University of Aberdeen, Scotland, UK Emeritus Prof

CURRICULUM VITÆ

DAVID JOHN BENSON

Education and Employment Dates Place Degree/Position 2017– University of Aberdeen, Emeritus Professor Scotland, UK of Mathematics 2005–17 University of Aberdeen, 6th Century Chair Scotland, UK of Pure Mathematics 2000–05 University of Georgia, Distinguished Research Athens GA, USA Professor (NSF grant held) 1994–00 University of Georgia, Full Professor Athens GA, USA (NSF grant held) 1993–94 University of Georgia, Visiting Associate Athens GA, USA Professor 1986–93 University of Oxford, University Lecturer and England, UK fellow of Wolfson College 1984–86 Northwestern University, Assistant Professor Evanston, IL, USA (NSF grant held) 1982–84 Yale University, Gibbs Instructor New Haven, CT, USA (NSF grant held) 1981–82 Arhus˚ Universitet, Danmark Royal Society exchange fellow 1978–81 Trinity College, Cambridge Ph.D. in Mathematics 1977–78 Trinity College, Cambridge Part III Mathematics, honours with distinction 1974–77 Trinity College, Cambridge First class honours in Mathematics tripos 1967–74 Maidstone Grammar School 8 O-levels, 3 A/S-levels (Mathematics A1, Physics A, Chemistry A1)

Awards and Honours 2018 Howard Rowlee Lecture, Lincoln, Nebraska, USA 2018 Research Professorship for the MSRI representation theory programme 2017–2020 Reappointed Honorary Visiting Professor at City, University of London 2017 Maurice Auslander Distinguished Lectures, Cape Cod, USA

Date: July 2020. 1 2 DAVID JOHN BENSON

2017 Elected Fellow of the Royal Society of Edinburgh (FRSE) 2016 Conference, PIMS, Vancouver, Canada to celebrate 60th birthday 2015 Conference, Isle of Skye, Scotland to celebrate 60th birthday 2015 Master of Mathematics, Trinity College, Cambridge 2014–2017 Honorary Visiting Professor at City, University of London 2013 Research Professorship for the MSRI commutative algebra programme 2012 Elected Fellow of the American Mathematical Society 2010 Invited speaker at the ICM in Hyderabad, India 2008 Simons Professorship for the MSRI representation theory programme 2004 Humboldt Research Award for Senior US Scientists, Germany 2004 Creative Research Award, University of Georgia 2003 Sandy Beaver Teaching Award, University of Georgia 1998 Creative Research Medal, University of Georgia 1993 Junior Whitehead Prize, London Mathematical Society 1980 Raleigh Prize, Trinity College, Cambridge 1977 Yeats Mathematics Essay Prize, Trinity College, Cambridge 1976 Senior Scholar, Trinity College, Cambridge 1974 Entrance Scholar, Trinity College, Cambridge

Research Visits 6 Jan to 18 Mar 2020, Newton Institute programme on “Groups, representations and applications: new perspectives,” Cambridge, UK (interrupted by Covid-19). 21 Oct to 21 Nov 2019, Research visit to University of Warwick, UK. 10–14 Sept 2018, AIM SQuaRE programme “Stratifying module categories” with Srikanth Iyengar, Henning Krause, and Julia Pevtsova in San Jos´e,California, USA. 15 Jan to 25 May 2018, Research Professor for the programme on Representation Theory, MSRI, Berkeley, California, USA. 23–27 Jan 2017, AIM SQuaRE programme “Stratifying module categories” with Srikanth Iyengar, Henning Krause, and Julia Pevtsova in San Jos´e,California, USA. 1 Sept to 30 Sept 2016, Invited visitor for the programme on Local Representation Theory and Simple Groups at the Bernoulli Centre, Lausanne, Switzerland. 25 Jun to 6 Aug 2016, Invited visitor at PIMS, Vancouver, Canada. Jan to May 2013, Research Professor for the programme on Commutative Algebra, MSRI, Berkeley, California, USA. 1 Feb to 11 Mar 2012, research visit to Department of Mathematical Sciences, University of Copenhagen, Denmark. 1–14 Jan 2012, Research in Pairs, Oberwolfach, Germany, with Srikanth Iyengar and Henning Krause. 20 July to 2 Aug 2008, Research in Pairs, Oberwolfach, Germany, with Srikanth Iyengar and Henning Krause. CURRICULUM VITÆ 3

Jan to May 2008, Simons Professor for the programme on Representation Theory of Finite Groups and Related Topics, MSRI, Berkeley, California, USA. Sept–Dec 2005, June–July 2006, March–April 2007, June–August 2008, visits to Paderborn University, Germany, supported by the Humboldt Foundation. Feb to April 2005, invited visitor for the programme on Group Representation Theory at the Bernoulli Centre, Lausanne, Switzerland. Sept 2002 to Mar 2003, invited visitor for the programme on Commutative Algebra, MSRI, Berkeley, California, USA. Sept to Dec 1991, research visit to School of Mathematics, University of Minnesota, Min- neapolis, USA. Sept to Dec 1990, invited visitor for the programme on Representations of Finite Groups, MSRI, Berkeley, California, USA.

Work address: Institute of Mathematics, University of Aberdeen, Aberdeen AB24 3UE, Scotland, UK. Tel: 01224-273807. Home page: http://homepages.abdn.ac.uk/d.j.benson/pages/

Ph. D. Thesis Supervisor: Prof. J. G. Thompson, Cambridge University Subject: Finite group theory. Title: The Simple Group J4. Date Received: 12th June, 1982.

Current Research Interests Cohomology of finite, infinite and compact Lie groups, modular representation theory; connections with algebraic topology, commutative algebra, algebraic geometry, invariant theory for finite groups.

Books and Monographs [1] Modular representation theory: New trends and methods. (231 pp.) Springer Lecture Notes in Mathematics 1081, Springer-Verlag, Berlin/New York 1984. MR 0765858 (86g:20013), Zbl 0564.20004 Second edition (with corrections), Springer-Verlag, 2006. [2] Representations and Cohomology, Vol. I: Basic representation theory of ﬁnite groups and associative algebras. (xi + 224 pp.) Cambridge Studies in Advanced Mathematics 30, Cambridge University Press, 1991. MR 1110581 (92m:20005), Zbl 0718.20001 Paperback edition (with corrections), Cambridge University Press, 1998. Reprinted 2008. MR 1644252 (99f:20001a), Zbl 0908.20001 [3] Representations and Cohomology, Vol. II: Cohomology of groups and modules. (x + 278 pp.) Cambridge Studies in Advanced Mathematics 31, Cambridge University Press, 1991. MR 1156302 (93g:20099), Zbl 0731.20001 Paperback edition (with corrections), Cambridge University Press, 1998. Reprinted 2008. MR 1634407 (99f:20001b), Zbl 0908.20002 4 DAVID JOHN BENSON

[4] (with F. R. Cohen.) Mapping class groups of low genus and their cohomology. (iv + 104 pp.) Memoirs of the Amer. Math. Soc. 443, 1991. MR 1052554 (91g:57002), Zbl 0732:57003 [5] Polynomial Invariants of Finite Groups. (v + 126 pp.) L.M.S. Lecture Notes in Mathematics 190, Cambridge University Press, 1993. Transferred to digital printing, 1999. MR 1249931 (94j:13003), Zbl 0864.13001 [6] Music: A Mathematical Offering. (xiii + 411 pp.) Cambridge University Press, 2006. ISBN 0521619998 (pbk), 0521853877 (hbk), MR 2283500 (2007k:00009), Zbl 1119.00008 Available in pdf from http://homepages.abdn.ac.uk/d.j.benson/html/maths-music.html [7] (with Stephen D. Smith.) Classifying Spaces of Sporadic Groups. (xvi + 285 pp.) Mathematical Surveys and Monographs 147, Amer. Math. Soc., 2008. ISBN 0123444741, MR 2378355 (2009f:55017), Zbl 1135.20001 [8] (with Srikanth Iyengar and Henning Krause.) Representations of Finite Groups: Local Coho- mology and Support. (x + 111 pp.) Oberwolfach Reports 43, Birkhäuser,2012. ISBN 9783034802598. MR 2951763, Zbl 1246.20002 [9] (with H. Krause and A. Skowroński,eds.) Advances in the Representation Theory of Algebras. (378pp.) Proceedings of ICRA 2012, Bielefeld. European Mathematical Society, 2014. ISBN 9783037191255. MR 3235188, Zbl 1279.00041, doi:10.4171/125 [10] Representations of Elementary Abelian p-Groups and Vector Bundles. (xviii + 328pp.) Cambridge Tracts in Mathematics 208, Cambridge University Press, 2017. ISBN 9781107174177, MR 3585474, doi:10.1017/9781316795699 [11] Commutative Banach Algebras and Modular Representation Theory. Submitted to Memoirs of the AMS, 2020.

