Curriculum Vitae

Daniel R. Grayson

Birthdate

• June 3, 1952.

Mathematics Education

• Department of Mathematics, Massachusetts Institute of Technology, Ph. D. in Mathematics, June 1976, under the direction of Steven Kleiman.
• Department of Mathematics, University of Chicago, B.S. and M.S. in Mathematics, June 1972.

Professional positions

• Professor Emeritus, Department of Mathematics, University of Illinois at Urbana-Champaign, from June 16, 2007.
• Chair, Department of Mathematics, University of Illinois at Urbana-Champaign, July 16, 2004, to March 27, 2006.
• Professor, Department of Mathematics, University of Illinois at Urbana-Champaign, August 21, 1988 - June 15, 2007.
• Maître de Conférences, Department of Mathematics, Université Louis Pasteur, Strasbourg, May 1988.
• Associate Professor, Department of Mathematics, University of Illinois at Urbana-Champaign, 1984-1988.
• Assistant Professor, Department of Mathematics, University of Illinois at Urbana-Champaign, 1981-1984.
• Member, School of Mathematics, Institute for Advanced Study, 1981-1982.
• Acting Chairman, Mathematics Department, Barnard College, 1980-1981.
• Ritt Assistant Professor, Department of Mathematics, Columbia University, 1976-1981.
• Mathematical Assistant, Fakultät für Mathematik, Universität Bielefeld, summer 1976.

