David Eisenbud

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  Research Interests

  My first paper was about permutation groups, and my thesis and subsequent few papers was 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 on the homological aspects of commutative algebra and algebraic geometry; and on computational tools for 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. In 2009 I joined Mike Stillman and Dan Grayson as Co-PI on the grant to (further) develop the Macaulay2 system for symbolic computation. Some of the papers I'm proudest of were partly inspired by computations with that system.

  Here are some of my current mathematical projects:
  

• With Marc Chardin, Craig Huneke, and Bernd Ulrich I've done some work on residual intersections. The most recent work is related to residual intersections in the first serious case beyond the ones satisfying the ``Artin-Nagata'' conditions that guarantee the Cohen-Macaulay property for residual intersections: the ideals of 2 x 2 minors of generic 2 x n matrices.
  
  
• Jeremy Gray and I wrote a biographical paper (for mathematicians) on the life and work of F. S. Macaulay, which was published in the Bulletin of the AMS. As of Summer 2024 we have nearly finished a book-length treatment, aimed at historians. Though his work contains aspects that look quite various, I think there's an 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. We have also written a book-length treatment, aimed more at historians of mathematics. It is currently under revision.
  
  
• With Hai Long Dao, Claudia Polini and Bernd Ulrich I've been working on infinite free resolutions. Most of the work on this over the past 40 years has focussed on the numerical growth of the free modules in the resolution; we are instead looking for regularities (or peculiarities) in the maps.

CV, Books, Papers, Students

• CV
• Students (listing at the Mathematical Genealogy Project)
• Electronic copies of some of my papers; others are at the arXiv

• Books

  My book, "Commutative Algebra with a View Toward Algebraic Geometry", published in 1995 by Springer-Verlag, won the AMS's Leroy P. Steele Prize for Exposition in 2010.

  Here are some correction lists:

  • Inserted in the second (1996) printing ( TeX source, pdf)
  • Inserted in the third (1999) printing (TeX source, pdf). Note that the page numbers changed a little between the first and second printings.
  The pages above are now rather out-of-date; this is a project I'll get to sooner or later. But if you are aware of further corrections or have any comments, I hope you'll send them to me.

  Joe Harris and I have written The Practice of Algebraic Curves: A Second Course in Algebraic Geometry It is now available on the AMS site as an actual book (hard and soft cover), and as a free ebook. Most books on this subject end with the Riemann-Roch theorem; that is where our book will start. Our hope is that it will be a grown-up book on curves parallel to Beauville's beautiful book on algebraic surfaces, less complete but more approachable than the great two-volume work of Arbarello, Cornalba, Griffiths and (for part 1) Harris. In Fall 2025 I taught a course at Berkeley from our book. In the process I found many typos and a few mathematical eerrors, gathered in this Errata.
  

• Our previous book was 3264 and All That - Intersection Theory in Algebraic Geometry. Intended as a second course on algebraic geometry, it takes intersection theory as a path through which many important aspects of the subject can be introduced. It was published by Cambridge University Press in the spring of 2016. Here are solutions to a large proportion of the exercises.
  

  Academic Background

  After getting my PhD at the University of Chicago in 1970, I taught at Brandeis University for twenty-seven years, with sabbaticals in Paris, Bonn, and Berkeley. In 1997 I became Director of the Mathematical Sciences Research Institute (MSRI) in Berkeley; at the same time I joined the faculty of UC Berkeley as Professor of Mathematics.

  As Director of MSRI from 1997 to 2007, I had the satisfaction of supporting a huge amount of mathematics and related activity at the Institute. From 2003 to 2005 I was also President of the American Mathematical Society, an organization I came to admire a great deal. I was elected Fellow of the American Academy of Arts and Sciences in 2006.

  Robert Bryant succeeded me as Director of MSRI in 2007, and from then until the fall of 2012 I divided my time between teaching at Berkeley and working as the first Director of Mathematics and Physical Sciences at the Simons Foundation in New York, where I initiated the public programs in Mathematics, Theoretical Physics, and Theoretical Computer Science.

  I returned to MSRI in the year 2012-13 as an organizer of the year-long program on Commutative Algebra, and became Director of MSRI again in August, 2013, in which role I served until August, 2022. I have now gone "back" to teaching as Professor in the department of mathematics at UC Berkeley.

  When I applied to become the Director of MSRI I wrote to the hiring committee saying that, while the strength of MSRI's scientific program was already recognized around the world, I felt that MSRI badly needed two things: a physical facility worthy of such a world-class institution (and in particular a better auditorium); and an endowment that could enable long-term planning and protect the institution from possible future fluctuations in NSF support, which was essentially the only source of funding at the time.

