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

• Fellow, Centre for Advanced Study at the Norwegian Academy of Science and Letters, October, November, 2018 and February, March, 2019, to participate in the special year on Homotopy Type Theory and Univalent Foundations, 2018-19.
• Visitor, School of Mathematics, Institute for Advanced Study, Spring, 2018, to work on Univalent Foundations of Mathematics.
• Visitor, School of Mathematics, Institute for Advanced Study, Spring, 2017, to work on Univalent Foundations of Mathematics.
• Visitor, School of Mathematics, Institute for Advanced Study, Fall, 2015, to work on Univalent Foundations of Mathematics.
• 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.

Online bibliographic resources

• See my papers on MathSciNet (behind a pay wall).
• See my papers on Zentralblatt.
• See my google scholar profile.

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.
  • See The K-theory of endomorphisms of spaces, by Filipp Levikov, 1511.08376, for a generalization.
• → 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, mr zb
• → Projections, cycles, and algebraic K-theory, Mathematische Annalen, volume 234, 1978, pages 69-72, pdf mr zb
• → Algebraic cycles and algebraic K-theory, Journal of Algebra, volume 61, 1979, pages 129-151, [pdf], 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, [pdf], 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 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 ], 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].
  • → 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].
  • See also An un-delooped version of algebraic K-theory, by T. Gunnarsson, R. Schwänzl, R. M. Vogt, and F. Waldhausen. They generalize this to the non-additive situation.
• → 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
  • See also Operations in A-theory, by Thomas Gunnarsson and Roland Schwänzl. They generalize this to the non-additive situation.
• → 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.
  • See also The Equivalence of Grayson and Friedlander-Suslin 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 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.
• → 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, pdf, [preprint].
  • See also Algebraic proofs of some fundamental theorems in algebraic K-theory by Tom Harris; it builds on the paper above to give elementary proofs of some basic theorems in K-theory.
  • See also An algebraic description of the algebraic K-theory groups by Bruno Stonek; it provides an expanded exposition of the arguments in the paper above.
  • See also Shortening binary complexes and commutativity of K-theory with infinite products by Daniel Kasprowski and Christoph Winges; it provides a proof of a much improved version of the "shortening" of binary complexes that I claimed in the paper.
  • See also Algebraic K-theory of stable infinity-categories via binary complexes by Daniel Kasprowski and Christoph Winges; it extends my basic construction to the context of stable infinity-categories.
  • See also K₁-groups via binary complexes of fixed length, by Daniel Kasprowski, Bernhard Köck, and Christoph Winges.
  • See also Two Formulae for Exterior power operations on higher K-groups, by Tom Harris and Bernhard Köck.
  • See also Exterior power operations on higher K-groups via binary complexes, by Tom Harris, Bernhard Köck and Lenny Taelman.
• → with Alexandra Seceleanu and Michael E. Stillman, Computations in intersection rings of flag bundles, arXiv:1205.4190, preprint, May, 2012.
• → Relative algebraic K-theory by elementary means, arXiv:1310.8644, preprint, October, 2013.
• → with Dinakar Ramakrishnan, Eisenstein series of weight one, q-averages of the 0-logarithm and periods of elliptic curves, arXiv:1806.04925, in book: Amir Akbary and Sanoli Gun (Editors); Geometry, Algebra, Number Theory, and Their Information Technology Applications; Toronto, Canada, June, 2016, and Kozhikode, India, August, 2016; Springer Proceedings in Mathematics & Statistics Series, volume 251, 2018.
• → with Marc Bezem, Ulrik Buchholtz, and Michael Shulman, Construction of the Circle in UniMath, arXiv:1910.01856, preprint, October, 2019; accepted for publication in the Journal of Pure and Applied Algebra.

Books

• → with the Univalent Foundations Program, Homotopy Type Theory, published by the Univalent Foundations Program, June, 2013; 603 pages.

Mathematical software

• → 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.
• → 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.

Videos

• Oct 22, 2012: Algebraic K-Theory Via Binary Complexes
• Dec 7, 2012: LF + OCAML + TS
• Jan 17, 2013: State of the New Proof Assistant
• Sep 11, 2018: The mathematical work of Vladimir Voevodsky, Vladimir Voevodsky Memorial Conference.

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, Volume 11 / Issue 03 / June 2013 (The Legacy of Daniel Quillen), pp 527-547, published online: 11 March 2013; available on CJO2013 at doi:10.1017/is012011011jkt203 and freely here (copyright 2013 Independent Scholarly Online and Print Publishing).
• → Vladimir Voevodsky (1966-2017), obituary, Nature, 9 November 2017, Vol. 551, p. 169, online: https://www.nature.com/articles/d41586-017-05477-9, pdf file: https://rdcu.be/bQcbb, doi: 10.1038/d41586-017-05477-9.
• → An introduction to univalent foundations for mathematicians, Bulletin of the American Mathematical Society, published online March 5, 2018, arXiv:1711.01477, preprint, November, 2017, Volume 55, Number 4, October 2018, Pages 427–450, doi, pdf.
• → In Memoriam: Vladimir Voevodsky 1966-2017, Bulletin of Symbolic Logic, Volume 24, Issue 2, June, 2018, pp. 186-191. Published online: 07 August 2018.

