Graham Evans

I was deeply sad to hear of Graham Evans’ death on March 20th, and I have been thinking about him. I want to share some memories:

Graham was one of my closest friends in grad school. He and Kay were already married then—I think they had been childhood sweethearts––and I remember being very impressed by their snug little apartment.

Graham was a student of Kaplansky, and I followed all of Kap’s marvelous lectures too. We both developed a fascination with free resolutions from this exposure. Graham wrote the notes for Richard Swan’s course in K-theory—I enjoyed learning the basics from them later. Graham took a Postdoc at MIT and I followed to Brandeis, nearby. There we continued our friendship and collaborated on basic elements (arising from Swan’s work) and on set-theoretic complete intersections—the latter resulting in the paper for which (I believe) I was given tenure at Brandeis.

Graham went on to a career at UIUC, while I stayed at Brandeis, but we continued many interactions and parallels. For example, Graham’s undergraduate student Mike Stillman wrote an early program to compute syzygies, while Buchsbaum and I employed an undergraduate, Ray Zibman, for the same purpose (none of us knew about Groebner bases, so the programs were only heuristic; Schreyer’s algorithm and the work of Bayer and Stillman on Macaulay lay, unsuspected, in the future.)

Graham and I both spent the year 1975–76 at the I.H.E.S, outside of Paris, supported by Sloan Fellowships.  He was already obsessed with (but making no progress on) the “Syzygy Problem”—the conjecture that a non-free n-th syzygy of finite projective dimension must have rank at least n. It took a long time, but his persistence paid off: he and his Urbana colleague Phillip Griffith published their proof in the Annals of Math in 1981. Their London Math Society book, published a few years later, has a nice exposition of the whole area. The paper continues to be influential: it already has 65 citations, 11 new ones in papers appearing in the last 5 years alone.

At Urbana, Graham and Kay continued to nurture many students, one of whom, Hara Charalambous, came  to me as a postdoc and is now chair of mathematics in Thessaloniki. In addition to his PhD students, listed  at the math genealogy site, there was a succession of undergraduates who enjoyed the welcoming warmth of that household, including Mike Stillman and, much more recently, Emily Riehl. I believe that Kay, an accomplished seamstress, even sewed wedding dresses for some of them! Graham was an excellent and enthusiastic cook—for example, he made the first and only “Christmas goose” that I ever tasted. He was active in teaching non-mathematicians at Urbana, too: he once told me about a course he gave regularly, in  which, on the first day, he would say: “Don’t be afraid! Now reach out and touch the computer.” I can hear  him saying it …

Soon after Graham retired from UIUC, he developed Parkinson’s disease, and Kay also suffered a series of medical troubles. Fortunately they had the local support of Carl, one of their two sons, who remained in Urbana at the University. For quite a while, Graham and Kay made frequent pilgrimages to the West coast where their other child, Michael, is a video game developer. They would often stop by in Berkeley on these trips, so we could renew our friendship. Kay died about a year ago. I had hoped to visit Graham in Urbana once more—it might have happened, but for the pandemic.

Graham Evans was my undergraduate mentor and had a profound impact on me. I met him through the Campus Honors Program soon after I arrived on campus in 1995. Sonia Carringer called George Francis and said they wanted a mentor for a freshman math major interested in algebra who had been a debater in high school, and George handed the phone to Graham, his officemate and an algebraist who had been a national champion debater in high school. It seemed like the CHP must have magical powers to create perfect mentors. From the day I met him, Graham was incredibly welcoming, and he and Kay treated me like a member of their family. I was astonished at (and very grateful for!) the number of times they invited me to dinners at their house, amazing meals that were always filled with great stories, laughter, and an interesting assortment of people. I felt lucky to be included, very fortunate to have a family away from home starting so early in my time in college. I learned so much mathematics from Graham while at Illinois and even more from reading his papers in graduate school that I was thrilled suddenly to be able to understand. When I was a freshman, Graham encouraged me to go to talks when he felt I might be able to get something out of them, and he counseled me as I struggled with courses that were a level above anything I had done before. I remember his recounting having told me, "It's supposed to be hard!That's how you learn!" in a commercial the university made about his mentoring late in my time at Illinois. But Graham always knew just how much to push and when to back off a bit and give a hint or some reassurances. He introduced me to commutative algebra during my sophomore year through Ideals, Varieties, and Algorithms, the wonderful book of Cox, Little, and O'Shea, and I knew this was the area of math in which I wanted to work. Throughout my time at Illinois, Graham would include me in reading courses or seminars he was organizing, quietly seek out opportunities for me, bring me along to dinners with visiting mathematicians, and look out for me in any way he could. I found that when Graham knew I might be seeing one of his colleagues while visiting grad schools, going to a conference, or on some other occasion, Graham would have often written to them ahead of time so they would know who I was if we happened to meet. He did everything he could, big and small, to make a nervous and anxious young mathematician more comfortable. It is no coincidence that I asked Mike Stillman, another of Graham's mentees, to be my adviser in graduate school, and I know both of us feel a great debt to Graham. We try to emulate the remarkable example Graham set for us. Graham and Kay were such good people and acted as second sets of parents for dozens of students. I have many great memories from their house, starting from the first time I walked up their steps with trepidation as a new freshman (with Kay immediately making me feel at ease before dinner) to watching the NBA Finals with them to a last big graduation dinner they held for Matt Rodriguez and me and our families. I am deeply grateful to both Graham and Kay and marvel at the outstanding impact they had on so many people.