Research articles

• The K-theory of hereditary categories, Journal of Pure and Applied Algebra, volume 11, 1977, pages 67-74, reviewed in MR 57 #16385 and ZBL 372.18004.
• The K-theory of endomorphisms, Journal of Algebra, volume 48, 1977, pages 439-446, reviewed in MR 58 #853 and ZBL 413.18010.
• Grothendieck rings and Witt vectors, Communications in Algebra, volume 6, 1978, pages 249-255, reviewed in MR 81e:13014 and ZBL 383.13009.
• K₂ and the K-theory of automorphisms, Journal of Algebra, volume 58, 1979, pages 12-30, reviewed in MR 80g:16029 and ZBL 413.18011.
• Products in K-theory and intersecting algebraic cycles, Inventiones Mathematicae, volume 47, 1978, pages 71-83, [GDZ], reviewed in MR 58 #10890 and ZBL 394.14004.
• Projections, cycles, and algebraic K-theory, Mathematische Annalen, volume 234, 1978, pages 69-72, [GDZ], reviewed in MR 58 #10891 and ZBL 369.18007.
• Algebraic cycles and algebraic K-theory, Journal of Algebra, volume 61, 1979, pages 129-151, reviewed in MR 81m:14007 and ZBL 436.18009.
• Localization for flat modules in algebraic K-theory, Journal of Algebra, volume 61, 1979, pages 463-496, pdf scan, reviewed in MR 82c:14011 and ZBL 436.18010.
• Coincidence formulas in enumerative geometry, Communications in Algebra, volume 7, 1979, pages 1685-1711, reviewed in MR 80k:14056 and ZBL 435.14016.
• K-theory and localization for noncommutative rings, Journal of Pure and Applied Algebra, volume 18, 1980, pages 125-127, reviewed in MR 81m:18010 and ZBL 441.16020.
• SK₁ of an interesting principal ideal domain, Journal of Pure and Applied Algebra, volume 20, 1981, pages 157-163, reviewed in MR 82m:18005 and ZBL 467.18004.
• Dilogarithm computations for K₃, Algebraic K-theory, Evanston 1980, Lecture Notes in Mathematics 854, pages 168-178, Springer, Berlin, Heidelberg, New York, 1981, reviewed in MR 82i:12012 and ZBL 509.18017.
• by Avner Ash, Daniel R. Grayson, and Philip Green, Computations of cuspidal cohomology of congruence subgroups of Sl(3,Z), Journal of Number Theory, volume 19, 1984, pages 412-436, reviewed in MR 86g:11032 and ZBL 552.10015.
• The K-theory of semilinear endomorphisms, [ocr.djvu], Journal of Algebra, volume 113, 1988, pages 358-372, reviewed in MR 89i:16021 and ZBL 656.16011.
• by Spencer Bloch and Daniel R. Grayson, K₂ and L-functions of elliptic curves: computer calculations, [ocr.djvu], Applications of Algebraic K-theory to Algebraic Geometry and Number Theory Contemporary Mathematics, American Mathematical Society, Providence, Rhode Island, 1983, reviewed in MR 88f:11061 and ZBL 629.14002.
• Reduction theory using semistability, [ocr.djvu GDZ], Commentarii Mathematicae Helvetici, volume 59, 1984, pages 600-634, reviewed in MR 86h:22018 and ZBL 564.20027. See also the exposition in Stability of lattices and the partition of arithmetic quotients, by Bill Casselman, Asian J. Math. 8 (2004), no. 4, 607-637.
• Universal exactness in algebraic K-theory, Journal of Pure and Applied Algebra, volume 36, 1985, pages 139-141, reviewed in MR 86f:18016 and ZBL 558.18007.
• Reduction theory using semistability: II, [ocr.djvu GDZ], Commentarii Mathematicae Helvetici, volume 61, 1986, pages 661-676, reviewed in MR 88e:22015 and ZBL 616.20020.
• by Henri Gillet and Daniel R. Grayson, The loop space of the Q-construction, Illinois Journal of Mathematics, 31 (1987) 574-597, reviewed in MR 89h:18012 and ZBL 628.55011. Also: Erratum to "The loop space of the Q-construction", Illinois Journal of Mathematics, 47 (2003) 745-748, reviewed in MR2007234 (2004h:18012), dvi ps pdf,
• Exact sequences in algebraic K-theory, [ocr.djvu], Illinois Journal of Mathematics, volume 31, 1987, pages 598-617, reviewed in MR 89c:18011 and ZBL 629.18010.
• The arithogeometric mean, [ocr.djvu], Archiv der Mathematik, volume 52, 1989, pages 507-512, reviewed in MR 90g:11071 and ZBL 686.14040.
• Exterior power operations on algebraic K-theory, pdf ps, K-theory, volume 3, 1989, pages 247-260, reviewed in MR 91h:19005 and ZBL 701.18007.
• Modules projectifs munis d'une métrique sur les anneaux des entiers de corps de nombres, Comptes Rendus de l'Acad'emie des Sciences, Paris, 1989, volume 309, pages 573-575, reviewed in MR 91e:14004.
• by James Glazebrook, Daniel R. Grayson, and Paul Hewitt, Galois representations on holomorphic differentials, Communications in Algebra, volume 19, 1991, pages 1375-1386, reviewed in MR 92j:14032 and ZBL 739.14018. See also the addendum, Communications in Algebra, volume 20, 1992, page 2791, reviewed in ZBL 777.14010
• Adams operations on higher K-theory, K-theory, volume 6, 1992, pages 97-111, reviewed in MR 94g:19005 and ZBL 776.19001, [pdf version].
• Weight filtrations via commuting automorphisms, K-theory, volume 9, 1995, pages 139-172, reviewed in MR 96h:19001 and ZBL 826.19003. (See also On the Grayson Spectral Sequence, by Andrei Suslin, which does what I couldn't do to complete the story, at least over a field.)
• with Herbert Edelsbrunner, Edgewise Subdivision of a Simplex, Discrete and Computational Geometry, volume 24, 2000, pages 707-719, (scan), reviewed in MR 2001j:52024. and ZBL 0968.51016.
• with Mark Walker, Geometric Models for Algebraic K-theory, K-theory, volume 20, issue 4, August 2000, pages 311-330, reviewed in MR 2001m:19006 and ZBL 01563902.
• with Luchezar L. Avramov, Resolutions and Cohomology over Complete Intersections, in Computations in Algebraic Geometry with Macaulay 2, Algorithms and Computation in Mathematics, volume 8, ISBN 3-540-42230-7, Springer, Berlin, Heidelberg, New York, pages 131-178, 2001.
• with Kevin Charles Jones, Youngsoo Kim, Andrea H. Mhoon, Rekha Santhanam, and Barry J. Walker, The additivity theorem in K-theory, K-theory 32 (2): 181-191, June 2004. Preprint available: http://www.math.uiuc.edu/K-theory/0657/].
• with Henri Gillet, Volumes of symmetric spaces via lattice points; preprint: February, 2004, math.NT/0402085; published paper: Documenta Mathematica 11 (2006) 425-447.