Refereed Papers

[12] The Loewy structure of the projective indecomposable modules for A8 in characteristic 2. Comm. in Algebra 11 (13) (1983), 1395–1432. MR 0700572 (84k:20006a), Zbl 0528.20007, doi:10.1080/00927878308822912 [13] The Loewy structure of the projective indecomposable modules for A9 in characteristic 2. Comm. in Algebra 11 (13) (1983), 1433–1453. MR 0700573 (84k:20006b), Zbl 0528.20008, doi:10.1080/00927878308822913 [14] (with R. A. Parker.) The Green ring of a ﬁnite group. J. Algebra 87 (1984), 290–331. MR 0739936 (86a:16013), Zbl 0489.20007, Zbl 0539.20009, doi:10.1016/0021-8693(84)90139-X [15] Lambda and psi operations on Green rings. J. Algebra 87 (1984), 360–367. MR 0739939 (86g:16013), Zbl 0539.20011, doi:10.1016/0021-8693(84)90142-X [16] (with J. H. Conway.) Diagrams for modular lattices. J. Pure & Applied Algebra 37 (1985), 111–116. MR 0796403 (87b:06018), Zbl 0575.06008, doi:10.1016/0022-4049(85)90091-X [17] Brauer trees for 12M22. J. Algebra 95 (1985), 398–408. MR 0801275 (87c:20030), Zbl 0574.20009, doi:10.1016/0021-8693(85)90111-5 [18] Some recent trends in modular representation theory. Proceedings of the group theory year at Rutgers, C.U.P. 1985, 249–259. MR 0817257 (86j:20003), Zbl 0648.20014 [19] (with W. Feit and R. Howe.) Finite linear groups, the Commodore 64, Euler and Sylvester. Amer. Math. Monthly 93 (9) (1986), 717–719. MR 0863974 (87m:05011), Zbl 0611.10013, doi:10.2307.2322289 [20] Modules for ﬁnite groups: representation rings, quivers and varieties. Three lectures given at the Fourth International Conference on the Representations of Algebras (ICRA IV). Representation The- ory II, Groups and Orders, Ottawa 1984. Springer Lecture Notes in Mathematics 1178, 1–24. Springer- Verlag, Berlin/New York 1986. MR 0842476 (87m:20031), Zbl 0592.20010, doi:10.1007/BFb0075287 [21] (with J. F. Carlson.) Nilpotent elements in the Green ring. J. Algebra 104 (1986), 329–350. MR 0866779 (88b:20021), Zbl 0612.20005, doi:10.1016/0021-8693(86)90219-X CURRICULUM VITÆ 5

[22] Representation rings of finite groups. (Two lectures given at the 1985 Durham Symposium on the Representations of Algebras) Representations of Algebras, Durham 1985. London Math. Soc. Lecture Note Series 116, 181–199. C.U.P., 1986. MR 0897325 (88i:16037), Zbl 0621.20003, doi:10.1017/CBO9780511565779.008 [23] (with J. F. Carlson.) Diagrammatic methods for modular representations and cohomology. Comm. in Algebra 15 (1&2) (1987), 53–121. MR 0876974 (87m:20032), Zbl 0615.20032, doi:10.1080/00927878708823414 [24] (with N. Habegger.) Varieties for modules and a problem of Steenrod. J. Pure & Applied Algebra 44 (1987), 13–34. MR 0885093 (88e:55020), Zbl 0617.55005, doi:10.1016/0022-4049(87)90013-2 [25] (with J. F. Carlson.) Complexity and multiple complexes. Math. Zeit. 195 (1987), 221–238. MR 0892053 (88e:20050), Zbl 0608.20041, doi:10.1007/BF01166459 [26] Some remarks on the decomposition numbers for the symmetric groups. The Arcata Conference on Representations of Finite Groups, Proc. Symp. Pure Math. 47, Part 1, Amer. Math. Soc. (1987), 381–394. MR 0933374 (89b:20037), Zbl 0654.20010, doi:10.1090/pspum/047.1/933374 [27] Spin modules for symmetric groups. J. London Math. Soc. (2) 38 (1988), 250–262. MR 0966297 (89k:20020), Zbl 0669.20005, doi:10.1112/jlms/s2-38.2.250 [28] Projective modules for the group of the twenty-seven lines on a cubic surface. Comm. in Algebra 17 (5) (1989), 1017–1068. MR 0993388 (90d:20022), Zbl 0678.20003, doi:10.1080/00927878908823773 [29] Cyclic homology and path algebra resolutions. Math. Proc. Camb. Phil. Soc. 106 (1989), 57–66. MR 0994079 (90f:18010), Zbl 0677.16014, doi:10.1017/S0305004100067979 [30] (with J. F. Carlson and G. R. Robinson.) On the vanishing of group cohomology. J. Algebra 131 (1990), 40–73. MR 1054998 (91c:20073), Zbl 0697.20043, doi:10.1016/0021-8693(90)90165-K [31] (with L. Evens.) Group homomorphisms inducing isomorphisms in cohomology. Comm. in Algebra 18 (1990), 3447–3452. MR 1063988 (91h:20080), Zbl 0743.20053, doi:10.1080/00927879008824085 n [32] (with S. Martin.) Mod 2 cohomology of the unitary groups U3(2 ). Comm. in Algebra 19 (1991), 3125– 3144. MR 1132779 (93a:20072), Zbl 0798.20037, doi:10.1080/00927879108824311 [33] (with V. Franjou.) Sériesde composition de modules instables et injectivitéde la cohomologie du groupe Z/2. Math. Zeitschrift 208 (1991), 389–399. MR 1134584 (93b:55022), Zbl 0725.55012, doi:10.1007/BF02571535 [34] (with J. F. Carlson.) The cohomology of extraspecial groups. Bull. London Math. Soc. 24 (1992), 209– 235. MR 1157256 (93b:20087), Zbl 0795.20038, doi:10.1112/blms/24.3.209 Erratum, Bull. London Math. Soc. 25 (1993), 498. MR 1233415 (94f:20099), Zbl 0801.20026, doi:10.1112/blms/25.5.498 [35] (with M. Feshbach.) Stable splittings of classifying spaces of finite groups. Topology 31 (1992), 157– 176. MR 1153243 (93d:55013), Zbl 0752.55008, doi:10.1016/0040-9383(92)90068-S [36] Resolutions and Poincaréduality for finite groups. In: Proceedings of the June 1990 Barcelona conference on Homotopy and Group Cohomology. Springer Lecture Notes in Mathematics 1509, Springer- Verlag, Berlin/New York 1992, 10–19. MR 1185957 (93i:20057), Zbl 0745.55004, doi:10.1007/BFb0087497 [37] (with J. F. Carlson.) Periodic modules with large period. Quarterly Journal of Mathematics (Oxford) 43 (1992), 283–296. MR 1176487 (93e:20011), Zbl 0807.20010, doi:10.1093/qmath/43.3.283 [38] (with J. F. Carlson.) Products in negative cohomology. J. Pure & Applied Algebra 82 (1992), 107–129. MR 1182934 (93i:20058), Zbl 0807.20044, doi:10.1016/0022-4049(92)90116-W [39] The image of the transfer map. Archiv der Mathematik 61 (1993), 7–11. MR 1222083 (94i:20095), Zbl 0815.20040, doi:10.1007/BF01258049 6 DAVID JOHN BENSON

