Lynne Heather Walling (1958–2021)

Introduction

Lynne Heather Walling lived with an enduring passion for community and a profound belief in the importance and value of everyone and everything. Throughout her life she thought deeply about the world of mathematics and mathematicians. When someone encountered unfairness, Lynne felt their struggle, and she had a lifelong quest to address the wrongs she saw.

Lynne Walling passed away on May 28, 2021 at her home in Bristol, England. About five weeks earlier, she had a seemingly innocent health event from which the subsequent medical examinations uncovered that she had aggressive and terminal cancer. In Lynne’s final days, she surrounded herself with friends not because of fear or sadness, but rather to show those near her how to accept her circumstance. It is said that a wise person learns from the experience of others, and Lynne was allowing others to understand what she was facing.

This article consists of remembrances from some of Lynne’s colleagues with the purpose of describing her contributions to mathematics and the mathematics community. The editors of this article wish to thank Erica Flapan, the Editor-in-Chief of the Notices of the American Mathematical Society, for initiating this project. By accepting Erica’s request to edit this tribute to Lynne, it is our aim to recognize, and celebrate, the important and unique place in the mathematical world which Lynne occupied.

Lynne was born on October 9, 1958. As we learn from comments below by Lynne’s father Stuart, Lynne’s early life in Northern California was filled with a sense of community and equity for all. After finishing high school, Lynne attended the University of California at San Diego but left after one year. Two years later, she enrolled in Sonoma State University, at first to study accounting, but then she returned to mathematics. After graduating from Sonoma State University, Lynne began her PhD studies at Dartmouth College in 1982.

While at Dartmouth Lynne’s mathematical work focused on Hilbert modular forms, and she completed her dissertation in 1987 under the direction of the second-named editor (T.S.). The contribution by Rainer Schulze-Pillot gives an excellent overview of Lynne’s research contributions. As Schulze-Pillot states, Lynne often tackled “the difficult technical questions that arise when one tries to make general results as explicit as possible.” This style of “hands-on” work was manifest in all other aspects of Lynne’s life. She would sew her own dresses, make the food for her animals, take on home construction projects such as roofing and plumbing, and build sculptures and artwork for herself and her friends. Lynne sought to participate in all aspects of life, and she did so with the traditional “heart, mind, and soul,” as well as with her hands.

After Dartmouth, Lynne briefly held faculty positions at St. Olaf College (Northfield, Minnesota) and Bates College (Lewiston, Maine) before moving to the University of Colorado (Boulder, Colorado) in 1990. She took a two-year leave from Colorado and worked at the National Science Foundation (Alexandria, Virginia) from 2000 to 2002. In 2007, she accepted a position at the University of Bristol (Bristol, UK) and stayed until her passing in 2021. Various contributors describe their interactions with Lynne at each of these times and places, so we will not duplicate their comments. Rather, we now describe some of Lynne’s highly influential efforts regarding issues of inclusion and diversity.

In 1987 Audrey Terras and Dorothy Wallace organized the first Automorphic Forms Workshop (AFW). The subsequent series has become an important annual event, and it is most often held in the Western United States. Soon after Lynne moved to Colorado, she emerged as a driving force in AFW. With Lynne’s influence, the workshop grew in the manner originally set forth by Audrey and Dorothy, which is to be, primarily, a friendly environment for mathematicians with all different types of experience; Lynne disliked the use of the word “level.” There were no invited speakers nor featured talks. There was only one allowed distinction between attendees and that was based on a single point: For any specific mathematical question, did you know the answer or not. Egos and all preconceived notions of hierarchy were not tolerated, and Lynne was unwavering when ensuring that the welcoming atmosphere was maintained.

In 1994 Lynne participated in a program in Berkeley, California whose aim was to encourage undergraduate women to attend graduate school in the mathematical sciences. The proceedings of the meeting is published in the book titled Women in Mathematics: Scaling the Heights, edited by Deborah Nolan. This wonderful volume is just as significant and relevant today as it was in 1994. Lynne’s contribution, titled “Quadratic Reciprocity and Continued Fractions,” consists of lectures followed with material intended for small group work. This style of teaching, which seems to stem from Lynne’s upbringing, became part of many of the classes she taught in the following years.

In 2002, Lynne attended a conference in honor of Audrey Terras’s 60th birthday. It is worth repeating Audrey’s statement below, which is that Lynne gave “a talk on an uncomfortable subject: ‘Women in Mathematics: Participating, Surviving, and Succeeding.’ ” For Lynne, the important issue was not that of comfort, hers or anyone else’s. Rather, only by openly and honestly discussing the problems of the mathematical community can one attain any meaningful improvement. Without question, Lynne retained and believed in the sense of community and equity she experienced in her childhood.

After Lynne moved to Bristol in 2007, she often said that she missed the environment of the AFW. As a result, she created the Building Bridges (BB) workshop and summer school. To date, there have been four BB conferences, and some of the contributions below describe these truly wonderful events. As with AFW, Lynne continued to promote the notion of community and inclusion for all, and again it was not always comfortable. As a panelist at one meeting, Lynne and an audience member engaged in a somewhat heated disagreement regarding the progress a particular institution was making toward equitable treatment of its members. The exchange was quite surprising, and uncomfortable, for everyone. After the panel discussion, Lynne, the audience member with whom she disagreed, and several others met for dinner, then drinks, and more discussion which went on for hours. For Lynne, the disagreement did not become disagreeable. Lynne was keen to continue the dialogue, because she felt that with such exchanges perhaps we could achieve further and, in her opinion, necessary change.

The fifth Building Bridges conference, BB5, was scheduled to be held in Sarajevo in July 2020, but it was postponed because of COVID-19. In March 2021, the organizers began in earnest to plan for BB5 to be held in Sarajevo in August 2022, and Lynne was leading the way. The summer school teachers were in place, and several grant applications were submitted. Soon it would be time to arrange local accommodations. Many of the participants from past BB conferences had contacted Lynne and asked about BB5, in anticipation of renewed friendship and mathematics. Anyone who spoke with Lynne at that time could sense her happiness and elation as she prepared for her next community event.

But then, all too suddenly, Lynne was gone.

It is often felt upon the passing of a friend or loved one that you did not have a chance to say “Good-bye.” Not only is that true with Lynne, but it seems as if we did not have enough time to say “Thank you,” so let’s do so now. Thank you, Lynne, for sharing your mathematical insight. Thank you for leading the way in seeking a more fair and equitable community and for showing us how to do our part. And to paraphrase what Misha Rudnev wrote in his contribution, thank you for demonstrating that one can face one’s own mortality by holding your head high in a manner which can only be described as steadfast and determined.

Thank you Lynne. May the memory of you and the lessons you taught us carry on.

Early Years

By Stuart Walling

I believe one of the things that developed Lynne’s character was the great variety of her experiences during her first twenty-two years. From age nine through high school, we lived in a large house in Santa Ana, California. This is the house Lynne always felt she “grew up” in—and she did! It was inhabited by me, her father; Anne Daniel, her stepmom; Lynne; her two-years-older brother, Alan; and David, Annie’s two-year-old son.