Former Doctoral Students

• Joshua P. Mullet, Ph.D. 2006, Ross Assistant Professor (2006-2009), Department of Mathematics, The Ohio State University.
• Sung Myung, Ph.D. 2002; Research Fellow (2004-2006), Korea Institute for Advanced Study; tenure track position (2006-*), Department of Mathematics Education, Inha University, Incheon, South Korea.
• Mark Walker, Ph.D. 1996, Associate Professor, Department of Mathematics, University of Nebraska-Lincoln.
• Judy Holdener, Ph.D. 1994, Associate Professor, Department of Mathematics, Kenyon College.
• Randy McCarthy, Ph.D. 1990, Professor, Department of Mathematics, University of Illinois at Urbana-Champaign at Urbana-Champaign.
• Saeja Oh Kim, Ph.D. 1988, Associate Professor, Department of Mathematics, University of Massachusetts Dartmouth.

Mathematical software

• by Daniel R. Grayson and Michael E. Stillman, Macaulay 2, a software system for research in algebraic geometry and commutative algebra, an ongoing project since 1993.
• by Stephen Wolfram, Daniel R. Grayson, Roman E. Maeder, Henry Cejtin, Theodore Gray, Stephen M. Omohundro, David Ballman, and Jerry Keiper, Mathematica, a system for doing mathematics by computer, 1988.

Expository works

• Higher algebraic K-theory II [after Daniel Quillen], [ocr.djvu], Algebraic K-theory, Evanston 1976, Springer, Berlin, Heidelberg, New York, Lecture Notes in Mathematics, volume 551, 1976, pages 217-240, reviewed in MR 58 #28137 and ZBL 362.18015.
• Finite Generation of higher K-groups of a curve over a finite field [after Daniel Quillen], [ocr.djvu], Algebraic K-theory, Oberwolfach 1980, Part I, Lecture Notes in Mathematics 966, Springer, Berlin, Heidelberg, New York, 1982, pages 69-90, reviewed in MR 84f:14018 and ZBL 502.14004.
• On the K-theory of fields, [ocr.djvu], Proceedings of a Conference on K-theory and Geometry, Contemporary Mathematics, volume 83, 1989, pages 31-55, reviewed in MR 90c:18010 and ZBL 705.19004.
• Weight filtrations in algebraic K-theory, Proceedings of Symposia in Pure Mathematics: Motives, Proceedings of the Summer Research Conference on Motives in Seattle, 1991, volume 55, part 1, 1994, pages 207-238, reviewed in MR 95a:19006 and ZBL 803.19001, [pdf scan].
• with David Eisenbud and Michael Stillman, Using Macaulay 2, Appendix to the book Computational Methods in Commutative Algebra and Algebraic Geometry, by Wolmer Vasconcelos, Algorithms and Computation in Mathematics, volume 2, Springer, 1997, [pdf version], reviewed in MR 99c:13048.
• The motivic spectral sequence, [dvi ps pdf], Handbook of K-theory, ISBN-10 3-540-23019-X, ISBN-13 978-3-540-23019-9, Springer, Berlin, Heidelberg, New York, 1163+xiv pages, 2005, in volume 1, pages 39-69.
• A Brief Introduction to Algebraic K-theory, [dvi pdf], preprint, January, 2008.