[40] (with J. Greenlees.) The action of the Steenrod algebra on Tate cohomology. J. Pure & Applied Algebra 85 (1993), 21–26. MR 1207065 (94b:55023), Zbl 0781.55009, doi:10.1016/0022-4049(93)90168-S [41] (with J. F. Carlson.) Projective resolutions and Poincaréduality complexes. Trans. Amer. Math. Soc. 132 (1994), 447–488. MR 1142778 (94f:20100), Zbl 0816.20044, doi:10.2307/2154636 [42] (with M. Feshbach.) On the cohomology of split extensions. Proc. Amer. Math. Soc. 121 (1994), 687– 690. MR 1186129 (94i:20096), Zbl 0819.20058, doi:10.1090/S0002-9939-1994-1186129-9 [43] Conway’s group Co3 and the Dickson invariants. Manuscripta Mathematica 85 (1994), 177–193. MR 1302871 (95h:55018), Zbl 0853.55018, doi:10.1007/BF02568192 [44] (with J. F. Carlson.) Functional equations for Poincaréseries in group cohomology. Bull. London Math. Soc. 29 (1994), 438–448. MR 1308360 (95j:20048), Zbl 0836.20076, doi:10.1112/blms/26.5.438 [45] (with J. Wood.) Integral invariants and cohomology of BSpin(n). Topology 34 (1995), 13–28. MR 1308487 (95m:55023), Zbl 0846.55013, doi:10.1016/0040-9383(94)E0019-G [46] (with W. W. Crawley–Boevey.) A ramification formula for Poincaréseries, and a hyperplane formula for modular invariants. Bull. London Math. Soc. 27 (1995), 435–440. MR 1338685 (96h:13020), Zbl 0860.13010, doi:10.1112/blms/27.5.435 [47] (with C. W. Wilkerson.) Finite simple groups and Dickson invariants. Homotopy theory and its applications, ed. Adem, Milgram and Ravenel, Contemp. Math. 188, 31–42, American Math. Society, 1995. MR 1349127 (96d:55009), Zbl 0840.55009, doi:10.1090/conm/188/02231 [48] (with J. F. Carlson and J. Rickard.) Complexity and varieties for infinitely generated modules. Math. Proc. Camb. Phil. Soc. 118 (1995), 223–243. MR 1341788 (96j:20006), Zbl 0848.20003, doi:10.1017/S0305004100073618 [49] (with P. Kropholler.) Cohomology of groups. Survey article, “Handbook of Algebraic Topology” North Holland (1995), 917–950. MR 1361903 (96j:20072), Zbl 0873.20038, doi:10.1016/B978-044481779-2/50019-5 [50] Cohomology of modules in the principal block of a finite group. New York Journal of Mathematics 1 (1995), 196–205. MR 1362976 (96h:20095), Zbl 0879.20004 [51] Stably splitting BG. Bulletin of the Amer. Math. Soc. 33 (1996), 189–198. MR 1362628 (97c:55015), Zbl 0859.55015, doi:10.1090/S0273-0979-96-00656-8 [52] Fusion in compact Lie groups. Quarterly Journal of Mathematics (Oxford) 47 (1996), 261–268. MR 1412554 (97j:22015), Zbl 0870.22005, doi:10.1093/qmath/47.3.261 [53] Decomposing the complexity quotient category. Math. Proc. Camb. Phil. Soc. 120 (1996), 589–595. MR 1401949 (97f:20007), Zbl 0884.20003, doi:10.1017/S0305004100001572 [54] (with J. F. Carlson and J. Rickard.) Complexity and varieties for infinitely generated modules, II. Math. Proc. Camb. Phil. Soc. 120 (1996), 597–615. MR 1401950 (97f:20008), Zbl 0888.20003, doi:S0305004100001584 [55] (with J. P. C. Greenlees.) Commutative algebra for cohomology rings of virtual duality groups. J. Al- gebra 192 (1997), 678–700. MR 1452682 (98d:20057), Zbl 0901.20040, doi:10.1006/jabr.1996.6944 [56] (with J. F. Carlson and J. Rickard.) Thick subcategories of the stable module category. Fundamenta Mathematicæ 153 (1997), 59–80. MR 1450996 (98g:20021), Zbl 0886.20007 [57] Complexity and varieties for infinite groups, I. J. Algebra 193 (1997), 260–287. MR 1456576 (99a:20054), Zbl 0886.20002, doi:10.1006/jabr.1996.6996 [58] Complexity and varieties for infinite groups, II. J. Algebra 193 (1997), 288–317. MR 1456576 (99a:20054), Zbl 0886.20003, doi:10.1006/jabr.1996.6997 [59] Infinite dimensional modules for a finite group. Representation Theory of Finite Groups, Proceedings of the 1995 Ohio State Conference, ed. Ron Solomon, de Gruyter (1997), 11–17. MR 1611006 (99k:20018), Zbl 0897.20008, doi:10.1515/9783110806298.11 CURRICULUM VITÆ 7

[60] (with J. P. C. Greenlees.) Commutative algebra for cohomology rings of classifying spaces of compact Lie groups. J. Pure & Applied Algebra 122 (1997), 41–53. MR 1479347 (98j:57054), Zbl 0886.57022, doi:10.1016/S0022-4049(96)00078-3 [61] Cohomology of sporadic groups, finite loop spaces, and the Dickson invariants. Proceedings of the 1994 Durham Conference on Geometry and Cohomology in Group Theory, ed. Kropholler, Niblo and Stöhr.London Math. Soc. Lecture Notes Series, 252 (1998), 10–23. MR 1709949 (2001i:55017), Zbl 0928.55017, doi:10.1017/cbo9780511666131.003 [62] (with A. Adem.) Elementary abelian groups acting on products of spheres. Math. Zeit. 228 (1998), 705–712. MR 1644440 (99k:57033), Zbl 0913.57020, doi:10.1007/pl00004637 [63] (with W. W. Wheeler.) Direct sum decompositions of infinitely generated modules. Trans. Amer. Math. Soc. 351 (1999), 3843–3855. MR 1608277 (99m:20009), Zbl 0933.20005, doi:10.1090/S0002-9947-99-02316-8 [64] (with D. G. Ph. Gnacadja.) Phantom maps and purity in modular representation theory, I. Funda- menta Mathematicæ 161 (1999), 37–91. MR 1713200 (2000k:20013), Zbl 0944.20004 [65] Flat modules over group rings of finite groups. Algebras and Representation Theory 2 (1999), 287–294. MR 1715750 (2000g:20013), Zbl 0938.20003, doi:10.1023/A:1009918813260 [66] (with J. F. Carlson.) Cohomology of the double cover of the Mathieu group M12. J. Algebra 226 (2000), 547–576. MR 1749904 (2001h:20076), Zbl 0953.20042, doi:10.1006/jabr.1999.8207 [67] Infinite dimensional modules for finite groups. Three lectures given at the Euroconference Workshop on Infinite Length Modules, Bielefeld, 1998. Appeared in: “Infinite Length Modules”, Trends in Mathematics, Birkhäuser Verlag (2000), 251–272. MR 1789219 (2002h:20012), Zbl 0985.20005, doi:10.1007/978-3-0348-8426-6_12 [68] (with K. Goodearl.) Periodic flat modules, and flat modules over group rings. Pacific J. Math. 196 (2000), 45–67. MR 1797235 (2002c:20006), Zbl 1073.20500, doi:10.2140/pjm.2000.196.45 [69] (with H. Krause.) Generic idempotent modules for a finite group. Algebras and Representation Theory (Special issue dedicated to Klaus Roggenkamp on the occasion of his 60th birthday) 3 (2000), 337–346. MR 1808130 (2002m:20013), Zbl 0968.20007, doi:10.1023/A:1009997808980 [70] (with W. W. Wheeler.) The Green correspondence for infinitely generated modules. Journal of the London Math. Soc. (2) 63 (2001), 69–82. MR 1801717 (2002h:20004), Zbl 1047.20010, doi:10.1112/S0024610700001472 [71] (with D. G. Ph. Gnacadja.) Phantom maps and purity in modular representation theory, II. Algebras and Representation Theory 4 (2001), 395–404. MR 1863392 (2002j:20017), Zbl 0998.20004, doi:10.1023/A:1012475019810 [72] Modules with injective cohomology, and local duality for a finite group. New York Journal of Mathe- matics 7 (2001), 201–215. MR 1856958 (2002f:20079), Zbl 0994.20009 [73] (with H. Krause.) Pure injectives and the spectrum of the cohomology ring of a finite group. Journal fürdie reine und angewandte Mathematik (Crelle’s journal) 542 (2002), 23–51. MR 1880824 (2002m:20086), Zbl 0987.20026 [74] Phantom maps and purity in modular representation theory, III. J. Algebra 248 (2002), 747–754. MR 1882119 (2003c:20007), Zbl 1002.20008, doi:10.1006/jabr.2001.9043 [75] The nucleus, and extensions between modules for a finite group. Proceedings of the Ninth Interna- tional Conference on Representations of Algebras (ICRA IX), Beijing, August 21–Sept 1 2000, second volume, Beijing Normal University Press (2002), 145–155. MR 2067376 (2005c:20018), Zbl 1086.20500 [76] (with D. Nakano.) The nucleus for restricted Lie algebras. Proc. Amer. Math. Soc. 131 (2003), 3395– 3405. MR 1990628 (2004d:17026), Zbl 1044.20032, doi:10.1090/S0002-9939-03-06939-9 8 DAVID JOHN BENSON

