David Eisenbud

Background

I enjoyed my work at MSRI greatly for 10 years, and retired from it, to go back to full-time teaching and research, on August 1, 2007. I had the satisfaction of supporting a huge amount of mathematics and related activity at the Institute, and in helping it develop two things I thought it needed badly: a physical facility worthy of such a world-class institution, and (the beginning of) an endowment. From 2003 to 2005 I was also President of the American Mathematical Society, an organization I came to admire a great deal.

Some Artifacts From My Years as Director (under construction)

• Interview when I became Director
• MSRI's Twentieth Anniversary.
• Nomination for President of the AMS, by Barry Mazur and Margaret Wright
• Interview after I was elected
• AMS/MSRI Congressional Luncheon
• Congressional Testimony
• Opinion Piece about Washington's lack of attention to Science
• Reflections on my Presidency
• Eisenbud Professorship created by Jim Simons at MSRI.

Interests and Current Activities

My first paper was about permutation groups, and my thesis and subsequent few papers on non-commutative ring theory (my thesis advisors were Saunders MacLane and, unofficially, the English ring-theorist J.C. Robson.) I turned to commutative algebra, and subsequently to singularity theory, knot theory, and algebraic geometry. My papers also include one on a statistical application of algebraic geometry and one on juggling. Recently I've worked mostly in commutative algebra, algebraic geometry and computational aspects of these fields.

Ever since the early 70s I've used computers to produce examples in algebraic geometry and commutative algebra, and I've developed algorithms to extend the power of computation in this area. I recently joined Mike Stillman and Dan Grayson in the project to (further) develop the Macaulay2 system for symbolic computation.

My interests outside mathematics include hiking, juggling, and, above all, music. Originally a flutist, I now spend most of my musical time singing art-songs (Schubert, Schumann, Brahms, Debussy, ...) I broke down and bought a digital camera in November 2001, and you can find some of the results on my photo page. Some pictures of the New Hampshire fall colors from October 9-11, 2004.
are more recent examples.

From my CV

• Biography
• Students and Postdocs
• Students (listing at the Mathematical Genealogy Project)
• Books (in particular, one on Macaulay 2 that I helped write and edit is available online )
• Electronic copies of my papers
• My mathematical genealogy (from the Mathematical Genealogy Project) )

Saunders Mac Lane: In Memoriam

Current Events Bulletin at the Winter AMS Meeting

Some Ongoing Work

Boij and Soederberg made some marvelously bold conjectures on the ``shape'' of free resolutions, which Frank Schreyer and I have proven. These things are closely related to the work on resolutions over exterior algebras that has interested us for years. There's lots more to do! Here is the preprint .


• The fibers of a generic projection of a curve into P^2 have length at most 2, and the fibers of a generic projection of a surface into P^3 have length at most 3. I always wondered whether the lengths of fibers of a projections of a smooth complex projective variety of dimension n into P^(n+1) would have length at most n+1. Many people proved special cases of this; for example, Mather has shown that it is true at least up to n=14, and that in general there are at most n+1 distinct points in any fiber. However, Lazarsfeld showed that it fails for large n: the length of the worst fibers can be exponential in the square root of n ! In recent work, Beheshti, Harris Huneke and I have noticed some further positive results. Conjecture: the Castelnuovo-Mumford regularity of any fiber is bounded by n+1.
  
  
• Having finished "The Geometry of Schemes", Joe Harris and I have been thinking about a new book. Intended as an advanced course, introducing a number of topics such as Hodge Theory, Deformation Theory, and Intersection Theory that are fundamental tools of the trade but don't make it into the basic texts. So far all that exists is an outline and some dreams...
  
  
• With Jeremy Gray I'm working on a biographical paper about the life and work of F.S. Macaulay. Though his work contains aspects that look quite various, I think there's a very strong underlying thread that can be traced from the early work on plane curves right through his invention (in the graded case) of the notion of what we now call a Gorentstein ring.

Commutative Algebra Book

Addresses

Links