Curriculum Vitae
Birthdate
Mathematics Education
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 UrbanaChampaign,
from July 1, 2007.
 Chair, Department of Mathematics,
University of Illinois at UrbanaChampaign,
July 16, 2004, to March 27, 2006.
 Professor,
Department of Mathematics,
University of Illinois at UrbanaChampaign,
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 UrbanaChampaign,
19841988.
 Assistant Professor,
Department of Mathematics,
University of Illinois at UrbanaChampaign,
19811984.
 Member,
School of Mathematics,
Institute for Advanced Study,
19811982.
 Acting Chairman,
Mathematics Department,
Barnard College,
19801981.
 Ritt Assistant Professor,
Department of Mathematics,
Columbia University,
19761981.
 Mathematical Assistant,
Fakultät für Mathematik,
Universität Bielefeld,
summer 1976.
Online bibliographic resources
Research articles
 → The Ktheory of hereditary categories,
Journal of Pure and Applied Algebra, volume 11, 1977, pages 6774,
mr
zb
 → The Ktheory of endomorphisms,
Journal of Algebra, volume 48, 1977, pages 439446,
mr
zb
 → Grothendieck rings and Witt vectors,
Communications in Algebra, volume 6, 1978, pages 249255,
[pdf, tif],
mr
zb
 → K_{2} and the Ktheory of automorphisms,
Journal of Algebra, volume 58, 1979, pages 1230,
mr
zb
 → Products in Ktheory and intersecting algebraic cycles,
Inventiones Mathematicae, volume 47, 1978, pages 7183,
gdz,
mr
zb
 → Projections, cycles, and algebraic Ktheory,
Mathematische Annalen, volume 234, 1978, pages 6972,
gdz,
mr
zb
 → Algebraic cycles and algebraic Ktheory,
Journal of Algebra, volume 61, 1979, pages 129151,
[pdf],
mr
zb
 → Localization for flat modules in algebraic Ktheory,
Journal of Algebra, volume 61, 1979, pages 463496,
[pdf],
mr
zb
 → Coincidence formulas in enumerative geometry,
Communications in Algebra, volume 7, 1979, pages 16851711,
mr
zb
 → Ktheory and localization for noncommutative rings,
Journal of Pure and Applied Algebra, volume 18, 1980, pages 125127,
[pdf, tif],
mr
zb
 → SK_{1} of an interesting principal ideal domain,
Journal of Pure and Applied Algebra, volume 20, 1981, pages 157163,
mr
zb
Manin refers to it in arXiv:0809.1564.
 → Dilogarithm computations for K_{3},
Algebraic Ktheory, Evanston 1980,
Lecture Notes in Mathematics 854, pages 168178,
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 412436,
mr
zb
 → The Ktheory of semilinear endomorphisms,
[ocr.djvu],
Journal of Algebra, volume 113, 1988, pages 358372,
mr
zb
 → by Spencer Bloch and Daniel R. Grayson,
K_{2} and Lfunctions of elliptic curves: computer calculations,
[pdf ocr.djvu],
Applications of Algebraic Ktheory 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 600634,
mr
zb.
 → Universal exactness in algebraic Ktheory,
Journal of Pure and Applied Algebra, volume 36, 1985, pages 139141,
mr
zb
 → Reduction theory using semistability: II,
[pdf
ocr.djvu
gdz],
Commentarii Mathematicae Helvetici, volume 61, 1986, pages 661676,
mr
zb
 → by Henri Gillet
and Daniel R. Grayson,
The loop space of the Qconstruction,
Illinois Journal of Mathematics, 31 (1987) 574597,
[pdf
mr
zb].
 → Exact sequences in algebraic Ktheory,
[ocr.djvu],
Illinois Journal of Mathematics, volume 31, 1987, pages 598617,
mr
zb
 → The arithogeometric mean,
[ocr.djvu],
Archiv der Mathematik, volume 52, 1989, pages 507512,
mr
zb
 → Exterior power operations on algebraic Ktheory,
[doi 10.1007/BF00533371
dvi
pdf
ps],
Ktheory, volume 3, 1989, pages 247260,
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 573575,
mr
 → by James Glazebrook, Daniel R. Grayson, and Paul Hewitt,
Galois representations on holomorphic differentials,
Communications in Algebra, volume 19, 1991, pages 13751386,
mr
zb.

