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Director, Mathematical Sciences Research Institute

Professor of Mathematics, UC Berkeley

Eisenbud's mathematical interests range widely over commutative and non-commutative algebra, algebraic geometry, topology, and computer methods.

His first paper was about permutation groups, and his thesis and subsequent few papers on non-commutative ring theory (his thesis advisors were Saunders MacLane and, unofficially, the English ring-theorist J.C. Robson.) he turned to commutative algebra, and subsequently to singularity theory, knot theory, and algebraic geometry. Ever since the early 70s he has used computers to produce examples in algebraic geometry and commutative algebra, and he has developed algorithms to extend the power of computation in this area. In recent times he has worked mostly in commutative algebra, algebraic geometry, and computation, but his recent papers include one on a statistical application of algebraic geometry and one on juggling.

Eisenbud is President of the American Mathematical Society (AMS). He is also a Director of Math for America, a foundation devoted to improving mathematics teaching. He has been a member of the Board of Mathematical Sciences and their Applications of the National Research Council, and a member of the US National Committee of the International Mathematical Union.

Resultants and Chow forms via exterior syzygies. (with F.-O. Schreyer and J. Weyman). J. Amer. Math. Soc. {bf 16} (2003), 537--579.

What is the Rees algebra of a module? (with C. Huneke and B. Ulrich). Proc. Amer. Math. Soc. {bf 131} (2003), no.3, 701--708

An Exterior View Of Modules And Sheaves. In {it Advances in Algebra and Geometry, University of Hyderabad Conference 2001}, ed. C. Musili. Hindustan Book Agency (2003) 209--217.

Hyperplane arrangement cohomology and monomials in the exterior algebra (with Sorin Popescu and Sergey Yuzvinsky.) Trans. Amer. Math. Soc. 355 (2003), 4365-4383.

Sheaf cohomology and free resolutions over exterior algebras (with Gunnar FlC8ystad and Frank-Olaf Schreyer). Trans. Amer. Math. Soc. 355 (2003), 4397-4426.

Fitting's Lemma for -graded modules (with Jerzy Weyman). Trans. Amer. Math. Soc. 355 (2003), 4451-4473.

Books

Hodge Algebras, (with C.DeConcini and C.Procesi), Asterisque 91, Société Mathématique de France, Paris (1982).

Three dimensional Link Theory and Invariants of Plane Curve Singularities, (with W.Neumann), Annals of Math.Studies 110, Princeton University Press Princeton NJ (1985).

Schemes: The Language of Modern Algebraic Geometry, (with J.Harris). Wadsworth, Belmont, California, 1992.

Proceedings of the Sundance Conference on Free resolutions in Commutative Algebra and Algebraic Geometry 1990, (editor, with C.Huneke) A.K. Peters, Boston Massachusetts, 1992.

Computational Algebraic Geometry and Commutative Algebra, Cortona 1991, (ed. D.Eisenbud and L.Robbiano) Symposia Mathematica XXXVI, Cambridge University Press, Cambridge, England, 1993.

Commutative Algebra With A View Toward Algebraic Geometry, Graduate Texts in Mathematics 150, Springer-Verlag, 1995.

Commutative Algebra, Algebraic Geometry, and Computational Methods, (editor) Springer-Verlag, 1999.

The Geometry of Schemes, (with J.Harris). Graduate Texts in Mathematics 197, Springer-Verlag, 1999.

Computations in Algebraic Geometry with Macaulay 2, (with Daniel R.Grayson, Michael Stillman, and Bernd Sturmfels (Eds.)). Algorithms and Computation in Mathematics. Springer-Verlag, 2002.

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