[77] (with A. Kumjian and N. C. Phillips.) Symmetries of Kirchberg algebras. Canadian Math. Bull. 46 (2003), 509–528. MR 2011390 (2004m:46155), Zbl 1079.46047, doi:10.4153/CMB-2003-049-7 [78] Dickson invariants, regularity and computation in group cohomology. Illinois Journal of Mathematics 48 (1) (2004), 171–197. MR 2048221 (2005c:20089), Zbl 1041.20036 [79] (with E. Green.) Nonprincipal blocks with one simple module. Quarterly Journal of Mathematics (Oxford) 55 (2004), 1-11. MR 2043003 (2004k:20017), Zbl 1098.20009, doi:10.1093/qmath/hag039 [80] (with H. Krause and S. Schwede.) Realizability of modules over Tate cohomology. Trans. Amer. Math. Soc. 356 (2004), 3621–3668. MR 2055748 (2005b:20102), Zbl 1070.20060, doi:10.1090/S0002-9947-03-03373-7 [81] Commutative algebra in the cohomology of groups (with an appendix by Srikanth Iyengar). Three lectures given at the MSRI introductory workshop on Commutative Algebra, Sept 2002. Trends in Commutative Algebra, MSRI publications, Volume 51, CUP 2004, 1–50. MR 2132647 (2006a:20096), Zbl 1113.20042 [82] UGA VIGRE algebra group, led by D. J. Benson, B. D. Boe and D. K. Nakano; the other participants were P. Bergonio, L. Chastkofsky, B. Cooper, G. M. Guy, J. Jungster, Jo JangHyun, G. Matthews, N. Mazza and K. J. Platt, Varieties of nilpotent elements for simple Lie algebras I. Good primes. J. Algebra 280 (2) (2004), 719–737. MR 2090060 (2005h:17016), Zbl 1063.17007, doi:10.1016/j.jalgebra.2004.05.023 [83] On the classifying space and cohomology of Thompson’s sporadic simple group. Finite Groups 2003: Proceedings of the Gainesville Conference On Finite Groups, March 6–12, 2003. Edited by Chat Ho, Peter Sin, Pham Tiep and Alex Turull. Walter de Gruyter (2004), 47–57. MR 2125065 (2005k:20031), Zbl 1073.20042 [84] (with M. Linckelmann.) Vertex and source determine the block variety of an indecomposable module. J. Pure & Applied Algebra 197 (2005), 11–17. MR 2123976 (2005k:20016), Zbl 1070.20013, doi:10.1016/j.jpaa.2004.08.032 [85] (with H. Krause and S. Schwede.) Introduction to realizability of modules over Tate cohomology. “Rep- resentations of Algebras and Related Topics,” Tenth International Conference on the Representations of Algebras (ICRA X), Toronto, 2002. Fields Institute Communications 45, Amer. Math. Soc. (2005), 81–97. MR 2146241 (2006h:20072), Zbl 1107.20043, doi:10.1090/fic/045/06 [86] UGA VIGRE algebra group, led by D. J. Benson, B. D. Boe and D. K. Nakano; the other participants were P. Bergonio, L. Chastkofsky, B. Cooper, G. M. Guy, J. Hower, M. Hunziker, Jo JangHyun, J. Kujawa, G. Matthews, N. Mazza, K. J. Platt and C. Wright, Varieties of nilpotent elements for simple Lie algebras II: bad primes. J. Algebra 292 (2005), 65–99. MR 2166796 (2006k:14083), Zbl 1124:17003, doi:10.1016/j.jalgebra.2004.12.023 [87] (with S. K. Chebolu, J. D. Christensen and J. Mináˇc.) The generating hypothesis for the stable module category of a p-group. J. Algebra 310 (2007), 428–433. MR 2307802 (2007k:16011), Zbl 1120:20002, doi:10.1016/j.jalgebra.2006.12.013 [88] UGA VIGRE algebra group, led by D. J. Benson, B. D. Boe and D. K. Nakano; the other participants were P. Bergonio, L. Chastkofsky, B. Cooper, J. Hower, Jo JangHyun, J. Kujawa, N. Mazza, K. J. Platt and C. Wright, Support varieties for Weyl modules over bad primes. J. Algebra 312 (2007), 602–633. MR 2333175 (2008g:20105), Zbl 1123:20038, doi:10.1016/j.jalgebra.2007.03.008 [89] (with K. Erdmann and M. Holloway.) Rank varieties for a class of finite-dimensional local algebras. J. Pure & Applied Algebra 211 (2007), 497–510. MR 2341266 (2008f:16006), Zbl 1184.16012, doi:10.1016/j.jpaa.2007.02.006 [90] (with R. Kessar.) Blocks inequivalent to their Frobenius twists. J. Algebra 315 (2007), 588–599. MR 2351880 (2008h:20014), Zbl 1135:20002, doi:10.1016/j.jalgebra.2007.03.044 [91] (with N. Lemire, J. Mináˇcand J. Swallow.) Detecting pro-p-groups that are not absolute Galois groups. Journal fürdie reine und angewandte Mathematik (Crelle’s journal) 613 (2007), 175–191. MR 2377134 (2009k:20063), Zbl 1204.12007, doi:10.1515/CRELLE.2007.096 CURRICULUM VITÆ 9

