# David Bayer

## Professor of Mathematics

## Chair of the Department of Mathematics

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.

**Selected Publications**

“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

212-854-2643

bayer@math.columbia.edu

BA, Swarthmore College

PhD, Harvard University