It was the time of Vietnam War protests, peace marches, love-ins in the park, a steady flow of Unitarians in and out of the house. Diverse ideas and opinions flowed freely, with Lynne absorbing it all like a sponge. We did a lot of hiking and camping, including a two-month cross-country trip with a station wagon, tent trailer, five kids, and two alleged adults. Lynne was eleven.

Figure 1.

Lynne at age 12 or 13.

We gave her a lot of freedom to try things, but I believe we also instilled a strong sense of personal responsibility. As a 10th grader, her Spanish teacher took a small group to Durango, Mexico, where they lived with local families—a great experience. She went to a girlfriend’s fundamentalist church, just to see what it was like. She took a music appreciation class in high school, “just because,” and questioned the teacher’s opinions on the music’s meaning. He gave her a “B”—the only non-A she ever got!

She had a disillusioning freshman year at UCSD; she found it hard to find enough people with whom to talk Math. She drifted for a couple of years—to Washington D.C. where she acquired her first dog, Chuck. She then gravitated to Sonoma County, California, where she eventually enrolled at Sonoma State College, and she loved it!

I truly believe all her experiences, both positive and negative, were a big factor in producing the unique person she was. She will forever be in my heart and mind, and I hope remembered with fondness by all the students she taught over the years.

Stuart Walling is Lynne Walling’s father; Donna Janesky is Lynne’s stepmother. They live in California. Their email address is janesky40@comcast.net.

By Thomas Shemanske

Lynne entered graduate school in 1982, my second year as an assistant professor at Dartmouth. Her first two years consisted mostly of classes and the required oral exams. I still remember bits of her algebra exam. She walked into the classroom and the other examiner and I asked her where she would like to start. She quipped about perhaps classifying all the finite groups. My colleague and I smiled and said that would be an excellent start. We did eventually segue to other topics.

As Lynne was my first PhD student, the mentoring process was evolutionary. We met regularly; she presented results; I asked questions; we explored options to circumvent obstructions and new paths to follow. Finally, perhaps near the end of her fourth year, she had amassed a nice set of results on integral weight Hilbert modular forms arising from theta series and explicit actions of Hecke operators on them. Already, those results were probably more than enough for a thesis, but it was clear that Lynne had a good deal of talent, momentum, and a well-developed tool set, so after telling her those results were very nice, I naturally asked, “What about the half-integral weight case?” I believe there was an emotional response on several levels to that question, and it remained a favorite story for her to tell to students who considered working with me.

Figure 2.

Lynne working on her thesis while on a road trip with her parents.

Since we are remembering a number theorist, it is no surprise that the notion of reciprocity played an important role in Lynne’s life. Now this is not about quadratic or Artin reciprocity, rather something else. At the end of Lynne’s fourth year of graduate school, my wife and I bought a house. This was the 1980s with interest rates in the teens, and we ended up purchasing a definite fixer-upper spending virtually every dime we had. We had seen the house and had it inspected in the winter. After closing in May, we peeked in the attic and saw bright sunshine filtering through a myriad of holes in the roof. Since we were then paupers and roof integrity tends to be a high-priority item, it fell to me to expand my own tool set to include roofing skills. So my comment to Lynne was that if she wanted to talk math with me, it would have to be on my roof. Well, at least that is how Lynne remembered what I said.

Now Lynne had always been a fan of the wood and metal shops at Dartmouth, so there was no question that she would show up. She would grab a bundle of shingles, hoist them over her shoulder, climb up the ladder, and help me roof while talking math. Admittedly a number of my neighbors did inquire “Who is that woman? She works harder than most guys I know.”

Years later, now working at Boulder, Lynne bought a house in Longmont; ah yes, you probably see where this is going. She and I were in the midst of a joint paper, so it hardly came as a surprise when she invited me out to work on it during a break. We worked hard that week, but I was not flying out until that Monday, which left the weekend. In unseasonable 90-degree heat we ripped off cedar shingles, redecked the roof with plywood, and covered everything with roofing felt to keep the rain out. That Monday when I left, it was 30 degrees and several inches of snow had fallen overnight. But the roof remained water tight, and Lynne (relying on her multi-faceted training as a graduate student) managed to finish the job that week. Whether she was mentoring any of her own graduate students at that time is unknown.

To return to Lynne’s graduate student years, she entered graduate school intent on procuring a job at a good liberal arts institution. Given her strong thesis, I encouraged her to apply for postdocs as well as to some liberal arts institutions, but advisors are only that. She did land a very nice job at St. Olaf. After two years, she was again on the market, this time landing at Bates, another wonderful institution. The next year she was on the market yet again, but in requesting a letter of recommendation, said she was now absolutely sure that mathematical research was her driving force. She loved doing math and wanted to be somewhere where that focus would be paramount. And so she began at Boulder.

By Dorothy Wallace

Once Lynne and I got into a friendly wrestling match. I outweighed her by quite a bit, yet she rather easily flipped me upside down. I will never forget this. In fact, everything about Lynne is hard to forget.

Lynne made substantial contributions to the field of modular forms, writing papers with a large number of coauthors. I was not one of these coauthors, and so I will leave mathematical details to others. For me, Lynne was first and foremost a friend, from the moment I met her. She was generous and loyal as well as fiercely protective, especially of her female colleagues.

When she was still a graduate student, an older colleague told Lynne she should stop wasting time and just finish her thesis. Lynne asked him, “Do you make your own dinner? Do you do your own laundry? Do you pack your own lunch? Do you clean your house?” The answer to all of these was no—his wife did all of those things. Lynne then explained that she did all of these chores for herself, and they took time. Lynne was never silent when she perceived an injustice, no matter how slight. And she was usually forgiving, taking personal affronts with grace and an unmatched sense of humor. Years later at a math related party, Lynne was first on the dance floor with this same colleague.

The year Lynne moved to Boulder she gave me several things that would not fit in her car. Foremost was a six-foot-tall stuffed velvet bird built on a sturdy iron base she welded herself. She called it the “lesser known greater emu” because it had the wrong number of toes for an ostrich. It sat over my daughter’s crib, then over her bed, then was disassembled (with Lynne’s permission) to become a plant trellis. It is now being refurbished as an outdoor sculpture, and will rise again as “Anhinga borealis splendens var. Wallingbird,” and be placed in a visible location for anyone to see. As a tribute to Lynne it will be inadequate. But it always has, and always will, remind me of her every time I look at it.

Dorothy Wallace is a professor of mathematics at Dartmouth College. Her email address is Dorothy.I.Wallace@dartmouth.edu.

By John Cremona

Lynne Walling was my good friend and colleague for nearly 40 years. We first met at a Halloween party in the Mathematics Department common room at Dartmouth in 1982. I had just arrived from the UK as an instructor, and was not sure how to approach such a distinctively American event, but I need not have worried: in walked Lynne, dressed as a witch, putting me at my ease and making me feel at home.

