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

• Member, School of Mathematics, Institute for Advanced Study, 2012 - 2014, for the special year on Univalent Foundations of Mathematics, 2012 - 2013.
• Professor Emeritus, Department of Mathematics, University of Illinois at Urbana-Champaign, from July 1, 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 30, 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, mr zb
• The K-theory of endomorphisms, Journal of Algebra, volume 48, 1977, pages 439-446, mr zb
• Grothendieck rings and Witt vectors, Communications in Algebra, volume 6, 1978, pages 249-255, [pdf, tif], mr zb
• K₂ and the K-theory of automorphisms, Journal of Algebra, volume 58, 1979, pages 12-30, mr zb
• Products in K-theory and intersecting algebraic cycles, Inventiones Mathematicae, volume 47, 1978, pages 71-83, gdz, mr zb
• Projections, cycles, and algebraic K-theory, Mathematische Annalen, volume 234, 1978, pages 69-72, gdz, mr zb
• Algebraic cycles and algebraic K-theory, Journal of Algebra, volume 61, 1979, pages 129-151, mr zb
• Localization for flat modules in algebraic K-theory, Journal of Algebra, volume 61, 1979, pages 463-496, [pdf], mr zb
• Coincidence formulas in enumerative geometry, Communications in Algebra, volume 7, 1979, pages 1685-1711, mr zb
• K-theory and localization for noncommutative rings, Journal of Pure and Applied Algebra, volume 18, 1980, pages 125-127, [pdf, tif], mr zb
• SK₁ of an interesting principal ideal domain, Journal of Pure and Applied Algebra, volume 20, 1981, pages 157-163, mr zb Manin refers to it in arXiv:0809.1564.
• Dilogarithm computations for K₃, Algebraic K-theory, Evanston 1980, Lecture Notes in Mathematics 854, pages 168-178, Springer, Berlin, Heidelberg, New York, 1981, mr zb
• 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, mr zb
• The K-theory of semilinear endomorphisms, [ocr.djvu], Journal of Algebra, volume 113, 1988, pages 358-372, mr zb
• by Spencer Bloch and Daniel R. Grayson, K₂ and L-functions of elliptic curves: computer calculations, [pdf ocr.djvu], Applications of Algebraic K-theory to Algebraic Geometry and Number Theory Contemporary Mathematics, American Mathematical Society, Providence, Rhode Island, 1983, mr zb
• Reduction theory using semistability, [ocr.djvu gdz dz ], Commentarii Mathematicae Helvetici, volume 59, 1984, pages 600-634, mr zb.
  • See the exposition in Stability of lattices and the partition of arithmetic quotients, by Bill Casselman, Asian J. Math. 8 (2004), no. 4, 607-637.
  • Our approach to reduction theory is used in arXiv:1204.2418v1 by Bartels, Lueck, Reich, and Rueping to give a proof of the K-theory Farrell-Jones conjecture for arithmetic groups.
• Universal exactness in algebraic K-theory, Journal of Pure and Applied Algebra, volume 36, 1985, pages 139-141, mr zb
• Reduction theory using semistability: II, [pdf ocr.djvu gdz], Commentarii Mathematicae Helvetici, volume 61, 1986, pages 661-676, mr zb
• by Henri Gillet and Daniel R. Grayson, The loop space of the Q-construction, Illinois Journal of Mathematics, 31 (1987) 574-597, [pdf mr zb].
  • See also the erratum below.
• Exact sequences in algebraic K-theory, [ocr.djvu], Illinois Journal of Mathematics, volume 31, 1987, pages 598-617, mr zb
• The arithogeometric mean, [ocr.djvu], Archiv der Mathematik, volume 52, 1989, pages 507-512, mr zb