Edited works

• as editor of a book, with David Eisenbud, Michael Stillman, and Bernd Sturmfels, Computations in Algebraic Geometry with Macaulay 2, Algorithms and Computation in Mathematics, volume 8, ISBN 3-540-42230-7, Springer, Berlin, Heidelberg, New York, 329+xv pages, 2001.
• as editor of a special volume of Communications in Algebra, dedicated to Steven Kleiman on his 60th birthday, with Susan Colley, Dan Edidin, and Ragni Piene, volume 31, number 8, 2003, 605 pages.
• as editor of a book, with Eric M. Friedlander, Handbook of K-theory, in two volumes, ISBN-10 3-540-23019-X, ISBN-13 978-3-540-23019-9, Springer, Berlin, Heidelberg, New York, 1163+xxiv pages, 2005.

Honors

• Prokasy Award for Excellence in Undergraduate Teaching, Spring, 1990.
• Beckman Associate in the Center for Advanced Study, University of Illinois, 1987-1988.
• University Scholar, University of Illinois at Urbana-Champaign, 1985-1988.
• On the (incomplete) list of teachers rated excellent by their students for some courses. An asterisk signifies that the instructor ratings were outstanding.
  • Math 416, Topics in Algebra, Algebraic K-theory, Spring, 2003.
  • Math 198*, Freshman Seminar, The Art and Practice of Mathematics, Fall, 2002.
  • Math 416, Topics in Algebra, Algebraic Geometry II, Fall, 2001.
  • Math 422, Algebraic Geometry, Spring, 2001.
  • Math 198, Freshman Seminar, The Art and Practice of Mathematics, Fall, 1997.
  • Math 416*, Topics in Algebra, Algebraic Geometry, Fall, 1993.
  • Math 422, Algebraic Geometry, Spring, 1993.
  • Math 198, Freshman Seminar, The Art and Practice of Mathematics, Fall, 1992.
  • Math 401, Abstract Algebra I, Fall, 1989.
  • Math 198, Freshman Seminar, The Art and Practice of Mathematics, Spring, 1989.

Editorships

• Editorial board, Communications in Algebra, 1990-1993.
• Editorial board, Homology, Homotopy and Applications, since 2002.

Conferences organized

• Tenth annual Great Lakes K-theory Conference at UIUC, May 8-9, 2004, with Randy McCarthy.
• Algebraic K-Theory at Oberwolfach, August 4-10, 2002, with Bruno Kahn and Uwe Jannsen.
• Learning Stacks and Computational Methods through Problem-Solving, at Urbana, June 12-15, 2002, with Sheldon Katz, Henri Gillet, and Herbert Clemens.
• Conference in Honor of Steven Kleiman's 60th Birthday, May 30 - June 2, 2002, Oslo, Norway with Susan Colley, Dan Edidin, and Ragni Piene.
• Eighth annual Great Lakes K-theory Conference, April 27, 2002, with Randy McCarthy.
• Algebraic K-theory, at Oberwolfach, held September 26 - October 2, 1999, with Uwe Jannsen (Cologne) and Bruno Kahn (Paris).
• Workshop on Parallel Symbolic Computation, October 1-3, 1998, with David Bailey, Alyson Reeves, and Nobuki Takayama.
• Fifth annual Great Lakes K-theory Conference, at UIUC, March 20-21, 1999, with Randy McCarthy (organized as a special session of the AMS meeting).
• Motives and Algebraic K-theory, special session/symposium at the AMS meeting in Milwaukee, October 24-25, 1997.
• A topology conference at UIUC, the Midwest Topology Seminar, September 27, 1997, with Randy McCarthy.
• Algebraic K-theory, at Oberwolfach June 10-14, 1996, with Andrei Suslin and Ulf Rehmann.
• First annual Great Lakes K-theory Conference, March 4-5, 1995, Urbana.