I have never met a graduate student quite like Lynne. She overshadowed her peers with her enthusiasm, hard work, and achievements. When she asked Tom Shemanske (who later became her advisor) to put on a course in class field theory, he responded by giving her some book titles and telling her to give the course herself. So that year’s Dartmouth students, and I, learned CFT out of Janusz’s book from lectures by Lynne. She was still, even to this year, regularly ribbing me about the qualifying exam which Tom and I gave her in number theory, which lasted a couple of hours though we knew from the first minutes that she would pass.

As well as working hard at mathematics, Lynne was the social focus of the Dartmouth graduate students. She instituted a weekly breakfast for faculty, cooked by the students in the common room, which ran from 10 a.m. to noon on a weekday. She also regularly turned her office into a barber’s shop and cut the hair of many of the other students—and some staff, though in my case she came to my apartment so that the proceedings could be overseen by my baby daughter. Lynne was one of her first babysitters.

Another of Lynne’s extra-curricular activities was making models of unusual objects out of satin. I have a cactus made by her, and she once managed to fly to the West Coast to visit her father carrying a life-sized parking meter (made of satin) as a gift. And at a party at her house in rural New Hampshire, she had to warn guests visiting the bathroom that one of the two toilets in there should not be used—it, too, was white satin.

The conferences and workshops which Lynne organized were distinctively different. The “Building Bridges” series which she ran every couple of years after her move to Europe, following a pattern she had set with a similar series in the US, were a bridge between the US and Europe and also a bridge between theoretical work on automorphic forms and more explicit or computational methods. As I saw for myself in the two of these I lectured at (Aachen 2012 and Bristol 2014), these meetings were characterized by a refreshing and stimulating atmosphere, which were truly inclusive and diverse, with participation including inexperienced people as well as big names, those from small colleges and top research institutions, and above all, well-balanced between female and male, among speakers and students. This is just one example of the service which Lynne gave to the community. Another is the quality of her reference letters: I remember one such, written by her about a younger colleague’s teaching, as being by far the best teaching reference I have ever read, not in how positive it was (though it was positive), but in the way that it told the reader everything they needed to know about the candidate as a teacher, rather than repeating generalized platitudes.

Lynne and I did not meet in person between my leaving Dartmouth in late 1984 (I last saw her driving away in the snow with my washing machine in the back of a van) and her arrival in Bristol in 2007, where by chance I was visiting for a year. That year gave us the chance to renew our friendship, which continued right up until this year. Whenever I visited Bristol we always met up for dinner, usually at the Lido (she always had scallops and Pedro Ximenes ice cream) so that she could go straight on to the pub quiz next door at the Victoria; but when I was there last week, the place seemed empty and quiet without Lynne. I will miss her.

Years at Boulder and the NSF

By Eric Stade

Lynne Walling was captivated by mathematics that’s beautiful, and by beauty that’s mathematical. Here at the University of Colorado Boulder, we came to expect and to appreciate her exclamations of “Ganz schön!,” which she would frequently declare in response to a bit of mathematics that she found particularly beautiful or elegant.

Lynne was equally enthusiastic about sharing this captivation with others. She was driven to impart her passion for mathematics on learners at all levels—students in service courses, math majors, mathematics graduate students, fellow mathematicians.

When Lynne arrived at Boulder, in 1990, the department was in the beginning stages of a large-scale, still-ongoing effort in course and curricular reform, especially at the lower level. Lynne became an active force behind these initiatives, both as a Mathematics Department “private citizen” and in her roles as undergraduate chair and, later, department chair. Culture change requires commitment and energy, and Lynne brought both of these, in substantial amounts, to our reform endeavors.

Through these and a variety of other enterprises—creation of a professional development series for math graduate students, efforts to encourage and support women in mathematics, and so on—Lynne showed an unstinting dedication to helping others learn and appreciate mathematics, and thrive in the mathematical community.

Lynne left our department for greener pastures in 2007, but the impact she has had on us, here at Boulder—particularly on our educational mission—persists. I know she’s had similar impacts throughout her journey in this world, and I hope her pastures are even greener in the next one.

Eric Stade is a professor of mathematics at the University of Colorado, Boulder. His email address is stade@colorado.edu.

By Kathy Merrill

Lynne Walling is one of my heroes. She was smart, creative, brave, generous, fun, and unapologetic. Her strong passion for mathematics was matched by an equal passion for living life boldly and on her own terms. No task was too daunting for her to take on, whether in mathematics, administration, or house reconstruction.

I met Lynne when I spent a sabbatical year at the University of Colorado from 1991 to 1992. I am a harmonic analyst, and was at the time working on questions in ergodic theory. In spite of my lack of proper background, Lynne generously invited me to collaborate with her on a project studying sums of squares over function fields.

Jacobi and Hardy solved the classical problem of counting the number of ways an integer can be represented as a sum of $k$ squares for small $k$ by examining Fourier coefficients of powers of the classical theta function. Lynne proposed using analogous techniques to count the number of ways a polynomial with coefficients in a finite field can be represented as a sum of $k$ squares with restricted degrees. The classical theta function would be replaced by a function field analogue. We carried out Lynne’s proposal by first finding an inversion formula, and then transformation formulas under the full modular group for this theta function. Using the inversion formula to move to a fundamental domain, we were able to find recursive formulas for the Fourier coefficients. This led us to the representation numbers in closed form for polynomials of small degree. The other representation numbers that came out of the recursive relationships involved sums of Kloosterman sums, and for these we could only provide asymptotics MW93. In joint work with Jeffrey Hoffstein HMW99, we were later able to use Poincaré series to find elementary formulas for all of the representation numbers.

This is just a glimpse of a small bit of Lynne Walling’s mathematics. Other contributors will discuss more of her impressive body of work. But even beyond her many papers and talks, Lynne substantially reshaped the mathematics community by enabling so many nontraditional mathematicians to succeed. She did this through friendship and teaching, as well as formal outreach efforts from her leadership positions.

Lynne’s own mathematical career had a nontraditional start: she dropped out of college, worked some low-paying jobs, then returned to get an accounting degree, before graduate school at Dartmouth. In addition, she faced the onslaught of small slights and unnecessary obstacles that are all too often thrown at women mathematicians. Lynne survived because she was talented, worked hard, and loved mathematics. She knew the importance of showing toughness and confidence, something I needed to learn from her.

Teaching was central to Lynne’s work, and her approach reflected her own experiences. She knew that potential mathematicians benefit from the chance to develop mathematics on their own early on. Nontraditional students, in particular, thrive under conditions of challenge and support rather than either coddling or cutthroat competition. Based on this, she developed discovery activities for all levels of her classes, which the students could work on either individually or in groups, with restrained help from the instructor. Lynne shared these activities widely with colleagues, and constantly revised them based on their success in the classroom.

Lynne built community with both senior women mathematicians like Audrey Terras, and women just starting their careers. She offered the latter advice based on her own experiences, as well as concrete opportunities to give talks, write papers, and apply for grants. When she held leadership positions, such as department chair and NSF Program Officer, Lynne used her power to make sure women received fair evaluations, and also to establish programs that supported young mathematicians in general.

What I have written, while true, is much too serious to capture Lynne Walling. When I think of her, the image that comes first is playful and fun. I still have earrings she made for friends out of matchbox cars. When we were together and not doing math, we drank too much scotch and red wine. She helped my son learn to drive, by telling him to make a revving noise like vrrroooommm! when letting out the clutch so that he wouldn’t stall. This is the Lynne I will never forget.

