. A. M. S.* **97** (1986), 347–351.

14. The mod p K-theory of classifying spaces of finite groups,* J. Pure Appl. Alg. ***44 **(1987), 269–271.

15. The rigidity of L(n), *Algebraic Topology – Seattle 1985, Springer Lect. Notes Math. ***1286 **(1987), 286–292.

16. The Morava K-theories of some classifying spaces, *Trans. A. M. S. ***304** (1987), 193– 205.

17. The transfer and James-Hopf invariants, *Math. Zeit. ***196 **(1987), 391–405.

18. (with J.C.Harris) Stable decompositions of classifying spaces of finite abelian p-groups, *Math. Proc. Camb. Phil. Soc. ***103** (1988), 427–449.

19. Morava K-theories and infinite loop spaces, *Algebraic Topology, Proc. Arcata, 1986, Springer Lect. Notes Math. ***1370 **(1989), 243–257.

20. (with D.Carlisle) Subalgebras of the Steenrod algebra and the action of matrices on truncated polynomial algebras, *J. Algebra* **121** (1989), 370–387.

21. (with D.Carlisle) Smash products of summands of \(B(\mathbb Z/p)^n_+\), *Northwestern Topology Conference, Proc. Evanston, 1988, A. M. S. Cont. Math. Series ***96 **(1989), 87–102.

22. Character rings in algebraic topology, *Advances in Homotopy Theory, Proc. Cortona 1988, L. M. S. Lectures Notes* **139 **(1989), 111–126.

23. (with J. F. Adams) Atomic spaces and spectra, *Proc. Edin. Math. Soc. ***32 **(1989), 473–481.

24. (with M.J.Hopkins and D.C.Ravenel) Morava K-theories of classifying spaces and generalized characters for finite groups, *Topology Conference, Proc. Barcelona, 1990, Springer Lecture Notes in Math. ***1509** (1992), 186–209.

25. Generic representation theory and Lannes’ T-functor, *Adams Memorial Symp., Proc. Manchester, 1990, L. M. S. Lecture Notes* **176 **vol.2 (1992), 235–262.

26. (with Jeanne Duflot and Mark Winstead) A classification of polynomial algebras as modules over the Steenrod algebra, *Comm. Math. Helv.* *68* (1993), 622–632.

27. (with Piotr Krason) On embedding polynomial functors in symmetric powers, *J.Algebra ***163** (1994), 281–294.

28. Constructions of families of elements in the stable homotopy groups of spheres, *Topology and Representation Theory, Proc. Evanston, 1992, A.M.S. Cont. Math. ***158 **(1994), 135–155. 2

29. Morita equivalence, GL(n,q) modules, and the Steenrod algebra, *Algebraic Topology and its Applications, Proc. Berkeley, 1989, M.S.R.I. Pub. ***27** (1994), 125–137.

30. Generic representations of the finite general linear groups and the Steenrod algebra:I,* Amer. J. Math. ***116** (1994), 327–360.

31. Generic representations of the finite general linear groups and the Steenrod algebra:II, *K-theory J.*** 8 **(1994), 395–428.

32. Generic representations of the finite general linear groups and the Steenrod algebra:III,* K-theory J.* **9 **(1995), 273–303.

33. On topologically realizing modules over the Steenrod algebra,* Annals of Math.* **141** (1995), 321–347.

34. (with M. Slack and F.Williams) Hopf constructions and higher projective planes for iterated loop spaces, *Trans. A.M.S. ***347 **(1995), 1201–1238.

35. (with M. Winstead) On torsion in the cohomology of certain mapping spaces, *Topology* **35 **(1996), 875–881.

36. Invariant subspaces of the ring of functions on a vector space over a finite field, *J. Algebra* **191** (1997), 212–227.

37. Computations in generic representation theory: maps from symmetric powers to composite functors, *Trans. A.M.S.***350** (1998), 4221–4233.

38. Rational cohomology and cohomological stability in generic representation theory, *Amer. J. Math.***120 **(1998), 1317–1341.

39. (with D. J. Hunter) Mahowaldean families of elements in stable homotopy groups revisited, *Math. Proc. Camb. Phil. Soc.* **127** (1999), 237–251.

40. (with D. J. Hunter) Characterizations of spectra with U-injective cohomology which satisfy the Brown–Gitler property,* Trans. A.M.S.***352** (2000), 1171–1190.

41. (with M.J.Hopkins and D.C.Ravenel) Generalized group characters and complex oriented cohomology theories,* Journal A.M.S.***13 **(2000), 553–594.

42. The generic representation theory of finite fields: a survey of basic structure, *Infinite Length Modules, Proc. Bielefeld, 1998, Trends in Mathematics, *Birkhauser (2000), 193–212.

43. New relationships among loopspaces, symmetric products, and Eilenberg MacLane spaces,* Cohomological Methods in Homotopy Theory, Proc. Barcelona, 1998, Birkhauser Verlag Progress in Math* **196**(2001), 185–216. 3

44. Splitting fields and twisted group rings for the finite general linear groups, *Modular Representation Theory of Finite Groups, Proc. Charlottesville, 1998, *de Gruyter (2001), 231–237.