• Exterior power operations on algebraic K-theory, [doi 10.1007/BF00533371 dvi pdf ps], K-theory, volume 3, 1989, pages 247-260, mr zb
• 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, mr
• by James Glazebrook, Daniel R. Grayson, and Paul Hewitt, Galois representations on holomorphic differentials, Communications in Algebra, volume 19, 1991, pages 1375-1386, mr zb.
  • See also the addendum, Communications in Algebra, volume 20, 1992, page 2791, reviewed in zb.
• Adams operations on higher K-theory, [doi 10.1007/BF01771009 pdf preprint], K-theory, volume 6, 1992, pages 97-111, mr zb.
• Weight filtrations via commuting automorphisms, K-theory, volume 9, 1995, pages 139-172, [doi 10.1007/BF00961457 preprint], mr zb.
  • See also On the Grayson Spectral Sequence, by Andrei Suslin, Tr. Mat. Inst. Steklova 241 (2003), Teor. Chisel, Algebra i Algebr. Geom., 218-253; translation in Proc. Steklov Inst. Math. 2003, no. 2 (241), 202-237; it does what I couldn't do to complete the story, at least over a field.
  • See also K-motives of algebraic varieties, by Grigory Garkusha and Ivan Panin, arXiv:1108.0375. They use my result to produce a motivic spectral sequence connecting bivariant K-theory to bivariant motivic cohomology.
  • See also On the Motivic Spectral Sequence, by Grigory Garkusha and Ivan Panin, arXiv:1210.2242. They show that my spectral sequence agrees with the one coming from Voevodsky's slice tower.
• with Herbert Edelsbrunner, Edgewise Subdivision of a Simplex, [doi 10.1145/304893.304897 pdf], Proceedings of the Fifteenth Annual Symposium on Computational Geometry (Miami Beach, Florida, 1999), electronic, pages 24-30, ACM, New York, 1999; mr.
• with Herbert Edelsbrunner, Edgewise Subdivision of a Simplex, [doi 10.1007/s004540010063 ps pdf], Discrete and Computational Geometry, volume 24, number 4, December, 2000, pages 707-719, mr zb.
• with Mark Walker, Geometric Models for Algebraic K-theory, [doi 10.1023/A:1026506218989 preprint mr zb], K-theory, volume 20, issue 4, August 2000, pages 311-330.
• 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.
• by Henri Gillet and Daniel R. Grayson, Erratum to "The loop space of the Q-construction", Illinois Journal of Mathematics, 47 (2003) 745-748, [dvi ps pdf mr].
• with Kevin Charles Jones, Youngsoo Kim, Andrea H. Mhoon, Rekha Santhanam, and Barry J. Walker, The additivity theorem in K-theory, [doi 10.1023/B:KTHE.0000037546.39459.cb preprint], K-theory 32 (2): 181-191, June 2004.
• with Henri Gillet, Volumes of symmetric spaces via lattice points, [preprint], Documenta Mathematica 11 (2006) 425-447, [mr zb].
• by Lara B. Anderson, James Gray, Dan Grayson, Yang-Hui He, and Andre Lukas, Yukawa Couplings in Heterotic Compactification; arXiv:0904.2186; Commun. Math. Phys. 297:95-127, 2010, [doi 10.1007/s00220-010-1033-8, mr 2011e:81203]
• The additivity theorem in algebraic K-theory, Documenta Mathematica 16 (2011) 457-464, pdf, preprint, January, 2011.
• Algebraic K-theory via binary complexes, posted: June 14, 2012, Journal of the American Mathematical Society, 25 (2012) 1149-1167, http://dx.doi.org/10.1090/S0894-0347-2012-00743-7, PII: S 0894-0347(2012)00743-7, [preprint].
• with Alexandra Seceleanu and Michael E. Stillman, Computations in intersection rings of flag bundles, arXiv:1205.4190v1, preprint, May, 2012.

