Alejandro Adem

Department of Mathematics
University of British Columbia
adem at math dot ubc dot ca

Curriculum Vitae

B.S. Faculty of Sciences, National University of Mexico, 1982

Ph.D. Department of Mathematics, Princeton University, 1986

Szego Assistant Professor, Department of Mathematics, Stanford University, 1986-89

Member, Institute for Advanced Study, Princeton, 1989-90

Department of Mathematics, University of Wisconsin-Madison
Assistant Professor, 1989-92
Associate Professor, 1992-96
Professor, 1996-2006
Chair, 1999-2002

Department of Mathematics, University of British Columbia
Professor, 2005 - present (on leave)

Pacific Institute for the Mathematical Sciences
Deputy Director, 2005 - 2008
Director, 2008 - 2015

CEO and Scientific Director, 2015 - 2019

Natural Sciences and Engineering Research Council
President, 2019 - present

Visiting Positions

MSRI (1990), ETH-Zurich (1993-94), Max Planck Institut-Bonn (1997-98, 2004),
University of Paris VII (1998), CRM-Barcelona (1998), University of Paris XIII (2000),
Hong Kong University of Science and Technology (2001), Princeton University (2004),
University of Michigan (2007), Centro di Ricerca Matematica, Pisa (2010), MSRI (2014),
Newton Institute (2018)


Fellow of the Royal Society of Canada

Fellow of the American Mathematical Society

Fellow of the Canadian Mathematical Society

Corresponding Member, Mexican Academy of Sciences

Jeffery-Williams Prize, Canadian Mathematical Society

Canada Research Chair at UBC

Vilas Associate Award (University of Wisconsin-Madison)

Romnes Faculty Fellowship (Wisconsin Alumni Research Foundation)

National Science Foundation Young Investigator Award (USA)

A.P. Sloan Doctoral Dissertation Fellowship


1. Z/pZ-Actions on (S^n)^k, Transactions of the American Mathematical Society, 300 (1987), 791-809

2. The Free Rank of Symmetry of (S^n)^k, (joint with W. Browder), Inventiones Mathematicae, 92 (1988), 431-440

3. Cohomological Restrictions on Finite Group Actions, Journal of Pure and Applied Algebra, 54 (1988), 117-139

4. Homology Representations of Finite Transformation Groups, Springer-Verlag Lecture Notes No. 1370, 1989

5. Cohomological Exponents of ZG-Lattices, Journal of Pure and Applied Algebra, 58 (1989), 1-5

6. Torsion in Equivariant Cohomology, Commentarii Mathematici Helvetici, 64 (1989), 401-411

7. On the Exponent of Cohomology of Discrete Groups, Bulletin of the London Mathematical Society, 21 (1989) 585-590

8. Generalized Tate Homology, Homotopy Fixed-Points and the Transfer, (joint with R. Cohen and W. Dwyer), Contemporary Mathematics 96 (1989), 1-13

9. Symmetric Invariants and Cohomology of Groups, (joint with J. Maginnis and R. J. Milgram), Mathematische Annalen 287 (1990), 391-411

10. Discrete Groups with Large Exponents in Cohomology, (joint with J. Carlson), Journal of Pure and Applied Algebra 66 (1990), 111-120

11. The Geometry and Cohomology of the Mathieu Group M_12, (joint with J. Maginnis and R. J. Milgram), Journal of Algebra 139 (1991), 90-133

12. Cohomological Non-Vanishing for Modules over p-Groups, Journal of Algebra 141 (1991), 376-381

13. Euler Characteristics and Cohomology of p-Local Discrete Groups, Journal of Algebra 149 (1992), 183-196

14. On the K-theory of the Classifying Space of a Discrete Group, Mathematische Annalen 292 (1992), 319-327

15. A_5-Invariants and the Cohomology of L_3(4) and Related Extensions, (joint with R. J. Milgram), Proceedings of the London Mathematical Society 66, Part 1 (1993), 187-224

16. On the Geometry and Cohomology of Finite Simple Groups, Proceedings of the 1990 Barcelona Topology Conference, Springer-Verlag Lecture Notes in Mathematics 1509 (1992), 1-9

17. Representations and K-theory of Discrete Groups, Bulletin of the American Mathematical Society Vol.28, No.1 (1993), 95-98

18. Characters and K-theory of Discrete Groups, Inventiones Mathematicae 114 (1993), 489-514, erratum

19. Invariants and Cohomology of Groups, (joint with R. J. Milgram), Boletin Sociedad Matematica Mexicana (Adem Memorial Volume), Vol. 37 (1995), 1-22

20. The Cohomology of the Mathieu Group M_22, (joint with R. J. Milgram), Topology, Vol. 34 No. 2 (1995), 389-410

21. Discrete Groups, Grothendieck Rings and Families of Finite Subgroups, Contemporary Mathematics Volume 188 (1995), 1-23