Kathy Merrill is a professor emerita of mathematics at Colorado College. Her email address is kmerrill@coloradocollege.edu.

By Andrew Pollington

I first met Lynne Walling in 1991. BYU had organized a special year of research in number theory for the academic year 1990–1991, and Lynne was invited to give a talk in our seminar. The University of Colorado was, at the time, the strongest number theory department in the Mountain West and Lynne was one of its young stars. Lynne arrived in Provo and rapidly became an integral part of the special year, both giving talks to the number theory group and taking an interest in the ambitions and research of the BYU students. Her enthusiasm for Mathematics and joy for life were infectious. That year we were doing some remodeling of our house and we soon discovered another side to her talents. She volunteered to assist, and was soon in our basement, sledgehammer in hand, removing sheetrock and later helping to restore studs and put up the new walls.

One aspect of the special year was a week-long conference attended by experts in Diophantine approximation and analytic number theory. At the end of the meeting, those who had not yet had to leave attended a dinner at a bistro in Salt Lake City. Lynne came to the dinner equipped with a bag of toys, including a radio-controlled car which was raced up-and-down the table.

This was an eventful year for me and was certainly enhanced by my now firm friendship with Lynne. Over the next few years, we would see each other a few times at conferences or when I traveled to Colorado to give talks. In 1999, I was invited to become an NSF rotator, a program officer with main portfolio in number theory. At the end of that year, I needed to find a replacement, and thought of Lynne. With the agreement of Philippe Tondeur, the division director at the time, we invited her to come to NSF for an interview for the position. The day before the interview I received a call from Lynne telling me, “I have fallen off a ladder and have broken my arm …but I am still coming.” She duly showed up, arm in plaster, on time for the interview. In September 2000 Lynne replaced me as a program officer at NSF. During her tenure we met a few times at conferences, such as a meeting NSF funded and organized at IAS, on the Langlands program. We also had many long discussions by phone concerning various aspects of the job of a program officer. Lynne spent two years as a program officer at NSF, and brought her encouraging persona to the position and did a lot to encourage underrepresented groups in mathematics.

I took a year-long leave from BYU to spend 2006 in Bristol working at the Heilbronn Institute. I had already had a number of connections to researchers in Bristol and continued to visit the University and the Heilbronn Institute for the next few years. This meant I was in Bristol when Lynne started her position at the University of Bristol. We would often meet in the department during subsequent summer visits.

Lynne had always been very active in conference and workshop organization and she and several colleagues in Europe and the US started a series of workshops, “Building Bridges,” that brought together new mathematicians and mathematics students to learn more in depth about a chosen research topic. Lynne (whose idea this was) provided leadership and active participation. These were supported by several funding organizations including NSF. On the US side the NSF PIs have been: Olav Richter, Jennifer Beineke, Jay Jorgenson, and Jim Brown. These are just a few of those involved in these workshops. A meeting was scheduled for summer 2020, but was curtailed by COVID and has been postponed.

I last saw Lynne the summer of 2019. We worked clearing weeds in her garden, and talking about mathematics. Her death came as a great shock to me and I will certainly miss her. She was a real star, mathematically and through her encouragement of others to take up and participate in the joy of mathematics.

Andrew Pollington is a program director at NSF (Algebra and Number Theory). His email address is adpollin@nsf.gov. These opinions are my own and do not in any way reflect the opinion of the National Science Foundation.

Years at the University of Bristol

By Jonathan Keating

Lynne Walling moved to the School of Mathematics at the University of Bristol in 2007, establishing a new avenue of research in automorphic forms, theta series, and Hecke operators. She was highly active in the international community in these areas, being closely involved in raising funding for, and organizing, several major workshops and postgraduate summer schools. Lynne had previously been a program officer at the NSF and she wrote the best end-of-grant reports I have encountered.

Lynne was a truly outstanding teacher, introducing several new courses and being a key contributor to redesigning the curriculum. She was extremely popular with the students, who could sense her commitment and dedication to their education.

Lynne was also willing to take on leadership roles. She was for several years the head of the Pure Mathematics Group in Bristol. Her fierce protectiveness of, and loyalty to, members of the group were legendary. She also went out of her way to befriend and mentor new faculty members. Lynne felt passionately about issues relating to women in mathematics. She was a catalyst for attracting excellent women mathematicians to Bristol and she influenced many people’s thinking on this, including my own.

Finally, Lynne was a distinctive character in the School. She was passionate in debate and unflinching in challenging policies she disagreed with (especially those coming from outside mathematics). She was also kind, generous, funny, and sociable (she rarely missed a post-seminar dinner), nurturing many deep friendships. It says a great deal that, when the end came, she was cared for, and finally laid to rest, by her mathematical friends.

Jonathan Keating, FRS, is a professor of mathematics at the University of Oxford. His email address is Jon.Keating@maths.ox.ac.uk.

By Jonathan Robbins

When Lynne arrived in Bristol in 2007, it was like a breath of fresh air, or rather, a gale. She was fearless in speaking up for what she believed in, and was especially supportive of junior colleagues, delighting in their successes.

Lynne and I had many occasions to work together when I became head of school and she became director of the Institute of Pure Mathematics. For her, it was a job she had done before (and she had been chair at Boulder, of course). I was the newbie. As a caricature of our relationship, I would cast myself as a newly licensed driver, nervously gripping the steering wheel of a vehicle of unaccustomed size. Lynne, sitting in the seat next to me, is, by turns, a wonderfully irreverent and distracting raconteur, a would-be joyrider urging “faster, faster,” and a somewhat cross driving instructor informing me that over the last mile I would have failed my driving test. In reality, she gave me much wise counsel and encouragement, and I will always be grateful.

Jonathan Robbins is a professor of mathematics at the University of Bristol. His email address is J.Robbins@bristol.ac.uk.

Mathematical Contribution

By Rainer Schulze-Pillot

I met Lynne first when she was about to finish her doctoral thesis and was impressed by her energy, temperament, and enthusiasm. Over the years we met many times at various places in the world and this impression never changed. A central theme in Lynne’s research activity was the theory of integral quadratic forms and their theta series, in particular the difficult technical questions that arise when one tries to make general results as explicit as possible. To try and make the readers feel some of the fascination that this classical but indeed quite technical subject had for Lynne (and also for me) let me give a sketch of the problems and tools.