See also the
addendum, Communications in
Algebra, volume 20, 1992, page 2791, reviewed in
zb.
 → Adams operations on higher Ktheory,
[doi 10.1007/BF01771009
pdf
preprint],
Ktheory, volume 6, 1992, pages 97111,
mr
zb.
 → Weight filtrations via commuting automorphisms,
Ktheory, volume 9, 1995, pages 139172,
[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., 218253;
translation in Proc. Steklov Inst. Math. 2003, no. 2 (241), 202237;
it does what I couldn't do to complete the story, at least over a field.
 See also Kmotives of algebraic varieties, by Grigory Garkusha and Ivan Panin,
arXiv:1108.0375. They
use my result to produce a motivic spectral sequence connecting bivariant
Ktheory 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.
 See also The Equivalence of Grayson and FriedlanderSuslin Spectral Sequences,
by Oleg Podkopaev,
arXiv:1309.7597. He shows
that my spectral sequence agrees with the one coming from the work of Friedlander and Suslin,
thereby removing the dependence of that work on the preprint of Bloch and Lichtenbaum,
which had a gap in the proof.
 → 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 2430, 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 707719,
mr
zb.
 → with Mark Walker,
Geometric Models for Algebraic Ktheory,
[doi 10.1023/A:1026506218989
preprint
mr
zb],
Ktheory, volume 20, issue 4, August 2000, pages 311330.
 → 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 3540422307, Springer, Berlin, Heidelberg, New York, pages 131178, 2001.
 → with Kevin Charles Jones, Youngsoo Kim, Andrea H. Mhoon, Rekha Santhanam, and Barry J. Walker,
The additivity theorem in Ktheory,
[doi 10.1023/B:KTHE.0000037546.39459.cb
preprint],
Ktheory 32 (2): 181191, June 2004.
 → with Henri Gillet,
Volumes of symmetric spaces via lattice points,
[preprint],
Documenta Mathematica
11 (2006) 425447,
[mr
zb].
 → by Lara B. Anderson, James Gray,
Dan Grayson, YangHui He, and Andre Lukas,
Yukawa Couplings in Heterotic Compactification;
arXiv:0904.2186;
Commun. Math. Phys. 297:95127, 2010,
[doi 10.1007/s0022001010338,
mr 2011e:81203]
 → The additivity theorem in algebraic Ktheory,
Documenta Mathematica 16 (2011) 457464,
pdf,
preprint, January, 2011.
 → Algebraic Ktheory via binary complexes, posted: June 14, 2012,
Journal of the American Mathematical Society, 25 (2012) 11491167,
http://dx.doi.org/10.1090/S089403472012007437,
PII: S 08940347(2012)007437,
pdf,
[preprint].
 → with Alexandra Seceleanu
and
Michael E. Stillman,
Computations in intersection rings of flag bundles,
arXiv:1205.4190, preprint, May, 2012.
 → Relative algebraic Ktheory by elementary means,
arXiv:1310.8644, preprint, October, 2013.
Books
 → with the Univalent Foundations Program,
Homotopy Type Theory,
published by the Univalent Foundations Program, June, 2013; 603 pages.
Former Doctoral Students
 Youngsoo Kim,
Ph.D. 2010, Assistant Professor (2010present),
Department of Mathematics,
Tuskegee University.
 Joshua P. Mullet, Ph.D. 2006, Ross Assistant Professor (20062009),
Department of Mathematics,
The Ohio State University.
 Sung Myung,
Ph.D. 2002;
Research Fellow (20042006), Korea Institute for Advanced Study;
tenure track position (20062013) and Associate Professor (2013*), Department of Mathematics Education,
Inha University, Incheon, South Korea.