[92] (with P. Webb.) Unique factorization in invariant power series rings. J. Algebra 319 (2008), 702–715. MR 2381803 (2008k:13007), Zbl 1146:13003, doi:10.1016/j.jalgebra.2006.01.059 [93] (with H. Krause.) Complexes of injective kG-modules. Algebra and Number Theory 2 (2008), 1–30. MR 2377361 (2009d:20010), Zbl 1167.20006, doi:10.2140/ant.2008.2.1 [94] (with J. P. C. Greenlees.) Localization and duality in topology and modular representation theory. J. Pure & Applied Algebra 212 (2008), 1716–1743. MR 2400738 (2009e:20016), Zbl 1161:20005, doi:10.1016/j.jpaa.2007.12.001 [95] Idempotent kG-modules with injective cohomology. J. Pure & Applied Algebra 212 (2008), 1744–1746. MR 2400739 (2009b:20096), Zbl 1156:20042, doi:10.1016/j.jpaa.2007.12.003 [96] The regularity conjecture in the cohomology of groups. Guido’s Book of Conjectures, a gift to Guido Mislin on the occasion of his retirement from ETH, Zürich. Enseignement Mathématique(2) 54 (2008), 25–27. Zbl 1143.00006 [97] Resolutions over symmetric algebras with radical cube zero. J. Algebra 320 (2008), 48–56. MR 2417976 (2009h:16006), Zbl 1185.16006, doi:10.1016/j.jalgebra.2008.02.033 [98] On the regularity conjecture for the cohomology of finite groups. Proceedings of the Edinburgh Math- ematical Society 51 (2008), 273–284. MR 2465907 (2009i:20100), Zbl 1202.20057, doi:10.1017/S0013091505001203 [99] (with J. Carlson.) Varieties and cohomology of infinitely generated modules. Archiv der Mathematik (Basel) 91 (2008), 122-125. MR 2430794 (2009e:20015), Zbl 1151.20040, doi:10.1007/s00013-008-2731-8 [100] (with S. Iyengar and H. Krause.) Local cohomology and support for triangulated categories. Annales Scientifiques de l’Ecole Normale Supérieur4e série,t. 41 (2008), 1–47. MR 2489634 (2009k:18012), Zbl 1171.18007 [101] (with P. Balmer and J. F. Carlson.) Gluing representations via idempotent modules and constructing endotrivial modules. J. Pure & Applied Algebra 213 (2009), 173-193. MR 2467395 (2009i:20016), Zbl 1177.20015, doi:10.1016/j.jpaa.2008.06.007 ∧ [102] An algebraic model for chains on Ω(BGp ). Transactions of the American Math. Soc. 361 (2009), 2225-2242. MR 2465835 (2009k:55014), Zbl 1167.55003, doi:10.1090/S0002-9947-08-04728-4 [103] Periodic resolutions for certain finite groups. International Electronic Journal of Algebra 6 (2009), 46–64. MR 2520956 (2010h:20119), Zbl 1196.20058 [104] (with S. Doty.) Schur–Weyl duality over finite fields. Archiv der Math. 93 (2009), 425–435. MR 2563588 (2010k:20070), Zbl 1210.20039, doi:10.1007/s00013-009-0066-8 [105] Modules of constant Jordan type with one non-projective block. Algebras and Representation Theory 13 (2010), 315–318. MR 2630123 (2011d:20015), Zbl 1215.20013, doi:10.1007/s10468-008-9124-3 [106] (with K. Erdmann and A. Mikaelian.) Cohomology of Hecke algebras. Homology, Homotopy and Applications 12 (2010), 353–370. MR 2771594 (2012b:20004), Zbl 1236.20002, doi:10.4310/HHA.2010.v12.n2.a12 [107] Modules for elementary abelian p-groups. Proceedings of the International Congress of Mathemati- cians, Hyderabad, India, 19–27 August 2010, Volume II, World Scientific (2011), 113–124. MR 2827787, Zbl 1248.20008, doi:10.1142/9789814324359_0042 [108] (with K. Erdmann.) Hochschild cohomology of Hecke algebras. J. Algebra 336 (2011), 391–394. MR 2802551 (2012d:20008), Zbl 1233.20004, doi:10.1016/j.jalgebra.2011.03.022 [109] (with S. Iyengar and H. Krause.) Stratifying triangulated categories. Journal of Topology 4 (2011), 641–666. MR 2832572 (2012m:18016), Zbl 1239.18013, doi:10.1112/jtopol/jtr017 [110] (with S. Iyengar and H. Krause.) Module categories for finite group algebras. Proceedings of Four- teenth International Conference on the Representations of Algebras and Related Topics (ICRA XIV), Tokyo, Japan 2010. A. Skowrońskiand K. Yamagata, eds., European Mathematical Society (2011), 55–83. MR 2931895, doi:10.4171/101-1/2 10 DAVID JOHN BENSON

[111] (with S. Iyengar and H. Krause.) Localising subcategories for cochains on the classifying space of a finite group. Comptes Rendus Acad. Sci. Paris, Ser. I, 349 (2011), 953–956. MR 2838242 (2012i:20067), Zbl 1237.18009, doi:10.1016/j.crma.2011.08.019 [112] (with S. Iyengar and H. Krause.) Stratifying modular representations of finite groups. Annals of Mathematics 174 (2011), 1643–1684. MR 2846489, Zbl 1261.20057, doi:10.4007/annals.2011.174.3.6 [113] (with J. Pevtsova.) A realization theorem for modules of constant Jordan type and vector bundles. Trans. Amer. Math. Soc. 364 (2012), 6459–6478. MR 2958943, Zbl 1286.20009, doi:10.1090/S0002-9947-2012-05482-1 [114] (with S. Iyengar and H. Krause.) Colocalizing subcategories and cosupport. Journal fürdie reine und angewandte Mathematik (Crelle’s journal) 673 (2012), 161–207. MR 2999131, Zbl 1271.18012, doi:10.1515/CRELLE.2011.180 [115] (with J. P. C. Greenlees and S. Shamir.) Complete intersections and mod p cochains, Algebraic and Geometric Topology 13 (2013), 61–114. MR 3031637, Zbl 1261.13007, doi:10.2140/agt.2013.13.61 [116] Modules of constant Jordan type with small non-projective part. Algebras and Representation Theory 16 (2013), 29–33. MR 3018178, Zbl 1266.20011, doi:10.1007/s10468-011-9291-5 [117] (with S. Iyengar and H. Krause.) Module categories for group algebras over commutative rings. With an appendix by Greg Stevenson. Journal of K-Theory 11 (2013), 297–329. MR 3060999, Zbl 1291.20010, doi:10.1017/is013001031jkt214 [118] Modules of constant Jordan type and a conjecture of Rickard. J. Algebra 398 (2014), 343–349. MR 3123769, Zbl 1326.20009, doi:10.1016/j.jalgebra.2012.10.010 [119] (with J. P. C. Greenlees.) Stratifying the derived category of cochains on BG for G a compact Lie group. J. Pure & Applied Algebra 218 (2014), 642–650. MR 3133695, Zbl 1291.18014, doi:10.1016/j.jpaa.2013.08.004 [120] A survey of modules of constant Jordan type and vector bundles on projective space. Advances in the Representation Theory of Algebras. Proceedings of ICRA 2012 Bielefeld, European Math. Society 2014, 39–63. MR 3220533, Zbl 1356.20006, doi:10.4171/125-1/2 [121] Phantom maps and purity in modular representation theory III, correction. J. Algebra. 406 (2014), 171–172. MR 3188334, Zbl 1298.20011, doi:10.1016/j.jalgebra.2014.01.013 [122] (with K. J. Lim.) Generic Jordan type of the symmetric and exterior powers. Journal of Algebra and Its Applications 13 (5) (2014), 1350163 (8 pages). MR 3190092, Zbl 1327.20007, doi:10.1142/S0219498813501636 [123] (with F. Reid.) Modules with small Loewy length. J. Algebra 414 (2014), 288–299. MR 3223400, Zbl 1330.20012, doi:10.1016/j.jalgebra.2014.05.028 [124] (with S. Witherspoon.) Examples of support varieties for Hopf algebras with noncommutative tensor products. Archiv der Math. (Basel) 102 (2014), 513–520. MR 3227473, Zbl 1310.16025, doi:10.1007/s00013-014-0659-8 [125] (with J. Grodal and E. Henke.) Group cohomology and control of p-fusion. Inventiones Mathematicae 197 (2014), 491–507. MR 3251827, Zbl 1311.20051, doi:10.1007/s00222-013-0489-5 [126] (with S. Iyengar and H. Krause.) A local-global principle for small triangulated categories. Math. Proc. Camb. Phil. Soc. 158 (2015), 451-476. MR 3335421, Zbl 1371.18008, doi:10.1017/S0305004115000067 [127] Modules for elementary abelian groups and hypersurface singularities. Commutative Algebra and Noncommutative Algebraic Geometry II: Research Articles, MSRI Publications, Volume 68, CUP 2015, 19–42. MR 3496859, Zbl 1359.13015 [128] (with R. Bruner.) A counterexample for lightning flashes over E(e1, e2). Archiv der Math. (Basel) 106 (2016), 323–325. MR 3475624, Zbl 1337.55020, doi:10.1007/s00013-016-0880-8 CURRICULUM VITÆ 11