For a positive definite symmetric $m \times m$ matrix $A$ with integral entries consider the quadratic form $Q_A(x_1,\dots ,x_m)=\sum _{i,j}a_{ij}x_ix_j$ in the integral variables $x_1,\dots ,x_m$. Call two such forms $Q_A,Q_B$ integrally equivalent if $B={}^tUAU$ holds for an integral matrix $U$ of determinant $\pm 1$, and say they are in the same genus if $B\equiv {}^tU_{p,r}AU_{p,r} \bmod p^r$ can be solved for all primes $p$ and all positive integers $r$ with matrices $U_{p,r}$ as above. It is known that a genus consists of finitely many integral equivalence classes. If $r_A(n)$ denotes the number of integral vectors $\mathbf{x}=(x_1,\dots ,x_m)$ satisfying $Q_A(\mathbf{x})=n$, the theta series $\vartheta _A(z)=\sum _{n=0}^\infty r_A(n) \exp (2 \pi i n z)$ defines a holomorphic function of the complex variable $z$ in the upper half plane. It turns out to be a modular form of weight $k=m/2$ for a subgroup of the modular group $SL_2({\mathbf{Z}})$ defined by congruences modulo an integer $N$ (the level of the group) dividing $4 \det (A)$, i.e., for all matrices $\bigl (\begin{smallmatrix} a&b\\ c&d \end{smallmatrix} \bigr )$ in that group one has $\vartheta _A((az+b)/(cz+d))=(cz+d)^k\vartheta _A(z)$. Modular forms have deep connections to many problems of number theory and arithmetic geometry; in our case their analytic properties can be used to reveal information about the representation numbers $r_A(n)$. Consider for simplicity the space $M_k=M_k(SL_2({\mathbf{Z}}))$ of modular forms of weight $k>2$ for the full modular group $SL_2({\mathbf{Z}})$; the theta series $\vartheta _A$ belongs to this space if the matrix $A$ has even diagonal entries and determinant $1$. One has a splitting $M_k={\mathbf{C}} E_k\oplus S_k$, where $E_k(z)=\sum _{(c,d)\in {\mathbf{Z}}^2\setminus \{(0,0)\}}(cz+d)^{-k}$ is called the Eisenstein series of weight $k$ and where $f(z)=\sum _{n=0}^\infty a_n\exp (2 \pi i n z)\in M_k$ belongs to the space $S_k$ of cusp forms if $a_0=0$ holds. By a celebrated theorem proven by C. L. Siegel in 1935 a suitably weighted average over a set of representatives $Q_{A'}$ of the integral equivalence classes in the genus of $Q_A$ of the theta series $\vartheta _{A'}$ (called the genus theta series $\vartheta _{\mathrm{gen} A}$) equals $E_k$. In particular it is easy to calculate explicitly its Fourier coefficients, i.e., the weighted averages $r_{\mathrm{gen} A}(n)$ of the representation numbers $r_{A'}(n)$. Moreover, $r_{\mathrm{gen} A}(n)$ factors into a product over all primes $p$ of $p$-adic densities $\alpha _p(A,n)$ which measure numbers of congruence solutions modulo powers of $p$. On the other hand, the differences $r_A(n)- r_{\mathrm{gen} A}(n)$ are the Fourier coefficients of a cusp form and hence by a theorem of Deligne, previously called the Ramanujan–Petersson conjecture, of slow growth for $n \to \infty$, which gives an asymptotic formula for the representation numbers $r_A(n)$. Analogous results with more complicated formulation hold for general $A$.

A further generalization due to Siegel, again with analogous results, involves the number $r_A(T)$ of solutions in integral $m\times g$ matrices $X$ of the matrix equation ${}^tXAX=T$ for a $g\times g$ matrix $T$. The $r_A(T)$ give rise to a holomorphic function of several complex variables, called the Siegel theta series of degree $g$ of $A$; it is a modular form for a group of integral symplectic $2g \times 2g$ matrices. Finally, one may allow the vectors and matrices above to have coefficients in the ring of integers of a totally real extension field of finite degree of the rationals and obtain Hilbert resp. Hilbert–Siegel modular forms. One of the arising complications in all these more general situations is that one has to deal in them with more than one Eisenstein series of given weight, and that it is difficult to express the genus theta series explicitly as a linear combination of basic Eisenstein series.

On all these spaces of modular forms one has for each prime $p$ not dividing the level of the group a commutative algebra of linear operators, the Hecke algebra ${\mathcal{H}}_p$. On the space of cusp forms this algebra can easily be diagonalized with the help of a natural scalar product on the space; on spaces of Eisenstein series the diagonalization is a difficult technical problem. The deep connections between the eigenvalues of such Hecke operators on modular forms and their generalizations on one hand and eigenvalues occurring in arithmetic geometry on the other hand are the subject of the famous Langlands program. In our context, an approach originating in work of Eichler, Andrianov, and Freitag is the study of the action of Hecke operators on theta series. In many cases, the space generated by theta series is invariant under the Hecke operators. Expressing $T(\vartheta _A)$ for an operator $T$ explicitly as a linear combination of theta series one can then prove multiplicativity properties of the average representation numbers $r_{\mathrm{gen}A}$ as well as Siegel’s theorem in a purely algebraic and very elegant way Wal97. Many of Lynne’s papers belong to this circle of ideas, starting with her thesis Wal87Wal90 where she studied the explicit action of Hecke operators in the case of Hilbert modular theta series. In later papers, some of them with coauthors, she derived explicit formulas for this action in the cases of Siegel Wal06aWal08Wal19 and of Hilbert–Siegel theta series FW21, considered applications to representation numbers of quadratic forms MW93HW99HMW99, computed eigenvectors and eigenvalues of the Hecke algebra in spaces of Eisenstein series Wal17aWal17b, and proved various auxiliary results which are also of independent interest for the various types of modular forms involved; see, e.g., SW93bSW93aSW95HW02Wal06bCW07Wal13Wal17b. In one of her last papers she solved the above-mentioned problem to find an explicit expression for the genus Siegel theta series as a linear combination of basic Eisenstein series Wal18. The problem had been around unsolved ever since Siegel’s groundbreaking papers from the 1930s, and she was particularly proud of this achievement. With all these results, Lynne left a mark in this favorite subject of hers.

Rainer Schulze-Pillot is a retired professor of mathematics at the Universitat des Saarlandes. His email address is schulzep@math.uni-sb.de.

By Solomon Friedberg

I first met Lynne when we were undergraduates at UC San Diego, and in later years when we crossed paths we always had that wonderful sense of seeing someone you’ve known and been friends with for a long time. We really got to know each other after she received her PhD from Dartmouth with Tom Shemanske. Our connection was a shared interest in theta series. These series provide a systematic way to construct automorphic forms out of certain geometric or algebraic information. Lynne’s work on theta series began in her 1987 thesis “Theta Series Attached to Lattices of Arbitrary Rank” Wal87 and her interest in them extended throughout her career—the latest paper FW21, with Dan Fretwell, is “Hecke operators on Hilbert–Siegel theta series.” Since these same functions appeared in my thesis, Lynne and I had a natural mathematical connection.

Figure 3.

Dr. Lynne Walling at Inspiring women at Bristol University | International Women’s Day 2020.

Theta series can be studied either as functions (following Eichler and Siegel, among others) or representation-theoretically (following Weil and Howe, among others). Lynne’s approach was function-theoretic. Since I had a foot in both areas, as our careers progressed I was pleased to talk with Lynne, occasionally as a sort of an interpreter and more often simply as a scholar who respected and found value in both points of view. We also both cared about students and teaching, and valued a certain openness to mathematicians who contributed in different ways. With these commonalities and Lynne’s energy, our meetings often led to intense discussions, about both math and about the profession.