It's hard to overstate how much I have benefited from the generosity of E.Graham Evans Jr., who went out of his way time and time again to create special opportunities for me as a teenager growing up in central Illinois.

We first met on a college visit sometime in 2001, during which I met with him in his office in his capacity as director of undergraduate studies. At that point, I had fond memories of UIUC from the Illinois state math competitions, but I had no real connection with the university. Much to my surprise, he stayed in touch and offered to use some department funding earmarked for student travel to send me to the Nebraska Conference for Undergraduate Women in my senior year of high school.

More incredibly, he invited me to participate as some sort of unofficial satellite to an REU program taking place at UIUC in the summer of 2002, the summer before I left for college. I was paid a stipend, which meant I didn't have to work another summer job. Instead I spent my days haunting empty classrooms at Illinois State University and then drove down to Urbana-Champaign once a week from Bloomington-Normal to meet with Graham.

Graham suggested we work on a special case of a Cayley–Bacharach conjecture, due to Eisenbud, Green, and Harris, which he distilled to an explicit problem that could be solved by induction: we prove that the maximal number of vertices of an n-dimensional hypercube that a polynomial of degree k can vanish at without vanishing at them all is 2^n – 2^{n – k}. We co-wrote and published a six-page paper with that result and some mild generalizations, on which he insisted on listing me as the first author, much to my later embarrassment when I learned about the convention to default to alphabetical order.

Midway through the summer, I also started working with John P. D'Angelo, who gave me a combinatorial problem about sources and sinks in some labeled lattice diagram associated polynomials that figured in some way in another joint paper "A Sharp Bound for the Degree of Proper Monomial Mappings Between Balls" with Šimon Kos. I'm sure behind the scenes Graham was the one who recruited John as a co-mentor. At the end of the summer, Graham also arranged for me to give a talk at UIUC about my Intel Science Talent Search research project, and he recruited people to actually show up, which was a particular thrill.

I have a lot of pleasant memories from that summer, including a backyard barbecue at Graham and Kay's house, where I was introduced to the pleasures of grilled portabello mushrooms. Graham and Kay were famous for their hospitality and hosted many international students over the years, including Winfried Bruns' daughter Julia. Somehow I ended up the beneficiary of a reciprocal exchange, and spent the summer of 2003 living with the Bruns in Osnabrück in a futile attempt to learn to speak fluent German.

We stayed in touch in the following years. I relied on Graham particularly as a letter writer for my graduate school and fellowship applications, since his was the only REU I participated in. I remembered him being surprised that I wanted to use him as a letter writer, but it's rare, when you're an undergraduate, to have a faculty member get to know you so well, so I'm sure I made the right choice.

A final instance of his generosity: when Graham retired, he gave me his entire math library, which was an incredible bounty to receive as a PhD student. I gave a few books away but kept most of them, and they still form a substantial part of my collection.

I'm very grateful that Graham and I were able to stay in touch over the past almost 20 years. Graham and Kay became friends with my parents, and would come up to Bloomington-Normal for the Illinois Shakespeare Festival every summer. I was able to see him a handful of times. Even as an emeritus faculty member, he'd come into the department whenever I was in town to give a talk.

In summary, I was profoundly lucky to have been adopted by such a wonderful mentor and role model. When I dreamt of what it might like to be a tenured faculty member, I imagined a house like Graham and Kay's, with a beautiful garden within walking distance of campus, and filled with interesting visitors and friends. I will really miss him.

I had Graham Evans for an undergrad class Math 305, A Teacher's Course, which basically meant that the teacher could teach anything he wanted. One of the lessons in that course that I remembered was Graham Evans playing the cello during class to demonstrate the mathematics of music. I've been a high school mathematics teacher since graduating from UIUC. Every time I encounter an exceptional math student who happens to also excel at music, I am reminded of how math and music are intertwined and Graham playing the cello.