Former Doctoral Students

• Youngsoo Kim, Ph.D. 2010, Assistant Professor (2010-present), Department of Mathematics, Tuskegee University.
• 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, Professor, Department of Mathematics, University of Nebraska-Lincoln.
• Judy Holdener, Ph.D. 1994, 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, Professor, Department of Mathematics, University of Massachusetts Dartmouth.

Mathematical software

• by Daniel R. Grayson and Michael E. Stillman, Macaulay2, 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, mr zb
• 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, mr zb
• 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, mr zb
• 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, mr zb, [pdf pdf-scan].
• with David Eisenbud and Michael Stillman, Using Macaulay 2, [pdf dvi], Appendix to the book Computational Methods in Commutative Algebra and Algebraic Geometry, by Wolmer Vasconcelos, Algorithms and Computation in Mathematics, volume 2, Springer, 1997, mr
• The motivic spectral sequence, [dvi ps pdf mobi], 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 zb], preprint, January, 2008; revised September, 2008; published in Cohomology of Groups and Algebraic K-theory, Advanced Lectures in Mathematics (ALM) 12; edited by Lizhen Ji 季理真, Kefeng Liu 刘克峰, and Shing-Tung Yau 丘成桐; Higher Education Press and International Press; 2009; pages 167-186.
• Quillen's work in algebraic K-theory, [preprint, December, 2011: dvi pdf], Journal of K-theory: K-theory and its Applications to Algebra, Geometry, and Topology, available on CJO2013 at doi:10.1017/is012011011jkt203 and here (copyright 2013 Independent Scholarly Online and Print Publishing).

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; online version available at http://k-theory.org/handbook/.
• Daniel Quillen, (a memorial article), May, 2012, co-edited with Eric Friedlander, to appear in the Notices of the American Mathematical Society.

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.
• Editorial board, The Journal of Software for Algebra and Geometry: Macaulay 2, since 2008.

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, David Eisenbud, Daniel R. Grayson, Michael E. Stillman, 2010-2015, NSF DMS 10-02171 $674667 MSRI, NSF DMS 10-02210 $525333 Cornell.
• Collaborative research: a software system for algebraic geometry research, Daniel R. Grayson, Michael E. Stillman, David Eisenbud, 2008-2010, NSF DMS 08-10909 $142000 Cornell, NSF DMS 08-10948 $139999 UIUC, NSF DMS 08-10918 $18000 Berkeley.
• Collaborative research: a software system for algebraic geometry research, with Michael E. Stillman (Cornell), 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

• 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
• three talks on Higher Algebraic K-theory at Korea Advanced Institute of Science and Technology (KAIST), Department of Mathematical Sciences, June 27-28, 2007.
• a mini-course consisting of 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.
• lecture on Groebner bases and intersection rings of flag bundles, May 26, 2008, at Oxford University.
• lecture on Groebner bases and intersection rings of flag bundles, May 30, 2008, at the Commutative algebra, complexes and applications of computer algebra workshop, during the 2007-2008 Warwick EPSRC Symposium on Algebraic Geometry, at the Warwick Mathematics Institute, on the campus of the University of Warwick.
• a mini-course consisting of six talks on Algebraic K-theory at the International Conference on K-Theory and Homotopy Theory, September 15 - 19, 2008, on the campus of Universidade de Santiago de Compostela in Santiago de Compostela, Spain.
• Macaulay2, at MaGiX@LiX 2011, September 19-23, 2011
• Voevodsky's new foundations for mathematics, Nagoya University, December 6, 2011
• Daniel Quillen and his work on algebraic K-theory, December 12, 2011, at the International Workshop on motives in Tokyo, 2011, University of Tokyo.
• The motivic spectral sequence via acyclic binary complexes, December 13, 2011, at the International Workshop on motives in Tokyo, 2011, University of Tokyo.
• Voevodsky's new foundations for mathematics, Chulalongkorn University, Bangkok, February 29, 2012.
• Computations in intersection theory, 12th ALGA Meeting IMPA, Rio de Janeiro, August 13 - 17, 2012.
• Computations in intersection theory, Rutgers Algebra Seminar Rutger University, New Brunswick, October 17, 2012.
• Algebraic K-theory via binary complexes, Members Seminar (video), Institute for Advanced Study, Princeton, October 22, 2012.
• TS+OCAML+LF Univalent Foundations Seminar, Institute for Advanced Study, Princeton, December 7, 2012.
• State of the New Proof Assistant Univalent Foundations Seminar, Institute for Advanced Study, Princeton, January 17, 2013.

Sports victories

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