University Service

• Promotion and Tenure Committee of the Department of Mathematics, 2001-2003; chair, 2001-2002.
• Executive Committee of the Department of Mathematics, 1999-2000.
• Executive Committee of the College of Liberal Arts and Sciences, 1996-1998.
• Promotion and Tenure Committee of the University of Illinois at Urbana-Champaign, 1994-1995.
• Executive Committee of the College of Liberal Arts and Sciences, 1992-1994.
• Promotion and Tenure Committee of the Department of Mathematics, 1991-1993.
• Area Committee II, LAS Resource Allocation Review, Fall 1992.
• Executive Committee of the Department of Mathematics, 1989-1991.
• Search Committee for the Dean of LAS, Summer, 1989.
• Search Committee for the Chair of the Department of Mathematics, Fall, 1987.

Grants

• Collaborative research: a software system for algebraic geometry research, with Michael E. Stillman (Cornell), current, NSF DMS 03-11806 (Cornell) and NSF DMS 03-11378 (UIUC), 2003-2008, $589010 (Cornell) and $251345 (UIUC).
• Support for K-theory Conferences; 2003-2006, (with Eric Friedlander), NSF DMS 03-03519, 2003-2006, $31,000.
• Algebraic Geometry Workshop, June 12-15, 2002, Urbana, Illinois, (with Sheldon Katz), NSF DMS 02-00459, 2002-2003, $15,000.
• A software system for algebraic geometry research, NSF DMS 99-70085, 1999-2002, $159,359, extended to 2003. See also the simultaneous award NSF DMS 99-70348 to Michael Stillman.
• as faculty associate, with Principal Investigator Robert Haber; Co-principal investigators: John Sullivan and David Padua; other associates: Jonathan Dantzig, Herbert Edelsbrunner, Michael Heath, Robert Jerrard, Sanjay Kale, Shang-Hua Teng, Daniel Tortorelli; Simulation and Optimization of Casting and Extrusion Processes, Center for Process Simulation and Design, funded by NSF and DARPA under the OPAAL program, NSF DMS 98-73945, October 1, 1998 to September 30, 2001, $2,198,851.
• A software system for algebraic geometry research, NSF DMS 96-22608, 1996-1999, $132,018. See also the simultaneous award NSF DMS 96-23232 to Michael Stillman.
• A software system for algebraic geometry research, NSF DMS 92-10807, 1993-1996, $230,000. See also the simultaneous award NSF DMS 92-10805 to Michael Stillman.
• Algebraic K-theory, NSF DMS 90-02715, 1990-1993, $82,250.
• Algebraic K-theory, NSF DMS 88-06785, 1988-1990, $37,800.
• Algebraic K-theory, NSF DMS 86-01980, 1986-1988, $32,070.
• Equipment grant (with Evans, Fossum, and Moreno), 1986-88, NSF DMS 85-04692 SCREMS, $23,500.
• Algebraic K-theory, NSF DMS 82-02692, 1982-86, $51,475.
• NSF grants at Columbia with Hyman Bass, 1976-1982.

Upcoming and recent talks

• six talks on Higher Algebraic K-theory at the summer school on Cohomology of groups and algebraic K-theory at the Center of Mathematical Sciences on the campus of Zhejiang University in Hangzhou, China, July 2-12, 2007.
• three talks on Higher Algebraic K-theory at Korea Advanced Institute of Science and Technology (KAIST), Department of Mathematical Sciences, June 27-28, 2007.
• Macaulay 2, a software system for algebraic geometry, Second International Congress on Mathematical Software (ICMS2006), September 1-3, 2006
• Macaulay 2, a software system for algebraic geometry, Software for Algebraic Geometry, IMA, October 23-27, 2006

Sports victories

• 2nd place, July 4, 2004, Champaign County Freedom 5K Race, men 50-59 years old