Alejandro Ádem Díaz de León


 Ph.D. 1986, Princeton University
Professor
Department of Mathematics
University of Wisconsin-Madison
(608) 263-1161
adem at math dot wisc dot edu

Curriculum Vitae

Date and Place of Birth: Mexico City, Mexico, November 24, 1961

B.S. National University of Mexico, 1982

Ph.D. Princeton University, 1986

Szego Assistant Professor, Stanford University, 1986-89

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

Assistant Professor, UW-Madison, 1989-92

Associate Professor, UW-Madison, 1992-96

Professor, UW-Madison, 1996-

Chair, UW-Madison, 1999-2002

Visiting Positions:
MSRI (1990), ETH-Zurich (1993-94), Max Planck Institut-Bonn (1997-98),
University of Paris VII (1998), CRM-Barcelona (1998), University of Paris XIII (2000),
Hong Kong University of Science and Technology (2001)
Princeton University & IAS (2004)


Awards

A.P. Sloan Doctoral Dissertation Fellowship, 1985

National Science Foundation Young Investigator Award, 1992

Romnes Faculty Fellowship, 1995

Vilas Associate Award, 2003


Publications

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

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

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

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

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

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

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

Generalized Tate Homology, Homotopy Fixed-Points and the Transfer, (joint with R. Cohen and W. Dwyer), Proceedings of the 1988 Evanston Algebraic Topology Conference, Contemporary Mathematics 96 (1989), 1-13

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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)

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)

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

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

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

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

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

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)

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

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

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

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

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

Toroidal Orbifolds, Gerbes and Group Cohomology, (joint with J.Pan), to appear in Transactions of the AMS.


Books

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


For an expository paper, check out my paper "Recent developments in the cohomology of finite groups", AMS Notices Vol. 44, No.7 pp 806-815 by clicking here


Here is the written account of my November 2001 lecture at the Bourbaki Seminar.


Here is a recent survey paper, partly based on my lecture ``Constructing and Deconstructing Group Actions''
at the Northwestern University Algebraic Topology Conference (March 2002).


For more papers on the cohomology of groups see Dave Benson's archive.



For some group cohomology calculations, check out Jon Carlson's website.


Here is the schedule for the Wisconsin String Theory Seminar.


Research Interests

General Areas
Topology and Algebra

Specific Topics
Cohomology of groups
Sporadic simple groups
Group actions
Arithmetic groups
K-theory
Orbifolds

Current and Graduated Students

Conference Information

Second Latin American Congress of Mathematicians, Cancun, Mexico (June 20-26, 2004)

Mathematics and Education

Remarks delivered at the Secretary of Education's Mathematics Summit, held in Washington D.C. on February 6, 2003.


I am PI of the new UW-Madison NSF VIGRE Grant (read about it in this news article).

Committees

I am currently co-chair of the Scientific Advisory Committee (SAC) at the Mathematical Sciences Research Institute in Berkeley, California. If you have suggestions or ideas for a program or conference, please contact us.


I am a member of the Scientific Advisory Board for the Banff International Research Station (BIRS).


Until May, 2005 I will be serving on the Physical Sciences Divisional Committee at the University of Wisconsin-Madison.


I serve as editor for the Transactions of the American Mathematical Society. Please submit any high quality papers on algebraic topology and related topics to my address above. Electronic submissions are strongly encouraged.