22. Linear Maps over Abelian Group Algebras, (joint with R. G. Swan), Journal of Pure and Applied Algebra 104 (1995) Vol.1 1-7

23. The Subgroup Structure and Mod 2 Cohomology of O'Nan's Sporadic Simple Group (joint with R. J. Milgram), Journal of Algebra 176 (1995), 288-315

24. The Mod 2 Cohomology Rings of Rank 3 Simple Groups are Cohen Macaulay (joint with R. J. Milgram), Annals of Mathematics Studies Vol.138 (1995) 3-13

25. Automorphisms and Cohomology of Discrete Groups, Journal of Algebra 182 (1996), 721-737

26. The Cohomology of the McLaughlin Group and Some Associated Groups (joint with R. J. Milgram), Mathematische Zeitschrift Vol. 224 No. 4 (1997) 495-517

27. Essential Cohomology of Finite Groups, (joint with D. Karagueuzian), Commentarii Mathematici Helvetici 72 (1997) 101-109

28. Elementary Abelian Groups Acting on Products of Spheres, (joint with D. J. Benson), Mathematische Zeitschrift 228 (1998) 705-712

29. On the Cohomology of SL_2(Z[1/p]) (joint with N. Naffah), London Mathematical Society Lecture Note Series 252, pp. 1-9 (1998), Cambridge University Press

30. Buildings, Groups Extensions and Cohomology of Congruence Subgroups, Contemporary Mathematics 220 (1998) 1-15

31. Periodic Cyclic Cohomology of Group Rings, (joint with M. Karoubi), Comptes Rendus de l'Academie des Sciences (Paris), t. 326, Serie I, pp. 13-17, 1998

32. Topological Models and the Cohomology of Galois Groups, (joint with Karagueuzian and Minac), Comptes Rendus de l'Academie des Sciences (Paris), t. 326, Serie I, pp. 919-924, (1998)

33. The Cohomology of the Lyons Group and Double Covers of the Alternating Groups (joint with D. Karagueuzian, R. J. Milgram and K. Umland), Journal of Algebra 208, pp. 452-479 (1998)

34. On Some Examples of Group Actions and Group Extensions (joint with E. Yalcin), Journal of Group Theory 2, pp. 69--79 (1999)

35. On Spaces with Periodic Cohomology, (joint with Jeff Smith), Electronic Research Announcements of the AMS 6 (2000)

36. On the Cohomology of Galois Groups Determined by Witt Rings (joint with Karagueuzian and Minac), Advances in Mathematics 148, pp.105-160 (1999)

37. Field Theory and the Cohomology of Some Galois Groups (joint with Gao, Karagueuzian and Minac), Journal of Algebra 235, pp.608-635 (2001)

38. On the Cohomology of Central Frattini Extensions (joint with Pakianathan), Journal of Pure and Applied Algebra 159, pp.1-14 (2001)

39. The Cohomology of the Sylow 2-subgroup of the Higman-Sims Group (joint with Carlson, Karagueuzian and Milgram), Journal of Pure and Applied Algebra 164, pp.275-305 (2001)

40. Periodic Complexes and Group Actions (joint with J.Smith), Annals of Mathematics 154, pp. 407-435 (2001).

41. Topics in transformation groups (joint with J.F. Davis). Handbook of geometric topology, pp. 1--54, North-Holland, Amsterdam (2002).

42. Finite Group Actions on Acyclic 2--Complexes, Bourbaki Lecture No. 894, in Astérisque, Vol. 290 (2003), pp. 1--17.

43. Twisted Orbifold K-theory (joint with Y.Ruan), Communications in Mathematical Physics 237, pp. 533--556 (2003).

44. On Representations and K-theory of the Braid Groups (joint with D.Cohen and F.Cohen), Mathematische Annalen 326, pp. 515--542 (2003).

45. Constructing and Deconstructing Group Actions, Contemporary Mathematics 346, pp. 1--8 (2004).

46. Fixity and Free Group Actions on Products of Spheres (joint with J.Davis and O.Unlu), Commentarii Mathematici Helvetici 79, pp. 758-778 (2004).

47. Toroidal Orbifolds, Gerbes and Group Cohomology (joint with J.Pan), Trans. Amer. Math. Soc. 358 (2006), 3969-3983.

48. Lectures on the Cohomology of Finite Groups, Contemporary Mathematics 436 (2007), 317-334.

49. Commuting Elements and Spaces of Homomorphisms (joint with F.Cohen), Mathematische Annalen 338 (2007), 587-626. Erratum (posted July 2009).

50. A Stringy Product on Twisted Orbifold K-theory (joint with Y.Ruan and B.Zhang), invited paper in Morfismos (10th Anniversary Issue), Vol. 11, No 2 (2007), 33-64.