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, co-edited with Eric Friedlander, Notices of the American Mathematical Society, Volume 59, 2012, Number 10, pages 1392-1406.

Honors

• Prokasy Award for Excellence in Undergraduate Teaching, College of LAS, 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.
• 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 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, 2002 - 2013.
• 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.

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, Professor, 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, Acting Chair (2013-2014), Chair (2014-present), Department of Mathematics, University of Massachusetts Dartmouth.

Student tributes

• Morgan Polikoff

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, 2015-2020, NSF DMS 15-02209 $424328 MSRI, NSF DMS 15-02294 $475671 Cornell.
• 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 and conferences

• Colloquium, March 11, 2020, Mathematics Department, University of Sheffield.
• An introduction to formalization of proofs in UniMath, March 28, 2019, Algebra and algebraic geometry seminar, Mathematics Department, University of Oslo
• Homotopy Type Theory and Univalent Foundations, November 30, 2018, colloquium, Mathematics Department, University of Oslo; slides
• Lumsdaine's proof of transfinite recursion, October 9, 2018, Homotopy Type Theory and Univalent Foundations, Center for Advanced Study, Norwegian Academy of Science and Letters, Oslo.
• The mathematical work of Vladimir Voevodsky, September 11, 2018, Vladimir Voevodsky Memorial Conference, in Princeton, slides, video.
• Some projects I'd like to work on, August 27, 2018, CAS project kick-off: 'Homotopy Type Theory and Univalent Foundations', Center for Advanced Study, Norwegian Academy of Science and Letters, Oslo.
• Formalization of Mathematics in Type Theory, August 19 - 24 , 2018, Dagstuhl Seminar, Germany, notes for my 30 minute talk.
• Voevodsky's work on formalization of proofs and the foundations of mathematics, July 10, 2018, ITP FLoC 2018, among the invited speakers.
• Macaulay2 Workshop 2018, June 4 - 8, 2018, Max Planck Institute for Mathematics in the Sciences, Leipzig, Germany, organized by Heather Harrington, Eliana Duarte Gelvez, and Thomas Kahle.
• Macaulay2 Workshop, at the University of Wisconsin in Madison, organized by Juliette Bruce, Daniel Erman, Steven Sam, and Jay Yang, April 14-17, 2018.
• Applied Macaulay2 tutorials at Georgia Tech, organized by Thomas Kahle and Anton Leykin, July 27-29, 2017.
• Macaulay2 workshop Warwick, UK, organized by Thomas Kahle and Diane Maclagan, May 23 - 26, 2016.
• support for a Macaulay2 workshop in Salt Lake City, Utah, organized by Adam Boocher, Karl Schwede, and Amelia Taylor, May 7 - 10, 2016.
• The UniMath project, a talk at the Workshop on Homotopy Type Theory, Feb 10-14, 2016, at the Max Planck Institute for Mathematics, Bonn, Germany.
• Minicourse on Unimath, three lectures, at Computational Aspects of Univalence, a workshop in Bergen, Jan 20-22, 2016.
• Homotopy Type Theory and Univalent Foundations, Colloquium, Math Department, Boise State University, May 28, 2015.
• support for a Macaulay2 workshop in Boise, Idaho, organized by Zach Teitler, Hirotachi Abo, and Frank Moore, May 27 - 30, 2015.
• Homotopy Type Theory and Univalent Foundations, March 30, 2015, in the topology seminar, University of Western Ontario, Department of Mathematics.
• Homotopy Type Theory and Univalent Foundations, February 10, 2015, in the topology seminar, University of Chicago, Department of Mathematics.
• support for a workshop on Symbolic and Numerical Methods for Tensors and Representation Theory, at the Simons Institute for the Theory of Computing.
• support for the 2014 Macaulay2 School and Research Meeting, organized by Sonja Mapes and Hal Schenck, at University of Illinois Urbana-Champaign, June 16-20, 2014.
• Computers and Mathematical Proofs, at the Las Vegas Ruby Users Group meeting, June 4, 2014, video.
• Formalization of elementary algebraic K-theory 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.
• support for a Macaulay2 workshop, organized by Sonja Mapes, Frank Moore, and David Swinarski, at the University of California, Berkeley, in Berkeley, California, January 6 - 10, 2014.
• An elementary approach to long exact sequences in algebraic K-theory, 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 K-theory and Motivic Cohomology, June 28, 2013.
• Homotopy type theory as a new foundation for mathematics, Colloquium, Mathematics Department, University of Osnabrück, June 12, 2013.
• support a Macaulay2 Day was held at MSRI February 7, 2013, organized by Eisenbud, Stillman, and Grayson. Here is the resulting wiki.
• 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 K-theory 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, Department of Mathematics and Computer Science, 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 K-theory, 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 19-23, 2011
• 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.
• 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.
• lecture on Groebner bases and intersection rings of flag bundles, May 26, 2008, at Oxford University.
• 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.
• 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, Software for Algebraic Geometry, IMA, October 23-27, 2006
• Macaulay2, a software system for algebraic geometry, Second International Congress on Mathematical Software (ICMS2006), September 1-3, 2006, Castro Urdiales, Spain.

Sports victories

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

Links

• validate this page