David Bayer

David Bayer

Professor of Mathematics




426 Mathematics Building on Columbia campus


David Bayer, Professor of Mathematics and Chair of the Department of Mathematics, began teaching at Barnard in 1987, and became a full-time faculty member in 1990. His teaching specialties include linear algebra, modern algebra, and combinatorics.

Professor Bayer served as mathematics consultant, hand double, and day player in A Beautiful Mind, the 2001 feature film based on the life of Nobel laureate John Forbes Nash, Jr.

Professor Bayer is the coauthor (with Mike Stillman) of Macaulay, a computer algebra system for computations in algebraic geometry and commutative algebra. This software uses Grobner basis methods for manipulating systems of polynomial equations.

Professor Bayer holds a U.S. Patent (with N. Karmarkar and J. Lagarias) for a method and apparatus for optimizing system operational parameters.

  • BA, Swarthmore College
  • PhD, Harvard University

“Syzygies of Lawrence Unimodular Ideals,” with S. Popescu and B. Sturmfels,Journal für die reine und angewandte Mathematik Vol. 534 (2001): 169–186.

“Extremal Betti Numbers and Applications to Monomial Ideals,” with H. Charalambous and S. Popescu, Journal of Algebra Vol. 221, No. 2, (1999): 497–512.

Cellular resolutions of monomial modules, with B. Sturmfels, Journal für die reine und angewandte Mathematik Vol. 502 (1998): 123–140.

“Monomial Resolutions,” with I. Peeva and B. Sturmfels, Mathematical Research Letters Vol. 5, No. 1-2, (1998): 31–46.

“Trailing the Dovetail Shuffle to Its Lair,” with P. Diaconis, Annals of Applied Probability Vol. 2, No. 2, (1992): 294–313.

“Karmarkar's Linear Programming Algorithm and Newton's Method,” with J. Lagarias, Math. Programming Vol. 50, No. 3, (Ser. A), (1991): 291–330.

“A Criterion for Detecting m-Regularity,” with M. Stillman, Inventiones Mathematicae Vol. 87, No. 1, (1987): 1–11.

  • Combinatorial commutative algebra
  • Algebraic geometry
  • Computer algebra

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