Lynne was not only an engaged researcher who cared a great deal about mathematics, she was also a tremendous force in organizing events. Dorothy Wallace had begun an automorphic forms workshop in the 1980s that was specifically welcoming to scholars studying automorphic forms from all points of view, and Lynne soon became involved in the organization of the series. In the 1990s, I attended and spoke at three of these conferences that Lynne organized or co-organized, and she was also kind enough to invite me to Boulder to give lectures on several occasions. It was fun to catch up with her; she would always have a great deal on her plate but find time to introduce me to a graduate student or postdoc. After she moved to England, Lynne helped create and organize a new series, the EU/US Summer School on Automorphic Forms and Related Topics. At the second of these summer schools, in 2014, I had the opportunity to co-teach a mini-course with Jim Cogdell, and with Ameya Pitale as assistant, on the Langlands Program. Lynne and her co-organizer Jennifer Beineke were very particular about the mini-course. They wanted to be sure that it was at the right level for the participants. I appreciated the guidance a great deal.

The theta functions that Lynne studied come in many flavors that are different; for example, there can be different underlying discrete objects that one sums over, and geometric configurations of different dimensions. Lynne showed that one may systematically understand spaces of theta functions attached to lattices by Hecke theory, and this understanding has ramifications.

For example, in her paper Wal97 and in her paper HW99 with Jim Hafner (of blessed memory), she gave an elegant new proof of Siegel’s famous mass formula for an integral quadratic form, computing the representation densities explicitly, by combining Hecke theory for Siegel theta functions with computations of Eisenstein series. In many other works, she showed that theta functions behaved in specific, understandable ways, from extending the Eichler commutation relation to higher degree Siegel theta series to using them (in joint work HMW99 with Hoffstein and Merrill) to count sums of squares over function fields. Her research, spanning more than three decades, constitutes a lasting contribution to the field.

Lynne’s love of mathematics and her dedication to scholarship were an inspiration for a generation of students, and she was a role model for a generation of female scholars, leaders, and teachers. I was privileged to be one of her many math friends, one with a particularly long connection. Lynne was a one-of-a-kind person, deeply caring, a committed teacher, full of energy and good cheer, an excellent scholar, and profoundly dedicated to mathematics. Her passing is a loss for our profession and, for all of us who knew her, a personal loss as well.

Solomon Friedberg is a professor (McIntyre Endowed Chair) of mathematics at Boston College. His email address is friedber@bc.edu.

By Jeffrey Hoffstein

I first met Lynne Walling during a trip to Boulder in the early 90s and liked her immediately. We didn’t engage mathematically until the special year on automorphic forms at MSRI in 1994–1995. I knew that Lynne liked thinking about sums of squares, and I had recently been spending some time working over the rational function field, and knew that there were no cusp forms when the level was 1. We ended up computing the spectral expansion of powers of the function field theta function, and using this to find exact formulas for the number of representations of an element as sums of a given number of squares. We could get exact formulas because in this context there are no cusp forms, so the expansion is very simple. The trouble was, I was supposed to be in charge of making sure the MSRI program ran smoothly, so I had a lot of trouble focusing. Luckily, this was no problem for Lynne! She just drove me like a merciless tyrant until the project was done. And it was fun being driven by this particular merciless tyrant. She loved what she was doing and was an irresistible driving force. I wish I had seen her more over the years and miss her tremendously.

Jeffrey Hoffstein is a professor of mathematics at Brown University. His email address is JHoff@brown.edu.

By Larry Gerstein

I first met Lynne in the fall of 1985, when I was a visitor at Dartmouth College and had the opportunity to teach a graduate course on the theory of quadratic forms. Lynne was in the class, and her talent and intensity were immediately evident. At the time she was hard at work on her dissertation research under Tom Shemanske, under whom she had already been introduced to the basics of quadratic forms.

The focus of her research was on quadratic forms over algebraic number fields, particularly on their theta series: functions that encode the representation data of those forms. This was all new to me, and so I was astonished and delighted to discover that from time to time I could tell her something about the mechanics of lattices over rings of algebraic integers that she found useful. Lynne had a particular interest in connections between lattices and their duals, and as I look back over her career I see that this interest continued to bubble up.

Over the years she showed herself to be a valued collaborator with many others on a broad range of topics, for instance the action of Hecke operators on Siegel modular forms, but she retained her interest in quadratic forms. I am particularly struck by her applying her analytic techniques to the context of quadratic forms over global function fields. Just to give one example, I cite her demonstration (with her collaborators) that every polynomial over a finite field can be represented as a sum of four squares, and going on to count the number of ways this can be done by summands of bounded degree.

Though her move to England limited our interaction, I did see her at occasional conferences, for instance at Oberwolfach, and we continued to exchange emails on mathematical mysteries of interest to both of us. She never lost her sparkle, and I’m saddened by her death.

Larry Gerstein is a professor emeritus of mathematics at the University of California, Santa Barbara. His email address is gerstein@math.ucsb.edu.

Passionate and Supportive Outreach

By Audrey Terras

Probably I first met Lynne when she was a graduate student at Dartmouth and subsequently I attended many of the meetings she organized. In fact, many of them were continuations of a meeting that my student Dorothy Wallace organized at MSRI in April, 1987. The name of the conference ultimately became Workshop on Automorphic Forms and Related Topics. It still exists. See the website for the 34th meeting. Lynne kept the spirit of these meetings which was friendly and open to all. The meetings were distinguished by having a large number of women speakers, something that was not true of meetings on the subject when I was a young mathematician.

She came to my 60th birthday party conference and gave a talk on an uncomfortable subject “Women in Mathematics: Participating, Surviving, and Succeeding.” It is on her website. I recommend it. The talk includes 11 ways harassment and discrimination are manifested. The most all-encompassing is “perpetual condescension.” Then it lists 23 survival strategies. My favorite is “prove theorems.” Finally it lists 11 suggestions for the math community to improve matters. The talk should be applied not just to women but to everyone on the receiving end of discrimination, particularly minority mathematicians.

It would be an example of abuse not to mention that Lynne’s mathematical work was indeed impressive. She was not afraid to work on higher-rank automorphic forms, a subject that is not for the faint of heart. Her explicit Siegel theory papers give a new and completely explicit version of Siegel’s important formula for the weighted average of the representation numbers over isometry classes of lattices in the genus of $L$. The joint work with Jeff Hoffstein and Kathy Merrill on function field analogs of automorphic forms showed that, as in the classical case, the main term of the number of representations of a number as a sum of $k$ squares of degrees $< m$, is given by the Fourier coefficient of an Eisenstein series. This implies that the representation number is nonzero for $m$ sufficiently large. Earlier formulas were not easily seen to be nonzero. Serre had only proved the non-vanishing in the case $k=3$.

Audrey Terras is a professor emerita of mathematics at the University of California, San Diego. Her email address is aterras@ucsd.edu.

By Jennifer Beineke

Lynne was a dear friend—funny, caring, and a good listener. Whenever I visited the UK in recent years, we would have fun reconnecting, usually meeting up at a train station. I’d find her waiting for me in a corner, reading a mystery (both of us being lovers of detective fiction). After our day together, she would send me off with a bag of books she had finished, for the rest of my trip.