45. Stable splittings and the diagonal, Homotopy Methods in Algebraic Topology, Proc. Boulder, CO, 1999,* A.M.S. Cont. Math.* **271** (2001), 169–181.

46. A stratification of generic representation theory and generalized Schur algebras, *K-theory J. ***26*** *(2002), 15–49.

47. (with S.T.Ahearn) Product and other fine structure in polynomial resolutions of mapping spaces,* Algebraic and Geometric Topology ***2 **(2002), 591–647.

48. The McCord model for the tensor product of a space and a commutative ring spectrum, *Categorical Decomposition Techniques in Algebraic Topology, Proc. Isle of Skye, Scotland, 2001, Birkhauser Verlag Progress in Math ***215** (2003), 213–236.

49. Tate cohomology and periodic localization of polynomial functors, *Invent. Math. ***157** (2004), 345–370.

50. Localization of Andr´e–Quillen–Goodwillie towers, and the periodic homology of infinite loopspaces, *Advances in Math.*** 201** (2006), 318–378.

51. Mapping Spaces and Homology Isomorphisms, *Proc. A.M.S. ***134** (2006), 1237–1248. With an appendix joint with G. Arone.

52. Goodwillie towers and chromatic homotopy: an overview, *Algebraic Topology, Proc. Kinosaki, Japan, 2003, Geometry and Topology Monographs ***10** (2007), 245–279.

53. Primitives and central detection numbers in group cohomology, *Advances in Math.*** 216 **(2007), 387–442.

54. The nilpotent filtration and the action of automorphisms on the cohomology of finite p–groups, *Math. Proc. Camb. Phil. Soc. ***144** (2008), 575–602.

55. A guide to telescopic functors, *Johns Hopkins Conference on Algebraic Topology, Proc. Baltimore, 2007, Homology, Homotopy, and Applications ***10** (2008), 291–319.

56. Topological nonrealization results via the Goodwillie tower approach to iterated loopspace homology, *Algebraic and Geometric Topology ***8 **(2008), 2109–2129. (Correction: 10 (2010), 531–533.)

57. Nilpotence in group cohomology,* Proc. Edin. Math. Soc.* **56** (2013), 151–175.

58. (with J. B. McCarty) The mod 2 homology of infinite loopspaces, *Algebraic and Geometric Topology* **13** (2013), 687–745. 4

59. The Krull filtration of the category of unstable modules over the Steenrod algebra, *Math. Zeit. ***277** (2014), 917–936.

60. The Whitehead Conjecture, the Tower of \(S^1\) Conjecture, and Hecke algebras of type A, *J. Topology* **8 **(2015), 118–146.

61. Generic representation theory of finite fields in nondescribing characteristic, *Advances in Math. ***272** (2015), 598–610.

62. (with Luis A. Pereira) Operad bimodules, and composition products on Andr´e–Quillen filtrations of algebras, *Algebraic and Geometric Topology ***17** (2017), 1105–1130.

63. Adams filtration and generalized Hurewicz maps for infinite loopspaces, *Invent. Math.* **214** (2018), 957--998.

64. Hopf algebras, quasi-shuffle algebras and the cohomology of \(\Omega \Sigma X\), *Advances in Math.* **369** (2020), 107013, 30pp.

65. (with Chris J.R.Lloyd) Chromatic fixed point theory and the Balmer spectrum for extraspecial 2--groups, *American J. Math.*, to appear.

66. (with Chris J.R.Lloyd) Computing the Morava K-theory of real Grassmanians using chromatic fixed point theory, *Algebraic and Geometric Topology*, to appear.

67. (with William Balderrama) An elementary proof of the chromatic Smith fixed point theorem, *Homology, Homotopy, and Applications*, to appear.

68. A short proof of the chromatic Smith Fixed Point Theorem, preprint, 2021. arXiv:2112.05001 (To be slightly revised and renamed.)

69. Dyer-Lashof operations as extensions of Brown Gitler modules, preprint, 2023. arxiv: 2306.14158.

**Reports and other miscellaneous publications **

1. Cohomology primitives associated to central extensions, *Oberwolfach Reports ***2** (2005), 2383–2386.

2. (with Carles Broto,, Nguyen H. V. Hung, John H. Palmieri, Stewart Priddy, and Nobuaki Yagita) The problem session. *Proc. School and Conference in Algebraic Topology, Hanoi, 2004, Geometry and Topology Monographs* **11** (2007), 435–441.

3. Adams filtration and infinite loopspaces, *Oberwolfach Reports* **4** (2007), 2703–2705.

4. Restriction to the center in group cohomology, *Oberwolfach Reports ***7** (2010), 1919–1922.

5. The mod 2 homology of infinite loopspaces,* Oberwolfach Reports* **8 **(2011), 2660–2663.

6. Generic representations of finite fields in nondescribing characteristic, *Oberwolfach Reports* **12** (2015), 1377–1379.

7. New results about the equivariant stable homotopy Balmer spectrum, *Oberwolfach Reports* **16** (2019), 2220-2223.