[129] (with S. Iyengar, H. Krause and J. Pevtsova.) Colocalising subcategories of modules over finite group schemes. Annals of K-Theory 2 (3) (2017), 387–408. MR 3658989, Zbl 1390.20009, doi:10.2140/akt.2017.2.387 [130] (with R. Kessar and M. Linckelmann.) On blocks of defect two and one simple module, and Lie algebra structure of HH1. J. Pure & Applied Algebra 221 (12) (2017), 2953–2973. MR 3666734, Zbl 1383.20009, doi:10.1016/j.jpaa.2017.02.010 [131] (with H. Krause) The variety of subadditive functions for finite group schemes. Fundamenta Mathe- maticae 239 (3) (2017), 289–296. MR 3691209, Zbl 1401.14194, doi:10.4064/fm262-1-2017 [132] Rings containing a field of characteristic zero. Archiv der Math. (Basel) 109 (5) (2017), 413–414. MR 3710761, Zbl 1382.16034, doi:10.1007/s00013-017-1100-x [133] (with S. Iyengar, H. Krause and J. Pevtsova.) Stratification and π-cosupport: Finite groups. Math Zeitschrift 287 (3) (2017), 947–965. MR 3719521, Zbl 06819400, doi:10.1007/s00209-017-1853-8 [134] (with J. P. C. Greenlees.) Stratifying the derived category of cochains on BG for G a compact Lie group, correction. J. Pure & Applied Algebra 222 (2018), 489. MR 3694466, Zbl 1417.18004, doi:10.1016/j.jpaa.2017.04.002 [135] (with S. Iyengar, H. Krause and J. Pevtsova.) Stratification for module categories of finite group schemes. J. Amer. Math. Soc. 31 (1) (2018), 265–302. MR 3718455, Zbl 06802408, doi:10.1090/jams/887 [136] (with J. F. Carlson.) Nilpotence and generation in the stable module category. J. Pure & Applied Algebra 222 (2018), 3566–3584. MR 3806742, Zbl 06881289, doi:10.1016/j.jpaa.2018.01.001 [137] (with C. Campagnolo, A. Ranicki and C. Rovi.) Cohomology of symplectic groups and Meyer’s signature theorem. Algebraic and Geometric Topology 18 (2018), 4069–4091. MR 3892239, Zbl 07006385, doi:10.2140/agt.2018.18.4069 [138] (with Z. Reichstein.) Fields of definition for representations of associative algebras. Proc. Edinburgh Math. Soc. 62 (1) (2019), 291–304. MR 3938833, Zbl 07091677, doi:10.1017/S0013091518000391 [139] (with S. Iyengar, H. Krause and J. Pevtsova.) Local duality for representations of finite group schemes. Compositio Mathematica 155 (2019), 424–453. MR 3914144, Zbl 07159511, doi:10.1112/S0010437X19007061 [140] Theta functions and a presentation of 21+(2g+1)Sp(2g, 2). J. Algebra 527 (2019), 204–240. MR 3924432, Zbl 07041659, doi:10.1016/j.jalgebra.2019.02.029 [141] (with P. Etingof.) Symmetric tensor categories in characteristic 2. Advances in Math. 351 (2019), 967–999. MR 3956002, Zbl 1430.18013, doi:10.1016/j.aim.2019.05.020 [142] (with R. Kessar and M. Linckelmann.) Blocks with normal abelian defect and abelian p0 inertial quotient. Quarterly Journal of Mathematics (Oxford) 70 (2019), 1437–1448. MR 4045109, doi:10.1093/qmathj/haz025 [143] (with P. Symonds.) The non-projective part of the tensor powers of a module. Journal of the London Math. Soc. (2) 101 (2020), 828–856. doi:10.1112/jlms.12288 [144] Some conjectures and their consequences for tensor products of modules over a finite p-group. J. Algebra 558 (2020), 24–42. MR 4102129, Zbl 07203045, doi:10.1016/j.jalgebra.2019.10.012 [145] (with J. F. Carlson.) Virtual projectivity and the stable module category. J. Algebra 558 (2020), 43– 69. MR 4102104, Zbl 07203046, doi:10.1016/j.jalgebra.2019.03.021 [146] (with J. F. Carlson.) Endotrivial modules for nilpotent restricted Lie algebras. Archiv der Math. (Basel) 114 (2020), no. 5, 503–513. MR 4088557, Zbl 07191874, doi:10.1007/s00013-019-01426-2 12 DAVID JOHN BENSON

[147] (with C. Campagnolo, A. Ranicki and C. Rovi.) Signature cocycles on the mapping class group and symplectic groups. J. Pure & Applied Algebra 224 (2020) no. 11. MR 4104487, Zbl 07206683, doi:10.1016/j.jpaa.2020.106400 [148] (with J. Pevtsova.) Representations and cohomology of a family of finite supergroup schemes. Journal of Algebra, to appear. doi:10.1016/j.jalgebra.2020.02.002 [149] (with S. Iyengar, H. Krause and J. Pevtsova.) Local duality for the singularity category of a finite dimensional Gorenstein algebra. Nagoya Math. Journal, to appear. doi:10.1017/nmj.2020.2 [150] (with P. Balmer.) Resolutions by permutation modules. Archiv der Math. (Basel), to appear. doi:10.1007/s00013-020-01493-w [151] (with S. Iyengar, H. Krause and J. Pevtsova.) Detecting nilpotence and projectivity over finite supergroup schemes. Submitted to Selecta Math, 2019. [152] (with P. Etingof and V. Ostrik.) New incompressible symmetric tensor categories in positive characteristic. Submitted to Inventiones, 2020. [153] (with R. Kessar and M. Linckelmann.) On the BV structure of the Hochschild cohomology of finite group algebras. Submitted to Pacific Journal of Mathematics, 2020. [154] (with J. P. C. Greenlees.) Massey products in the homology of the loopspace of a p-completed classifying space: finite groups with cyclic Sylow p-subgroups. Submitted to Proc. Edinburgh Math. Soc., 2020. [155] (with S. Iyengar, H. Krause and J. Pevtsova.) Support theory for elementary supergroup schemes. In preparation. [156] (with J. F. Carlson.) Bounded complexes of permutation modules. In preparation. [157] (with S. Iyengar, H. Krause and J. Pevtsova.) Stratification and duality for finite unipotent supergroup schemes. In preparation. [158] (with S. Iyengar, H. Krause and J. Pevtsova.) Stratifying the derived category of the Schur algebra. In preparation. [159] (with P. Etingof.) Some algebras related to symmetric tensor categories in prime characteristic. In preparation.

Other Items

[160] The Simple Group J4. Ph. D. Thesis, Cambridge 1982. Scan of thesis downloadable from http://homepages.abdn.ac.uk/d.j.benson/html/archive/benson.html [161] Book review: C. W. Curtis and I. Reiner. Methods of Representation Theory, with Applica- tions to Finite Groups and Orders, Volume II. (Wiley & Sons Ltd., 1987) Bull. London Math. Soc. 20 (1988), 535–542. [162] The Brauer homomorphism. One page article, Encyclopædia of Mathematics Supplement Volume I, Editor-in-Chief M. Hazewinkel, Kluwer Academic Publishers (1997), 151. Online at http://eom.springer.de/B/b110860.htm. [163] Editor for problem session: A.M.S. Summer Research Institute on Cohomology, Representations and Actions of Finite Groups, Seattle, July 7–27 1996. Proc. Symp. Pure Math. 63 (1998), 519–532. [164] Commutative algebra and duality in the cohomology of groups, Four lectures given at the ICTP in Trieste, 2004. Lecture notes available online from ICTP website, 17 pages. [165] The geometry of surprise. This contributed essay on elementary teacher education appeared as pages 495–497 of R. J. Milgram, The Mathematics Pre-Service Teachers Need to Know (2005), a document prepared with support from the US Department of Education, and distributed for free at ftp://math.stanford.edu/pub/papers/milgram/FIE-book-high-res.pdf [166] Modules with injective cohomology, Oberwolfach Reports 2 (1) (2005), 350–352. [167] Complexes of injective kG-modules, Oberwolfach Reports 3 (2) (2006), 930–933. [168] Musical scales and the baker’s dozen. Matilde, Nyhedsbrev for Dansk Matematisk Forening, vol. 28 (2006), 15–16. [169] Book review: J. E. Humphreys. Modular Representations of Finite Groups of Lie Type. (CUP, 2006) SIAM Review 49 (2007), 129–131. CURRICULUM VITÆ 13

[170] Modules of constant Jordan type, Oberwolfach Reports 6 (1) (2009), 921. [171] C. Okonek, M. Schneider and H. Spindler, Vector Bundles on Complex Projective Space, Birkhäuser2011 3ed. Retyped in LATEX by D. J. Benson. [172] Stanley’s invariant theory survey, Bull. Amer. Math. Soc. 48 (2011), 507–508. MR 2823018 [173] Around a theorem of Mislin in the cohomology of finite groups, Oberwolfach Reports 9 (1) (2012), 969–970. [174] The derived category of cochains on the classifying space of a compact Lie group, Oberwolfach Reports 12 (1) (2015), 741–744. [175] Stratifying the stable module category for a finite group scheme, Oberwolfach Reports 12 (2) (2015), 978–980. [176] Cohomology of Finite Groups: Interactions and Applications (with A. Adem, J. Carlson and H. Krause, eds.) Oberwolfach Reports 12 (2) (2015), 1317–1384. MR 3443139 [177] Signature of surface bundles mod 8 and cohomology of finite groups, Oberwolfach Reports 13 (4) (2016), 3153–3156. [178] Completing the representation ring of a finite dimensional Hopf algebra I, Oberwolfach Reports 16 (1) (2019), 689–691. [179] Completing the representation ring of a finite dimensional Hopf algebra II, Oberwolfach Reports 16 (1) (2019), 847–849.