51. Compatible Actions and Cohomology of Crystallographic Groups (joint with J.Ge, J.Pan and N.Petrosyan), Journal of Algebra 320 (2008), 341-353.

52. On decomposing suspensions of simplicial spaces (joint with A.Bahri, M.Bendersky, F.Cohen, and S.Gitler), Boletín Sociedad Matemática Mexicana (3) Vol.15 (2009), 91-102.

53. Stable splittings, spaces of representations and almost commuting elements in Lie groups (joint with Frederick R. Cohen and Jose Manuel Gomez), Math. Proc. Camb. Phil. Soc. Vol. 149 (2010), 455-490.

54. Lectures on orbifolds and group cohomology (joint with M.Klaus), Advanced Lectures in Mathematics 16 (Higher Education Press, edited by L.Ji and S-T Yau), Transformation Groups and Moduli Spaces of Curves (2010), 1-17.

55. Bundles, cohomology and truncated symmetric polynomials (joint with Zinovy Reichstein), Documenta Mathematica 15 (2010), 1029-1047.

56. Cohomology of toroidal orbifold quotients (joint with Ali Duman and Jose Manuel Gomez), J. Algebra 344 (2011) 114-136.

57. Commuting elements, simplicial spaces, and filtrations of classifying spaces (joint with F.Cohen and E.Torres-Giese), Math. Proc. Cam. Phil. Soc. Vol. 152 (2011), 91-114.

58. On generators of crystallographic groups and actions on flat orbifolds (joint with K.Dekimpe, N.Petrosyan and B.Putrycz), Journal of Group Theory, Vol. 15, Issue 4, pp. 553--561 (2012).

59. Equivariant K-theory of compact Lie group actions with maximal rank isotropy (joint with Jose Manuel Gomez), Journal of Topology Vol. 5, No. 2, 431-457 (2012).

60. On the structure of spaces of commuting elements in compact Lie groups (joint with Jose Manuel Gomez), pp. 1-26, in Configuration Spaces: Geometry, Topology and Combinatorics, Publ. Scuola Normale Superiore, Vol. 14 (CRM Series), 2012 (Birkhauser).

61. Commuting elements in central products of special unitary groups (joint with Frederick R. Cohen and Jose Manuel Gomez), Proc. Edinburgh Math. Soc. (Series 2), Vol. 56, Issue 1, pp 1--12 (2013).

62. A classifying space for commutativity in Lie groups (joint with Jose Manuel Gomez), Algebraic & Geometric Topology 15 (2015) 493-535.

63. Representation spaces for central extensions and almost commuting unitary matrices (joint with Man Chuen Cheng), J. London Math. Soc. 94 (2): pp 503-524 (2016).

64. Topology of Fermi surfaces and anomaly inflows (joint with O. Antolin-Camarena, G. Semenoff and D. Sheinbaum), J. High Energ. Phys. (2016) 2016: 83. doi:10.1007/JHEP11(2016)083.

65. Infinite loop spaces and nilpotent K-theory (joint with Jose Manuel Gomez, John Lind and Ulrike Tillmann), Algebraic & Geometric Topology 17 (2017) 869-893.

66. Twisted equivariant K-theory of compact Lie group actions with maximal rank isotropy (joint with Jose Maria Cantarero and Jose Manuel Gomez), Journal of Mathematical Physics 59, 113502 (2018).

67. On the moduli spaces of commuting elements in the projective unitary groups (joint with Man Chuen Cheng), Journal of Mathematical Physics 60, 071703 (2019).

68. Free finite group actions on rational homology 3-spheres (joint with Ian Hambleton), Forum of Mathematics, Sigma,7, E28. doi:10.1017/fms.2019.24 (2019).

69. On the second homotopy group of spaces of commuting elements in Lie groups (joint with Jose Manuel Gomez and Simon Gritschacher), International Mathematics Research Notices, rnab259, (2021).

70. Minimal Euler Characteristics for Even-Dimensional Manifolds with Finite Fundamental Group (joint with Ian Hambleton), Forum of Mathematics, Sigma , Volume 11 , 2023 , e24 DOI: (2023).


Cohomology of Finite Groups (with R.J. Milgram),
Springer-Verlag Grundlehren 309 (1st edition 1994, second edition 2004)

Orbifolds and Stringy Topology (with J. Leida and Y. Ruan),
Cambridge Tracts in Mathematics, Volume 171 (2007)

Research Interests

General Areas
Topology and Algebra

Specific Topics
Cohomology of groups
Sporadic simple groups
Group actions
Arithmetic groups
Homotopy theory
Spaces of homomorphisms

Ph.D. Students Supervised

Committee Membership

NSERC Council

Chair, Canada Research Coordinating Committee

Chair, Governing Board of the Global Research Council

Advisory Board of the Association for Women in Mathematics

Chief Editor of the Bulletin of the American Mathematical Society