I am very sad to report that my Ph.D. advisor, Robert Coleman, died last night in his sleep at the age of 59. His loving wife Tessa called me this afternoon with the heartbreaking news. Robert was a startlingly original and creative mathematician who has had a profound influence on modern number theory and arithmetic geometry. He was an inspiration to me and many others and will be dearly missed.

Robert was born on November 22, 1954 and earned a mathematics degree from Harvard University. He subsequently completed Part III of the mathematical tripos at Cambridge, where he worked with John Coates and made important contributions to local class field theory. By the time he entered graduate school at Princeton, Robert had essentially already written his doctoral dissertation, but his formal thesis advisor was Kenkichi Iwasawa. He began teaching at UC Berkeley in 1983 and was a recipient of a MacArthur “Genius” Fellowship in 1987. Robert published 63 papers, including 8 papers in the prestigious journal* Inventiones Mathematicae* and 5 in the *Duke Mathematical Journal*. He had an amazing intuition for everything p-adic. Long before the invention of Berkovich spaces, Robert could somehow visualize paths and structures in p-adic geometry which no one else in the world saw as keenly or as profoundly. I rarely saw him reading papers or books. He seemed to figure out whatever he needed to know almost from scratch, which often made his papers quite difficult to read but this went hand in hand with his brilliance and originality.

When I was a graduate student at Berkeley, Robert hosted an invitation-only wine and cheese gathering in his office every Friday afternoon code-named “Potatoes”. Among the regular attendees were Loïc Merel and Kevin Buzzard, who were postdocs at the time. It was a wonderful tradition. In the summer of 1997, while I was still a graduate student, Robert invited me to accompany him for three weeks in Paris to a workshop on p-adic Cohomology at the Institut Henri Poincare. That was the first time I met luminaries like Faltings, Fontaine, and Mazur. Since the workshop was (a) totally in French and (b) on a topic I knew almost nothing about, I was in completely over my head. But I fell in love with Paris (which I’ve since returned to many times) and my best memories from that trip are of dining with Robert and seeing the city with him.

The trip also taught me to appreciate the significant challenges which Robert, who had Multiple Sclerosis, bravely faced every day. I remember helping Robert check into his hotel room near the Luxembourg Gardens, only to find out that his wheelchair did not fit in the elevator. We had to find another hotel room for him, which was not so easy given the level of our French! Curbs were a constant challenge for Robert, as finding on- and off- ramps for wheelchairs in Paris was like trying to get a vegan meal in rural Arkansas.

Robert hosted a Hoppin’ John party at his house every year, and it was delicious. (It’s somewhat ironic that I now live in the South but the only place I’ve ever had Hoppin’ John was in Berkeley, California.) Robert had a mischievous and impish sense of humor, and consequently he surrounded himself with colorful and funny people. For many years Robert’s closest companion was his guide dog Bishop, who would join Robert everywhere. Bishop eventually passed away and Robert found a new canine companion named Julep.

My advisor was always very supportive of me, and I owe him a tremendous debt of gratitude for helping me obtain a Benjamin Peirce Assistant Professorship at Harvard after I graduated from Berkeley. That position helped my career in immeasurable ways. More recently, Robert helped recruit me for a professorship at Berkeley where I spent a memorable year as his colleague during the 2011-12 academic year. (I eventually returned to Georgia Tech for family reasons.) It was wonderful to reconnect with him, introduce him to my kids, and meet his lovely fiancee Tessa, who he married in Summer 2012. I was very touched and honored that Robert asked me to be in his wedding party, and I’ve never seen him as happy as he looked on his wedding day. I am heartbroken for Tessa, who has been so fiercely devoted to Robert.