UK Grants 2008–9: LMS Grant for Support of Skye Conference

DE Grants 2005–8: Humboldt Research Award

NSF Grants 6/1/2003–9/1/2005: DMS-0242909 University of Georgia (three summers’ support) 6/1/2000–11/30/2003: DMS-9988110 University of Georgia (three summers’ support) 5/1/2000–11/30/2000: DMS-9988229 Conference Support, Representation Theory and Computational Algebra, University of Georgia, May 2000. 6/1/1997–11/30/2000: DMS-9700416 University of Georgia (three summers’ support) 6/1/1994–11/30/1997: DMS-9401004 University of Georgia (three summers’ support) 6/1/1985–11/30/1986: DMS-8503300 Northwestern University (two summers’ support) 6/1/1983–11/30/1984: Yale University (two summers’ support)

Graduate Students (Aberdeen) Th´eophileKrosi Dout´e(joint advisor with Paul Mealor), 2020 Thesis: Establishing methods of composition through the creation of mathematical processes allow- ing the translation of astronomical data into musical elements: A portfolio of original compositions.

Mark Rush, 2014 Thesis: An analogue of the Bernstein–Gelfand–Gelfand functor for elementary abelian p-groups. Fergus Reid, 2013 Thesis: Varieties for modules of small dimension. Shawn Baland, 2012 Thesis: Some results on modules of constant Jordan type for elementary abelian p-groups. 14 DAVID JOHN BENSON

Kay Jin Lim, 2009 Thesis: Varieties for Specht modules

Graduate Students (Georgia) Peter Hindman, 2002 Thesis: Representation rings of ﬁnite groups. Gilles Gnacadja, 2000 Thesis: Phantom maps and purity over ﬁnite-dimensional self-injective algebras.

Graduate Students (Oxford) Katrina Hicks (joint advisor with Karin Erdmann), 1994 Thesis: The representation theory of some groups with blocks of defect group C3 × C3 in characteristic three. Paul Day, 1994 Thesis: The May spectral sequence. Dan Brown, 1993 Thesis: The relative cohomology of ﬁnite groups and products in negative Tate cohomology. Jon Clark, 1993 Thesis: Cohomology of some ﬁnite groups. Laurence Barker, 1991 Thesis: Blocks of endomorphism algebras of modules. John Fitzgerald, 1990 Thesis: Weyl modules for groups of type B2 and G2.

Journals and Book Series Chief Editor, London Mathematical Society Student Texts, published by Cambridge University Press, 2007–2017. Editorial board, Algebra and Number Theory, Mathematical Science Publishers, 2006–2017. Editorial board, Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 2013– 2015. Editorial board, Bulletin of the American Mathematical Society, 2005–2015. Editorial board, Transformation Groups, Birkh¨auser,2010–14. Editor responsible for algebra, Forum Mathematicum, 2011–13. Editorial Advisor, London Mathematical Society, 2011–12. Editorial board, Journal of Mathematics and Music, Taylor and Francis, 2005–2009. Editorial board, Advances in Mathematics, Elsevier, 2001–2009. Editorial board, Electronic Research Announcements of the American Mathematical Society, 1999– 2005. CURRICULUM VITÆ 15

Committees, etc. Organiser, with A. Adem,´ N. Castellana and H. Krause, of the workshop “Cohomology of Finite Groups: Interactions and Applications.” Oberwolfach, Germany, 9–15 Aug 2020. Organiser, with A. Adem,´ J. Carlson and H. Krause, of the workshop “Cohomology of Finite Groups: Interactions and Applications.” Oberwolfach, Germany, 3–9 May 2015. Organiser, with Lucho Avramov and Peter Symonds, of the focus period on Invariant Theory at MSRI, Berkeley CA, USA, 4 Feb–1 Mar 2013. External advisor for Workshop and International Conference on Representations of Algebras (ICRA 2012) Bielefeld, Germany, 8–17 Aug 2012. DFG panel to evaluate research proposals for the Schwerpunktprogramm in representation theory, Köln,Germany, 16–17 Jan 2012. Organiser with Henning Krause and Srikanth Iyengar for the Oberwolfach Seminar, Representations of finite groups: local cohomology and support, Oberwolfach, Germany, 23–29 May 2010. Organising committee for the Conference on Algebraic Topology, Group Theory and Representation Theory, Isle of Skye, 9–15 June 2009. DFG panel to evaluate research proposals for the Schwerpunktprogramm in representation theory, Köln,Germany, 15–16 Jan 2009. Organising committee for the Workshop, Homological Methods in Representation Theory, MSRI, Berkeley, California, 31 Mar to 4 Apr 2008. Committee to design a new M.Sc. Degree, Aberdeen, 2006. Scientific committee for Sound and Music Computing ’05, Salerno, Italy, 24–26 Nov 2005. Coorganiser with Henning Krause of joint AMS–DMV conference on Representation Theory, Mainz, Germany, June 2005. Executive committee, University of Georgia, 2003–2005. NSF Grant Panel, Autumn 2003. Coorganiser with Henning Krause of conference on Representation Theory, Canberra, as part of the special year in Geometry and Topology organised by Amnon Neeman, June 2003. Chair of Personnel Committee, University of Georgia, 2000–2001. Principal Organiser of Conference at the University of Georgia, on Representation Theory and Computational Algebra, May 2000. Search committee for “Mildred Goodrum Heyward” Endowed Professorship of Choral Music, Uni- versity of Georgia, 1998–9. Executive committee, University of Georgia, 1998–2000. Faculty research grants committee, University of Georgia, Autumn 1998. Graduate committee, University of Georgia, 1994–8. Organiser of special session at the regional meeting of the AMS in Orlando, Florida, March 1995. Maintainer of the electronic preprint archive “Groups, Representations and Cohomology” since 1995. Current location: http://www.maths.abdn.ac.uk/∼bensondj/html/archive.html Advisory board, Musical Bridges, Inc. from 1994 (became Siberian Intercultural Bridges, Inc. in 2002). 16 DAVID JOHN BENSON

NSF postdoc selection panel, Autumn 1994. Algebra speaker selection committee for the 1994 International Congress of Mathematicians in Z¨urich, Switzerland. Editorial committee of Romulus, college magazine of Wolfson College, Oxford, 1988–1991.