I first met Lynne in 1997 at the 11th Annual Workshop on Automorphic Forms and Related Topics (AFW), which she organized at the University of Colorado Boulder. The conference was advertised as “small and friendly.” As a nervous graduate student, I thought it would be a good opportunity for presenting my research, and the workshop lived up to its promise. Lynne was a force to behold as organizer, not only running everything adeptly, but taking the junior researchers under her wing, making sure they interacted meaningfully with the senior mathematicians. I was amazed when she took the time to speak with me and introduce me to others to discuss research. She also invited me to call her in the future if I had questions or concerns. That was the beginning of our friendship.

Before she left for England, Lynne organized five more of these annual workshops, continuing to mentor the junior members of the number theory research community. In 2003, she introduced panel discussions into the meeting format, on topics such as research collaborations, applying for grants, publishing, and encouraging and retaining women and other underrepresented groups. When Lynne moved to Bristol in 2007, it was hard for her to say good-bye to the AFW. Then, at the 2010 conference “Durham Days on Modular Forms,” organized by Jens Funke, I remember her moment of inspiration. We were sitting over pizza and wine, bemoaning the lack of an AFW in Europe, when it clicked—Why not start one? In her inimitable Lynne way, she made it happen, and the “Building Bridges: EU/US Summer School + Workshop on Automorphic Forms and Related Topics” was born.

Collaborating with Lynne on Building Bridges, I saw that she didn’t just want to recreate the AFW in Europe—she wanted to foster new connections. She created partnerships across continents, finding funding from agencies in both the United States and Europe to support international graduate students and junior faculty. She created new connections between advanced researchers by stipulating that each mini-course be led by two specialists who had never collaborated. This arrangement also provided the students with different perspectives on a topic. Lynne added panels, poster sessions, and “speed talks” to the meetings. And, of course, the social events! Lynne was the life of the party.

At the 2014 Building Bridges workshop in Bristol, ahead of current trends, Lynne wanted to bring the lack of diversity in mathematics to everyone’s attention. For the panel that year, we therefore chose the topic “Encouraging and supporting diversity in the mathematics community.” We had hoped for a mix of panelists from the United States and Europe, but could only find one European participant—Nils Skoruppa—willing to serve. The other five were all American. Though the resulting discussion was tentative, it was a start, and thanks to Lynne’s perseverance, the conversation has continued.

Always nearest to Lynne’s heart, however, were the opportunities she created for junior mathematicians and women. At the workshops, many women (including myself) found we had been given more time to speak than we had requested. Lynne pointed out that women never asked for the longer slots—but men did. I also learned, behind the scenes, that the friendly, supportive atmosphere was due in no small part to Lynne keeping a close eye on the senior mathematicians. If one of them said something at the meeting that could have been viewed as disparaging or critical, she immediately took that person out to the hall to “have a word.” With a fierce passion, Lynne made sure everyone was treated with kindness and respect.

Like many others, I owe an enormous debt of gratitude to Lynne and miss her deeply. When reflecting on our time together, I have found some solace in watching her online talks: “Women in Mathematics: Ambition in an ambivalent society” (2015, https://www.youtube.com/watch?v=-FQWpfZIPT8) and her University of Bristol’s Best of Bristol Lecture, “The art and beauty of pure mathematics” (2016, https://www.youtube.com/watch?v=XoKIfCgiA_w). Lynne found inspiration in music, and enjoyed quoting one of her favorite singers, Ani de Franco, in some talks. To honor Lynne’s memory, I hope each of us will continue to mentor and advocate for others the way she did, and, in the words of de Franco, be “willing to fight.”

Figure 4.

Building Bridges 2. Conference photo

Jennifer Beineke is a professor of mathematics at Western New England University. Her email address is jbeineke@wne.edu.

By Samuele Anni and Jim Brown

Most mathematicians in the United States that work in the area of automorphic forms are aware of the annual Automorphic Forms Workshop (AFW). This is a long running and well-established workshop; the 34th AFW will be meeting in Spring 2022. Lynne was an active organizer and participant in the AFW while she was a faculty member in the United States and was known for promoting early career researchers and student involvement in the AFW. Lynne was particularly focused on increasing female participation both in attendance and giving talks. In 2017 Lynne relocated from the University of Colorado at Boulder to the University of Bristol in the United Kingdom. This relocation was the starting point for Building Bridges: EU/US Summer School and Workshop on Automorphic Forms and Related Topics (BB). Lynne saw the benefit of the AFW to researchers in the US, particularly those early in their careers, and felt the model could be beneficial to researchers in the EU as well. Moreover, rather than just having a conference to bring together researchers, a summer school was included. Automorphic forms can be a difficult research area to break into for new researchers; the school was designed to allow a smoother transition for students with a desire to work in this area. “Building Bridges” refers to building stable connections, bridges, between automorphic forms research communities in Europe and the US, but it stands for more. It also refers to Lynne’s idea to “bridge” two instructors that had never worked together before for each summer school session and foster further collaborations among more senior researchers. It is also an occasion for seeding the future: PhD students have the chance of building connections, bridges for their tomorrow, and Lynne was always a strong support toward these achievements.

In addition to stellar mathematics, Lynne was instrumental in ensuring that BB included panel discussions and presentations on important topics such as increasing diversity in mathematics. Recently “speed talks” have been introduced to promote a fun and positive atmosphere for both first-time speakers and more seasoned ones.

Various prizes, selected personally by Lynne, were given out after each session of speed talks to keep it light and fun. BB is a testament to Lynne’s impact on the mathematics community, indeed during and after these events she was promoting and coaching early career researchers.

The first BB took place in 2012 at RWTH Aachen University in Germany and was co-organized by Lynne, Aloys Krieg, Martin Raum, and Olav Richter. The second BB was held in 2014 at the University of Bristol and was organized by Lynne, Jennifer Beineke, and Jonathan Bober; the third at the University of Sarajevo organized by Lynne, Jay Jorgenson, and Lejla Smajlović; the fourth at the Alfred Renyi Institute of Mathematics in Budapest organized by Lynne, Jim Brown, Gergely Harcos, Jay Jorgenson, and Árpád Tóth. Plans for the fifth BB were in place to be held at the University of Sarajevo in 2020 before the school and workshop were forced to be postponed because of the COVID-19 epidemic. While Lynne was always the driving force behind BB, the current organizers (Samuele Anni, Jim Brown, Jay Jorgenson, Almasa Odžak, and Lejla Smajlović) are determined to continue to realize Lynne’s vision for an inclusive and welcoming school and workshop in automorphic forms for years to come. We currently plan to hold BB5 at the University of Sarajevo in the summer of 2022. While still in the process of finalizing plans for BB5, we will certainly include a tribute to Lynne’s contributions to the mathematical community. We hope to see a large turnout of the automorphic forms community.

Samuele Anni is the maître de conférences at Aix-Marseille Université. His email address is samuele.anni@gmail.com.

Jim Brown is professor of mathematics at Occidental College. His email address is jimlb@oxy.edu.