 Mark Walker,
Ph.D. 1996, Professor,
Department of Mathematics,
University of NebraskaLincoln.
 Judy Holdener,
Ph.D. 1994,
Professor,
Department of Mathematics, Kenyon College.
 Randy McCarthy,
Ph.D. 1990, Professor,
Department of Mathematics,
University of Illinois at UrbanaChampaign at UrbanaChampaign.
 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; see also the manual front matter, 1988.
Expository works
 → Higher algebraic Ktheory II [after Daniel Quillen],
[ocr.djvu],
Algebraic Ktheory, Evanston 1976,
Springer, Berlin, Heidelberg, New York,
Lecture Notes in Mathematics, volume 551, 1976, pages 217240,
mr
zb
 → Finite Generation of higher Kgroups of a curve over a finite field [after Daniel Quillen],
[ocr.djvu],
Algebraic Ktheory, Oberwolfach 1980, Part I,
Lecture Notes in Mathematics 966, Springer, Berlin, Heidelberg, New York, 1982, pages 6990,
mr
zb
 → On the Ktheory of fields,
[ocr.djvu],
Proceedings of a Conference on Ktheory and Geometry,
Contemporary Mathematics, volume 83, 1989, pages 3155,
mr
zb
 → Weight filtrations in algebraic Ktheory,
Proceedings of Symposia in Pure Mathematics:
Motives, Proceedings of the Summer Research Conference
on Motives in Seattle, 1991, volume 55, part 1, 1994, pages 207238,
mr
zb,
[pdf pdfscan].
 → 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 Ktheory, ISBN10 354023019X, ISBN13 9783540230199,
Springer, Berlin, Heidelberg, New York, 1163+xiv pages, 2005, in volume 1, pages 3969.
 → A Brief Introduction to Algebraic Ktheory,
[dvi
pdf
zb],
preprint, January, 2008; revised September, 2008;
published in
Cohomology of Groups and Algebraic Ktheory,
Advanced Lectures in Mathematics (ALM) 12;
edited by Lizhen Ji 季理真, Kefeng Liu 刘克峰, and ShingTung Yau 丘成桐;
Higher Education Press
and
International Press; 2009; pages 167186.
 → Quillen's work in algebraic Ktheory,
[preprint, December, 2011:
dvi
pdf],
Journal of Ktheory: Ktheory and its Applications to Algebra, Geometry, and Topology,
Volume 11 / Issue 03 / June 2013 (The Legacy of Daniel Quillen),
pp 527547, published online: 11 March 2013;
available on CJO2013 at
doi:10.1017/is012011011jkt203
and freely 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 3540422307,
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 Ktheory, in two volumes, ISBN10 354023019X, ISBN13 9783540230199,
Springer, Berlin, Heidelberg, New York,
1163+xxiv pages,
2005; online version available at
http://ktheory.org/handbook/.
 → Daniel Quillen, (a memorial article), May, 2012,
coedited with Eric Friedlander,
to appear in the Notices of the American Mathematical Society.
Honors
 Prokasy Award for Excellence in Undergraduate Teaching, College of LAS, Spring, 1990.
 Beckman Associate in the Center for Advanced Study, University of
Illinois, 19871988.
 University Scholar, University of Illinois at UrbanaChampaign, 19851988.
 Placed on the list of teachers rated excellent by their students for the
following courses (an asterisk signifies that the instructor ratings were
outstanding):
 Math 416,
Topics in Algebra, Algebraic Ktheory, 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
Conferences organized
 Tenth annual Great Lakes Ktheory Conference at UIUC, May 89, 2004, with Randy McCarthy.
 Algebraic KTheory at Oberwolfach, August 410, 2002, with Bruno Kahn and Uwe Jannsen.
 Learning Stacks and Computational Methods through ProblemSolving, at Urbana, June 1215,
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 Ktheory Conference, April 27, 2002, with Randy McCarthy.
