# David Eisenbud

**Director, Mathematical Sciences Research Institute, and Professor of Mathematics, UC Berkeley**

Seminar on Commutative Algebra and Algebraic Geometry

## 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, 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. 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 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.

- MacTutor Biography from my first term as director.
- 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.

## From my third term as Director, 2013-2017:

MSRI's biggest outreach project to date was the National Math Festival, April 16--18, 2015, a joint project with the Institute for Advanced Study. Here is an Op-Ed piece that I wrote in the Notices of the AMS to spread the word, and here are articles from The New Yorker and from the MAA Focus that appeared afterwards.

## Current Activities Outside MSRI

### 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 Algorithms and Computation in Mathematics. While President of the AMS I helped plan the Math Research Communities Program, and have chaired its Advisory Board since it came into being in 2007.

### 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 available at the meeting and online. Almost all of them become articles in the Bulletin of the American Mathematical Society afterwards.

### Research Interests

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 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.

### 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 results (alas, not up-to-date!) on my photo page.

## CV, Papers, Students

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

## Saunders Mac Lane: In Memoriam

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.

## Some Ongoing Work

Here are some of my current mathematical projects:

- Joe Harris and I have finally finished a book that could be a "second course" on algebraic geometry, taking intersection theory as a path through which many important aspects of the subject can be introduced: 3264 and All That; Intersection Theory in Algebraic Geometry. It is being published by Cambridge University Press, and should appear in the spring of 2016.
- With Daniel Erman and Frank Schreyer I'm working on understanding the analogues of Tate resolutions for Toric varieties. The case of projective space is explained in a paper of mine with Floystad and Schreyer some years ago. In November 2014, Erman and Schreyer and I posted a preprint solving the problem for the "easiest difficult" case -- Products of projective spaces.
- Irena Peeva succeeded in fulfilling a dream of many years: we found a good analogue for complete intersections of the description of minimal free resolutions over hypersurfaces by matrix factorizations. There are many questions that are opened up by this work, and Frank Schreyer and Jesse Burke have joined us on various aspects of the project that are still developing.
- With Bernd Ulrich and Marc Chardin I've done some work on residual intersections. The latest preprint is Duality and Socle Generators for Residual Intersections. This is a greatly expanded and improved version of a preprint we posted at the end of the MSRI Commutative Algebra year, 2012-13. The whole project was inspired by work of Duco van Straten and Huneke-Ulrich, who discovered two pieces in what turns out to be a whole series of dualities, and by conjectures of van Straten and Warmt that the socle of the canonical module of a residual intersection is, under good circumstances, defined by a Jacobian determinant.
- 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.

I am grateful to the National Science Foundation for partial support in my work on these projects!

## Commutative Algebra Book

My book, "Commutative Algebra with a View Toward Algebraic Geometry", published in 1995 by Springer-Ver lag, 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.

## Address

David Eisenbud

Director, MSRI

17 Gauss Way

Berkeley, CA 94720

email: <de@msri.org>