Personal Remembrances

By Jeffrey Stopple

I first met Lynne at one of the very earliest Workshop on Automorphic Forms conferences, maybe 1988 or 1989. She called me afterward and informed me we were going to be friends, such a very “Lynne thing to do.” Before we knew it, we were organizing the workshops ourselves in Santa Barbara and in Boulder. In those days invitations went out by snail mail and we had to look up addresses one at a time in the printed AMS Membership Directory. Lynne was from the beginning adamant that the workshop be friendly and inclusive, and the language about that on the earliest Workshop website is still copied and pasted from year to year. We even discussed the idea that maybe the name was too restrictive—maybe it should just be the “Workshop on …and Related Topics.” I still have in front of me the very first ceramic mug, from the 6th Annual in Boulder in 1992—Lynne discovered ceramic mugs could be custom printed in China cheaply, but the minimum order was a case, vastly more than we needed. I’ve been “gifting” excess workshop coffee mugs ever since.

I was always impressed by Lynne’s independence and self-reliance. While teaching at St. Olaf in Minnesota, Lynne lived on a rural property with no indoor plumbing. When the outhouse was “full,” she described to me the process of digging a new pit with a backhoe, and dragging the old outhouse over to sit above it.

Lynne was my best friend for over two decades, but we drifted apart when she moved to Bristol and I got married. I can’t believe she’s gone. She will be missed.

Jeffrey Stopple is a professor of mathematics at the University of California, Santa Barbara. His email address is stopple@math.uscb.edu.

By Donna Janesky

Figure 5.

Lynne painting pottery from https://www.lynnewalling.org/.

My stepdaughter, Lynne Walling, was a truly unique individual. She had a true love of math, perhaps influenced by her father, Stuart, who had a lengthy career teaching math. But in addition to her math prowess, she was an expert in many other areas, and this expertise often came to her through self-learning. They say necessity is the mother of invention, and this was certainly true for Lynne. Need a new roof? A new dress, fence, garden, plumbing, iron bed? Lynne could do it. She always availed herself of the opportunities to learn new things, and quickly put her knowledge to good use. Those of you who knew Lynne are aware of her unique sense of style, fashioning her own clothes and surrounding herself with unique furnishings.

Lynne surrounded herself with plants and animals wherever she lived, planting lovely flower and vegetable gardens where her dog and cats could roam. And yes, even some chickens. “Au Naturale” comes to mind when remembering Lynne. There was no pretense or “artificial ingredient” injected into her joyous lifestyle. She truly loved what she did and spoke glowingly of her own mentors. She herself became a mentor and an example, especially to women entering this difficult field for women. Lynne gave 100% to her students, colleagues, family, and friends. She was truly one of a kind, and we were blessed to have her in our family.

Donna Janesky is Lynne Walling’s stepmother. Her email address is janesky40@comcast.net.

By Suzanne Caulk

Lynne Walling has said “As mathematicians we look at things differently, which means that we can produce things that other people aren’t going to, and that’s exciting”.⁠¹ Well, I would say, that Lynne looked at things differently than anyone I have ever met and that meant she did things that other people wouldn’t do and she was definitely exciting and fun to be around.

¹

from Dr. Lynne Walling’s web page at the University of Bristol.

✖

Lynne’s mathematics was focused on the beauty of the objects she studied, and she effectively conveyed that to her students. She was a creative person who found beauty in many things, and expressed herself in a variety of ways. When she took me on as her PhD student, I didn’t realize that together we would learn to tile her new bathroom, but we did!

One of the things Lynne was passionate about was diversity and justice within the mathematical and academic communities. This meant she took on leadership positions that required a lot of hard work because she believed this was how she could best help others and improve her community. Lynne’s efforts will live on in all of us who she mentored over the years.

Suzanne Caulk was a professor of mathematics at Regis University; her current affiliation is unknown. Her email address is scaulk@regis.edu.

By YoungJu Choie

Lynne left a lasting impression on me as a colleague and a friend with her strong but charming charisma since I met her for the first time at the special year program on Automorphic forms at MSRI, Berkeley, USA in 1994. In our generation, there were not many female mathematicians working on Automorphic forms, so that we naturally shared a looming anxiety, an uncertain, sometimes fearful future as inexperienced mathematicians at the early-career stage at that time.

Light drinking parties led by her with like-minded friends were always lively and enjoyable, full of life with her loud chatter. No one could stop her presence and charming charisma at all occasions. I am particularly grateful for her serving as the keynote speaker at the Memorial Workshop of the Foundation of Korean Women in Mathematical Sciences in 2005, visiting me and Korea several times afterward. I believe that even now Lynne may be somewhere talking about mathematics and other matters with her charismatic voice.

YoungJu Choie is a professor of mathematics at Pohang University of Science and Technology. Her email address is yjc@postech.ac.kr.

By Misha Rudnev

On the evening of Monday 10 May 2021, Lynne Walling phoned me, after having had her first, and only appointment with an oncology consultant earlier on that day. “I’m gonna die,” she said. “It sucks. I don’t have much time. I want a party on Friday.”

On Friday I arrived from my London flat at her Bristol home. There, I met some 30 friends, colleagues, and students, all in a similar state of disbelief. Lynne, too weak to engage in the mingling and beers, mustered her strength to have people follow her around the house, telling them to put their names on things they’d like to have after she was gone. She was matter-of-fact forcing on these arrangements as if she was making plans to cook jam out of the blackcurrants in the garden when they ripen.

Unflagging courage, directness, honesty, and generosity have always been among the defining characteristics of the person Lynne was. They largely accounted for the kind of mathematics that attracted her as a number theorist—explicit and constructive versions of classical questions in the theory of theta series and automorphic forms. They also laid foundational principles for her interactions with students, colleagues, and institutions. In response, students worshiped her; colleagues respected and trusted her; and institutions reckoned with, delegated powers to, and feared her.

Roughly half the time throughout her Bristol tenure that started in 2007 she headed the Pure Mathematics Division in the School. “I like being in charge of people,” she would tell me. In positions of power, she would invariably look down, only in a good way. She would always do everything she could to help people in positions of lesser rank or privilege. Quoting one of her colleagues, she wanted to lift people up, not stamp people down.

As a feminist mathematician and true artist in all aspects of her life, she has become a role model to a whole generation of scholars, both men and women. Since 1998, she gave some 20 invited presentations on Women, Diversity, and Education. Her commitment to matters of equal opportunity, justice, and equality was so contagious that it reached even the most hardened cynics.

One of the exclusive luxuries in today’s world rank-and-file is being in position to say no. Being uniquely fearless, Lynne could say no to God himself and face the consequences. This goes at least as far back as an incident of her giving an adult malefactor a stern lecture as to why one should not feed the bears in the Yellowstone National Park when she was seven. (Was this also an early example of her later universally renowned excellence in teaching?) When she had to face death, she stood bold, undefeated, and slightly sardonic. Of all the many things and experiences she taught and shared with me, this may be the most precious and memorable one.

Misha Rudnev is an associate professor of mathematics at the University of Bristol. His email address is m.rudnev@bristol.ac.uk.