Robert Coleman’s fundamental contributions to mathematics include:

- His Ph.D. thesis “Division Values in Local Fields”, worked out when Robert was still an undergraduate and published in
*Inventiones*. - His theory of p-adic integration, introduced in his seminal 1985
*Annals of Math*paper “Torsion Points on Curves and p-adic Abelian Integrals”. Coleman’s theory has had significant applications to the theory of rational points on curves, starting with his*Duke*paper “Effective Chabauty” and continuing to the present day with non-abelian analogues due to Minhyong Kim and others. The method of Coleman-Chabauty is currently one of the best ways to explicitly calculate the rational points on a curve of genus at least 2. Coleman’s method of proof, which he calls “analytic continuation along Frobenius”, helped inspire Kiran Kedlaya’s influential p-adic algorithm for counting points on hyperelliptic curves over finite fields, which is important in modern cryptography. Coleman’s theory of p-adic integration has been generalized by Colmez, Berkovich, and other prominent mathematicians. - His work on p-adic families of modular forms, introduced in his 1996 and 1997
*Inventiones*papers “Classical and Overconvergent Modular Forms” and “p-adic Banach Spaces and Families of Modular Forms”. These papers introduced important new methods from the theory of Banach spaces, coined the term “overconvergent modular form”, and proved an important criterion for such a form to be classical. Those papers, along with Coleman’s subsequent work with Barry Mazur constructing the so-called “eigencurve”, have had a huge impact on the theory of Galois representations. - A new proof of the Manin-Mumford conjecture, influential work on stable models of modular curves (which Jared Weinstein has recently refined and applied to the Local Langlands Program), the Coleman-Voloch supplement to Gross’s work on companion forms, contributions to p-adic Hodge theory, and much more…

For the last year, Kiran Kedlaya, Ken Ribet, Richard Taylor, Annette Werner and I have been organizing a conference on p-adic methods in number theory in honor of Robert Coleman’s 60th birthday which is scheduled to take place in Berkeley, California in May 2015. The conference will now be a tribute to the legacy and influence of Robert’s mathematical work. It will feature an all-star line-up of speakers, including John Coates, Jean-Marc Fontaine, Barry Mazur, Peter Scholze, and many others. Stay tuned for more detailed announcements…

Robert Coleman was a kind, brave, and brilliant man whose influence on mathematics and on his friends and loved ones will long outlive his fragile body. Please share your memories of Robert as a mathematician and inspirational human being in the comments section below.

[Note added 4/8/14] There will be a memorial service on Saturday, May 31, 2014 at the Bancroft Hotel in Berkeley from 2-4pm. People are encouraged to bring remarks, pictures, videos, etc. Please let Ken Ribet (ribet@math.berkeley.edu) and Arthur Ogus (ogus@math.berkeley.edu) know if you plan to attend, and if you plan to speak or bring any mementos.

My first mathematical discussion with Robert in 1994 was the defining moment of my mathemathematical career. At MSRI, while searching for a p-adic counterpart to complex integration used in defining the Abel-Jacobi map, Udi de Shalit pointed out that I was just at the right place… Robert patiently explained the basics of his integration theory and was kind enough to share with me his Minnesota notes on the subject.

Coleman’s integration theory has been further developed since by many people, but to this day his approach remains the most concrete and is being used, and probably will continue to be used, in most of the applications of the theory.

I was fortunate and privileged to be Robert’s high school mathematics teacher. I had him as a student for 3 years from grades 6 through 12. One of the courses I taught him was Abstract Algebra when he was in 11th grade. The text we used was “Topics in Algebra” by Herstein which was quite advanced for high school students. While in the 12th grade, he was student in my mathematics seminar class which was for student who had completed all our our formal courses. The students researched and presented various math topics to each other. That year Robert was a finalist (top 40) in the Westinghouse Science Talent search.

Robert inspired me as a teacher. He loved mathematics and couldn’t get enough of it. When he was applying to colleges, I would say, ” Just put him in a math library for 4 years, and he’ll know more math than than any other undergraduate. Though I taught him more than 42 years ago. I often think of him as the highlight of my 30 years in education.

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