Teaching Experience (i) Cambridge University (undergraduate supervisions, 1978–1981)

Group theory Representation theory Algebraic geometry Galois theory Number theory First year algebra and analysis Second year complex variables

(ii) Yale University

1982–3: (undergraduate) Calculus 112 (Diﬀerentiation) Calculus 115 (Integration) (graduate) Modular representation theory

1983–4: (undergraduate) Early Concentration Mathematics for Freshmen (Topics included: ordinary diﬀerential equations, Fourier series and Fourier transforms, and some analytic number theory) (graduate) Ordinary representations of ﬁnite Chevalley groups

(iii) Northwestern University

1984–5: (undergraduate) B20 Calculus of several variables A11 Finite mathematics (Probability and Markov chains) (graduate) E11–1 Integral and modular representation theory

1985–6: (undergraduate) C35 Number theory (graduate) D46–1 Algebraic topology: Homotopy theory D46–3 Topological K-theory CURRICULUM VITÆ 17

(iv) University of Oxford

1986–7: (graduate) Representation theory and cohomology of groups I, II

1987–8: (3rd year undergraduate) Representation theory of ﬁnite groups (graduate) Representations of algebras

1988–9: (graduate) Representation theory and cohomology of ﬁnite groups I, II, III

1989–90: (graduate) Block theory Introduction to algebraic geometry

1990–1: (graduate) Commutative algebra I: Intersection theory Commutative algebra II: Invariant theory

1991–2: (3rd year undergraduate) Representation theory of ﬁnite groups (graduate) Classifying spaces of ﬁnite groups (seminar) Cohomology of groups seminar (2 terms)

1992–3: (graduate) Simplicial and cosimplicial homotopy theory (2 terms) Introduction to algebraic geometry

(v) University of Minnesota

1991: (undergraduate) 1211 Diﬀerential calculus 5245 Introduction to abstract algebra

(vi) University of Georgia

1993–4: (graduate) 843–5 Algebra (3 terms) (undergraduate) 256 Linear algebra

1994–5: (graduate) 810–2 Topology (3 terms) (undergraduate) 254 Integral calculus 18 DAVID JOHN BENSON

1995–6: (graduate) 892 Lie algebras, Lie groups and representation theory (3 terms) (undergraduate) 254 Integral calculus

1996–7: (graduate) 892 Cohomology of groups (undergraduate) 263 Honors diﬀerential calculus 255 Calculus of several variables 264 Honors integral calculus

1997–8: 263 Honors diﬀerential calculus 255 Calculus of several variables 264 Honors integral calculus 465/665 Complex analysis

1998–9: 2310 Honors integral calculus 2200 Diﬀerential calculus 3100 Sequences and series

1999–2000: (graduate) 8000 Algebra (undergraduate) 4760 Mathematics and music

2000–1: 2700 Diﬀerential equations 4760 Mathematics and music

2001–2: 2210 Integral calculus 2700 Diﬀerential equations 2200 Diﬀerential calculus 2500 Calculus of several variables 5002 Mathematics for elementary teachers: Geometry and problem solving

2002–3: No teaching (visiting MSRI, Berkeley, California, USA)

2003–4: FRES 1010 (Freshman seminar): Mathematics and music 2210 Integral calculus 5001 Mathematics for elementary teachers: Numbers and operations 8040 Representations of ﬁnite groups

2004–5: 2210 Integral calculus 4000 Abstract algebra GRSC 7770: Graduate student teaching seminar

(vii) University of Aberdeen CURRICULUM VITÆ 19

2005–6: (undergraduate) MX3528 Optimisation

2006–7: (graduate) MA5003 Commutative algebra and algebraic geometry (undergraduate) MA2004 Sets and algebraic structures MA1505 Topics in mathematics (Mathematics and Music, and Elementary Number Theory; 2 of 6 topics taught with other staﬀ)

2007–8: (graduate) MA5003 Modular representation theory (undergraduate) MA2004 Sets and algebraic structures

2008–9: (undergraduate) MX3022 Optimisation and numerical analysis MA2506 Linear algebra

2009–10: (undergraduate) MA2004 Sets and algebraic structures MA2506 Linear algebra

2010–11: (undergraduate) MA2004 Sets and algebraic structures

Invited Talks (selection) “Matrix factorisations and modular representation theory.” Colloquium, Lancaster University, 5 Mar 2014. “Matrix factorisations and modules for elementary abelian p-groups.” Representation theory and K-theory, in celebration of Eric Friedlander’s 70th birthday, University of Southern California, Los Angeles, California, USA, 20 May 2014. “Matrix factorisations and elementary abelian p-groups.” Journéesde théoriede l’Homotopie en l’honneur de Jean Lannes et Bob Oliver, UniversitéParis 7 et Paris 13, Paris, France, 4 July 2014. “The derived category of cochains on the classifying space of a compact Lie group.” Oberwolfach, Germany, 12 Mar 2015. “Stratifying the stable module category for a finite group scheme.” Oberwolfach, Germany, 6 April 2015. “The derived category of cochains on the classifying space of a compact Lie group.” Conference workshop, “Brave New Algebra,” Barcelona, Spain, 20 April 2015. “The stable module category of a finite group scheme.” Algebraic Groups Seminar, University of British Columbia, Vancouver, Canada, 28 Jun 2016. “Signature mod eight of surface bundles over surfaces, and cohomology of finite groups.” Topology Seminar, Pacific Institute of Mathematical Sciences, Vancouver, Canada, 4 Jul 2016. “Signature mod eight of surface bundles over surfaces, and cohomology of finite groups.” Algebra Seminar, University of Washington, Seattle, Washington, USA, 12 Jul 2016. 20 DAVID JOHN BENSON

“The mathematics of musical harmony.” SIMUW afternoon session for high school students, Seattle, Washington, USA, 13 Jul 2016. “Signature mod eight of surface bundles over surfaces, and cohomology of finite groups.” Topology Seminar, University of Geneva, Switzerland, 20 Sep 2016. “Module categories for finite groups, finite group schemes, and finite supergroup schemes.” Maxi- mals algebra preseminar and seminar, University of Edinburgh, UK, 8 Nov 2016. “The signature mod 8 of surface bundles and the cohomology of finite groups.” Oberwolfach, Germany, 8 Dec 2016. “Module categories for finite group schemes and finite supergroup schemes.” Masterclass, Strati- fications and duality in modular representation theory, Copenhagen, Denmark, 29 Mar 2017. “Symmetry: A unifying thread in mathematics.” Maurice Auslander Distinguished Lectures (two talks), Woods Hole, Cape Cod, Massachusetts, USA, 29–30 Apr 2017. “Surface bundles over surfaces, and cohomology of finite groups.” BIREP Seminar, Bielefeld, Germany, 26 May 2017. “Representations and cohomology of finite group schemes and finite supergroup schemes.” BLOC 20th anniversary meeting, Oxford, UK, 23 Aug 2017. “Projective summands of tensor powers.” Group Representation Theory and Applications Seminar, MSRI, Berkeley, California, USA, 30 Jan 2018. “Summands of tensor powers of modules for a finite group.” Algebra Seminar, University of Nebraska, Lincoln, Nebraska, USA, 26 Apr 2018. “Symmetry in mathematics.” Howard Rowlee Lecture, University of Nebraska, Lincoln, Nebraska, USA, 27 Apr 2018. “Tate cohomology of finite groups.” Conference on Stable Cohomology: Foundations and Appli- cations, Snowbird, Utah, USA, 28 May 2018. “Music and mathematics.” Composers’ Forum, University of Aberdeen, UK, 8 Oct 2018. “Completing the representation ring of a finite dimensional Hopf algebra,” Oberwolfach, Germany, 8 Mar 2019. “Completing the representation ring of a finite dimensional Hopf algebra, II,” Oberwolfach, Ger- many, 27 Mar 2019. “Some exotic symmetric tensor categories in characteristic two,” BIREP Seminar, Bielefeld, 12 Apr 2019. “Some exotic symmetric tensor categories in characteristic two,” Conference on Equivariant Topol- ogy and Derived Algebra, Trondheim, 31 Jul 2019. “Cohomology of groups: a crossroads in mathematics,” 50 Jahre Mathematik in Bielefeld—die Einheit der Mathematik, Germany, 26 Sep 2019. “Hochschild cohomology of finite groups,” Topology seminar, University of Warwick, UK, 22 Oct 2019. “Some exotic symmetric tensor categories in characteristic two,” Algebra Seminar, University of Warwick, UK, 31 Oct 2019. “Symmetry: a unifying thread in mathematics,” Colloquium, University of Warwick, UK, 15 Nov 2019. CURRICULUM VITÆ 21

“Some exotic tensor categories in prime characteristic,” London Algebra Colloquium, City, Uni- versity of London, UK, 13 Feb 2020. “Some exotic tensor categories in prime characteristic,” Algebra Seminar, DPMMS, University of Cambridge, UK, 19 Feb 2020. “Summands of tensor powers of modules for a ﬁnite group,” Colloquium, Isaac Newton Institute, Cambridge, UK, 27 Feb 2020.