 Algebraic Ktheory, at Oberwolfach, held September 26  October 2,
1999, with Uwe Jannsen (Cologne) and Bruno Kahn (Paris).
 Workshop on Parallel Symbolic Computation, October 13, 1998,
with David Bailey, Alyson Reeves, and Nobuki Takayama.
 Fifth annual Great Lakes Ktheory Conference, at UIUC, March 2021, 1999,
with Randy McCarthy (organized as a special session of the AMS meeting).
 Motives and Algebraic Ktheory, special session/symposium
at the AMS meeting in Milwaukee, October 2425, 1997.
 A topology conference at UIUC, the Midwest Topology Seminar, September 27, 1997, with Randy McCarthy.
 Algebraic Ktheory, at Oberwolfach June 1014, 1996, with Andrei Suslin and Ulf Rehmann.
 First annual Great Lakes Ktheory Conference, March 45, 1995, Urbana.
University Service
 Promotion and Tenure Committee of the Department of Mathematics, 20012003; chair, 20012002.
 Executive Committee of the Department of Mathematics, 19992000.
 Executive Committee of the College of Liberal Arts and Sciences, 19961998.
 Promotion and Tenure Committee of the University of Illinois at UrbanaChampaign, 19941995.
 Executive Committee of the College of Liberal Arts and Sciences, 19921994.
 Promotion and Tenure Committee of the Department of Mathematics, 19911993.
 Area Committee II, LAS Resource Allocation Review, Fall 1992.
 Executive Committee of the Department of Mathematics, 19891991.
 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, 20102015,
NSF DMS 1002171 $674667 MSRI,
NSF DMS 1002210 $525333 Cornell.
 Collaborative research: a software system for algebraic geometry research,
Daniel R. Grayson, Michael E. Stillman, David Eisenbud, 20082010,
NSF DMS 0810909 $142000 Cornell,
NSF DMS 0810948 $139999 UIUC,
NSF DMS 0810918 $18000 Berkeley.
 Collaborative research: a software system for algebraic geometry research,
with Michael E. Stillman (Cornell),
NSF DMS 0311806 (Cornell)
and NSF DMS 0311378 (UIUC),
20032008, $589010 (Cornell) and $251345 (UIUC).
 Support for Ktheory Conferences; 20032006,
(with Eric Friedlander),
NSF DMS 0303519,
20032006, $31,000.
 Algebraic Geometry Workshop, June 1215, 2002, Urbana, Illinois,
(with Sheldon Katz),
NSF DMS 0200459,
20022003, $15,000.
 A software system for algebraic geometry research,
NSF DMS 9970085,
19992002, $159,359, extended to 2003.
See also the simultaneous award
NSF DMS 9970348
to Michael Stillman.
 as faculty associate, with Principal Investigator
Robert Haber;
Coprincipal investigators:
John Sullivan
and
David Padua;
other associates:
Jonathan Dantzig,
Herbert Edelsbrunner,
Michael Heath,
Robert Jerrard,
Sanjay Kale,
ShangHua 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 9873945,
October 1, 1998 to September 30, 2001, $2,198,851.
 A software system for algebraic geometry research,
NSF DMS 9622608,
19961999, $132,018.
See also the simultaneous award
NSF DMS 9623232
to Michael Stillman.
 A software system for algebraic geometry research,
NSF DMS 9210807,
19931996, $230,000.
See also the simultaneous award
NSF DMS 9210805
to Michael Stillman.
 Algebraic Ktheory,
NSF DMS 9002715,
19901993, $82,250.
 Algebraic Ktheory,
NSF DMS 8806785,
19881990, $37,800.
 Algebraic Ktheory,
NSF DMS 8601980,
19861988, $32,070.
 Equipment grant (with Evans, Fossum, and Moreno), 198688,
NSF DMS 8504692 SCREMS,
$23,500.
 Algebraic Ktheory,
NSF DMS 8202692,
198286, $51,475.
 NSF grants at Columbia with Hyman Bass, 19761982.