  Now, in my retirement from the directorship, I have the satisfaction of having helped bring about both of these changes: The renovation and extension of the building to approximately twice its original size was accomplished in 2006, near the end of my first two terms, and a centerpiece of the construction was the beautiful and airy Simons auditorium, where Roger Penrose gave the inaugural lecture in 2006

  Jim Simons made the first substantial contribution to the Endowment, including the establishment of the "Eisenbud Professorship" at MSRI, at my retirement party in 2007. I undertook a major endowment campaign in my fourth term, and as I leave MSRI, its endowment stands at about $130 million; the extraordinary generosity of the lead gifts made by Jim and Marilyn Simons and matched by Henry and Marsha Laufer, led to the renaming of MSRI as the Simons Laufer Mathematical Sciences Institute, or SLMath for short.

  Biography

  MacTutor Biography

  Souvenirs from my four terms as Director of MSRI:

  • 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.
  MSRI's biggest outreach projects on my watch were the National Math Festivals held in the spring of 2015, 2017, 2019 and 2021 as joint projects with the Institute for Advanced Study. I worked very closely with MSRI staffmember Kirsten Bohl, whose energy, skill, and sensitivity made these programs a great success, each one drawing over 12,000 kids and adults to the Washington Convention Center. Here is a typical scene: I wrote a piece for the AMS notices Op-Ed piece to spread the word, and there were articles from The New Yorker and from the MAA Focus that appeared afterwards. Kirsten Bohl and I co-authored a piece with pictures, that appeared in the April 2021 Notices of the AMS just before the last of the festivals.

  Activities Outside Berkeley

  Organizational

  I remain connected to the Simons Foundation as member, since 2012, of its Board of Directors; and I have been on the Board of Directors of Math for America since its inception in 2004.

  I helped found the Journal of Algebra and Number Theory in 2006, and the Journal of Software for Algebra and Geometry in 2009, and I'm Chair of the Editorial Board of the former. I'm also an editor of Springer-Verlag's book series Graduate Texts in Mathematics and Algorithms and Computation in Mathematics

  While President of the AMS I helped plan the Math Research Communities Program, and chaired its advisory board for several years.

  Current Events Bulletin at the Winter AMS Meeting

  Since 2004 I've been organizing a session at each of the Winter AMS meetings on Current Events in Mathematics. The format is simple: four accessible 50-minute lectures on some of the most interesting pure and applied mathematics of the last few years, presented by people who are speaking on the work of others. The inspiration is of course the famous Bourbaki Seminar, but the aim is to be broader and represent a wider range of mathematics, particularly on the applied side. A booklet with writeups of the talks is permanently available online. Almost all of them become articles in the Bulletin of the American Mathematical Society afterwards.
• Beamer presentations. It seems I make these once a year, for talks at the winter AMS meetings. I strongly prefer blackboards for communication, but it is nice to have a permanent record.
• My mathematical genealogy from the Mathematical Genealogy Project
• For a course I taught, Craig Huneke and I made a list of relatively accessible papers on commutative algebra and algebraic geometry that some students may find useful (badly in need of pruning and updating.) <

  Some Mathematicians who were important for me

  Saunders Mac Lane

  Saunders Mac Lane died on April 14, 2005. He was my thesis advisor---Irving Kaplansky was his first student, I was nearly his last; perhaps John Thompson is the most illustrious. I wrote a preface that contains some of my favorite stories about him for his Autobiography, which was originally published by AK Peters. He was a great figure, and very important for me personally.

  David Buchsbaum

  David Buchsbaum was my postdoctoral mentor at Brandeis, and we worked closely together for most of the first 10 years of my career. In addition to math, we spent a lot of time discussing department and university politics, and the history of the math department, great preparation for my future administrative activity. When he died in January 2021, at the age of 91, his former student Jerzy Weyman and I collected reminiscences from many of David's friends and students, and published them along with lots of photos in Remembering David Buchsbaum, which was published in the Notices of the American Mathematical Society.

  Yuri Ivanovich Manin

  It was my privilege to get to know Yuri Manin, and even to interview him for the Simons Foundation's Science Lives. I contributed an couple of memories of our friendship to the Homage to be published in the Gazette of the SMF

  Recreation

  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 early results on my photo page.

  Addresses

  David Eisenbud
  Dept of Mathematics,
  University of California, Berkeley
  Berkeley, CA 94720
  
  email: <de@msri.org>

  Links

  MSRI
  UC Berkeley Mathematics

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  A film about χiralbacks (= chiral rattlebacks) by Tadashi Tokieda (the password is msri)
  

  Two spinning turtles 5 2 14 from Zala Films on Vimeo.

  
  Created: August 2, 1995. Last updated: August 4, 2024.