Upcoming and recent talks
 March 30, 2015, in the topology seminar, University of Western Ontario, Department of Mathematics.
 February 10, 2015, in the topology seminar, University of Chicago, Department of Mathematics.
 Macaulay 2 Tutorial II, November 17th, 2014, at the workshop on Symbolic and Numerical Methods for Tensors and Representation Theory, at the Simons Institute for the Theory of Computing.
 Computers and Mathematical Proofs, at the Las Vegas Ruby Users Group meeting, June 4, 2014, video.
 Formalization of elementary algebraic Ktheory in Coq with Univalent Foundations, May 7, 2014, at the workshop on Formalization of mathematics in proof assistants, occuring during the trimester Semantics of proofs and certified mathematics, at Institut Henri Poincaré.
 Homotopy Type Theory and Univalent Foundations, Algebra Seminar, Mathematics Department, University of Pennsylvania, February 24, 2014.
 Homotopy Type Theory and Univalent Foundations, Graduate School of Mathematics, Nagoya University, February 18, 2014.
 An elementary approach to long exact sequences in algebraic Ktheory, International Workshop on motives in Tokyo, 2013, Graduate School of Mathematics, University of Tokyo, November 29, 2013.
 Proof assistant design, Centre de Recerca Matemàtica, Conference on Type Theory, Homotopy Theory and Univalent Foundations, September 26, 2013.
 Homotopy type theory, Mathematisches Forschungsinstitut Oberwolfach, Workshop on Algebraic Ktheory and Motivic Cohomology, June 28, 2013.
 Homotopy type theory as a new foundation for mathematics, Colloquium, Mathematics Department, University of Osnabrück, June 12, 2013.
 State of the New Proof Assistant, Univalent Foundations Seminar, Institute for Advanced Study, Princeton, January 17, 2013.
 TS+OCAML+LF, Univalent Foundations Seminar, Institute for Advanced Study, Princeton, December 7, 2012.
 Algebraic Ktheory via binary complexes, Members Seminar (video), Institute for Advanced Study, Princeton, October 22, 2012.
 Computations in intersection theory, Rutgers Algebra Seminar Rutger University, New Brunswick, October 17, 2012.
 Computations in intersection theory, 12th ALGA Meeting IMPA, Rio de Janeiro, August 13  17, 2012.
 Voevodsky's new foundations for mathematics, Chulalongkorn University, Bangkok, February 29, 2012.
 The motivic spectral sequence via acyclic binary complexes, December 13, 2011, at the International Workshop on motives in Tokyo, 2011, University of Tokyo.
 Daniel Quillen and his work on algebraic Ktheory, December 12, 2011, at the International Workshop on motives in Tokyo, 2011, University of Tokyo.
 Voevodsky's new foundations for mathematics, Nagoya University, December 6, 2011
 Macaulay2, at MaGiX@LiX 2011, September 1923, 2011
 a minicourse consisting of six talks on Algebraic Ktheory at the International Conference on KTheory and Homotopy Theory, September 15  19, 2008, on the campus of Universidade de Santiago de Compostela in Santiago de Compostela, Spain.
 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 20072008 Warwick EPSRC Symposium on Algebraic Geometry, at the Warwick Mathematics Institute, on the campus of the University of Warwick.
 lecture on Groebner bases and intersection rings of flag bundles, May 26, 2008, at Oxford University.
 a minicourse consisting of six talks on Higher Algebraic Ktheory at the summer school on Cohomology of groups and algebraic Ktheory at the Center of Mathematical Sciences on the campus of Zhejiang University in Hangzhou, China, July 212, 2007.
 three talks on Higher Algebraic Ktheory at Korea Advanced Institute of Science and Technology (KAIST), Department of Mathematical Sciences, June 2728, 2007.
 Macaulay 2, a software system for algebraic geometry, Software for Algebraic Geometry, IMA, October 2327, 2006
 Macaulay 2, a software system for algebraic geometry, Second International Congress on Mathematical Software (ICMS2006), September 13, 2006
Sports victories