In Memory of Peter Linnell

Peter Linnell: an appreciation by those who knew him

Amanda Welch (Ph.D., Virginia Tech, 2019; currently Assistant Professor of Mathematics, Eastern Illinois University)

Dr. Peter Linnell was the advisor on my master’s thesis and the professor of my favorite class in graduate school, Abstract Algebra. He was a wonderful teacher, showing both a great love and knowledge of the subject, and I’ll always be thankful for the tremendous amount of help he gave while I was prepping for my Abstract Algebra prelim. Dr. Linnell was a staple in the Virginia Tech math department, and he made my time there much richer. I’ll always remember the support he provided at the start of my mathematics career, and I know VT won’t be the same without him.

Mike Puls (PhD, Virginia Tech, 1995; Peter Linnell’s first PhD student; currently Professor of Mathematics, John Jay College of Criminal Justice)

In Peter’s earlier years, he was a promising chess player with an extremely sharp playing style. In 1973, when he was 20, he was ranked the 17th best chess player in England. However, he gave up chess in order to pursue his university studies in mathematics.

The one thing I remember most about Peter’s classes was how fast he returned homework. We would turn our assignments in at the end of class at 9:50 and by 10:15 are work was graded and returned to our mailboxes!

I’m always amazed at how many people at VT think Peter was an algebraist, and the math department’s website still lists him as one. In reality he was a harmonic analyst. He did have a few papers that were purely algebraic, but most of his work involved analysis. Specifically, he applied techniques from ring theory to problems in geometric analysis. One such problem where he made many contributions was the strong Atiyah conjecture, which was a natural progression of his work on the classical zero-divisor conjecture.

A big problem in harmonic analysis is the HRT conjecture, which states that the set of any finitely many time-frequency shifts of a non-zero square Lebesgue integrable function is linearly independent. By accident, Peter made a major contribution to resolving this conjecture in his paper von Neumann algebras and linear independence of translates. In fact, every talk I have ever attended concerning the HRT conjecture, the speaker usually says something like “Linnell’s result is the gold standard.’’ I then comment from the audience ,that he obtained the result by accident when he was looking at a zero-divisor-type problem.

Peter knew an enormous amount of mathematics. I would call him a ring theoretic sledgehammer! I think this is how his research career evolved. He started in algebra, mostly in ring theory. Then he got interested, along with his VT colleagues Dan Farkas and Robert Snider, in the classical zero divisor conjecture for group rings. Group rings are purely algebraic objects. However another way to thing of them is as smooth functions with compact support on a discrete group. Somehow Peter must have stumbled across l2(G) and from there von Neumann algebras. People who work in the area of von Neumann algebras are considered to be operator algebraists. In reality they are functional analysts since the only thing those people know about algebra is the definition of an algebra. Peter of course knew that an algebra is also a ring and used his vast knowledge of ring theory in attacking problems with von Neumann algebras.

Peter was tricky to figure out. He seemed like a mild mannered math professor. However I have copies of some chess games that he played in the early 70’s and his chess style was hyper aggressive, he definitely went for his opponent’s jugular. People thought he was a vegetarian, but I saw him eat steak; Heath Hart was a witness to this, too. Of course he can be considered an algebraist but some people might think he was an analyst!

One fact that everyone agreed on was that, whether algebraist or analyst or both, Peter was a mathematician of the first rank.

On February 2nd, Peter and I had our paper, "The two-sided Pompeiu problem for discrete groups," accepted by the Proceedings of the American Mathematical Society, Series B. I was the corresponding author and so the journal sent me the news but didn’t send it to Peter. I sent him an email to tell him the good news and I was surprised when I didn’t hear back from him. When I read my email on the morning of February 3rd, I found out why he hadn’t replied.

Jackson Walters, BS, Mathematics, Virginia Tech, 2013; PhD, Mathematics, Boston University, 2019)

Dr. Linnell and I spent some time together during the end of my undergraduate in 2012 or so. He taught me representation theory, all the way up to the Peter-Weyl theorem and harmonic analysis. I learned a lot from him.

I fondly recall days with a handful of other young mathematicians where he explain representations using absurdly large letters, especially ρ. At first I found this to be a mistake, but later appreciated as a feature, and of course stole the style. I also abbreviate representation as rep’n, which I didn’t know one was “allowed” to do, and I’ve carried that style to other words as well (like int’l).

The wonderful thing about learning about Lie algebras and groups with Dr. Linnell was the way one could go all the way to the nuts and bolts, and really just write down and look at all, say, 2- dimensional Lie algebras, but also pave the way for high abstraction down the road.

We also did an undergraduate research project together, my first in mathematics. We studied ideals in a non-commutative ring, the group ring RG = R < x, y >, where G here is the free group on two symbols. It’s pretty far out (like ping pong in outer space far out), and there are a lot of representations. I believe I found a few ideals and bounded their size using some computer algebra. I presented the research at a conference in Ohio, the Young Mathematicians Conference at Ohio State, and at the Layman prize competition. He introduced me to the research network MathSciNet, and essentially helped me get started doing math research.

During a long drive recently, I came to appreciate that project even more. The space of ideals in rings is something I enjoy thinking about, and can be quite horrifying depending on the ring one is interested in. A group algebra (if one is working over a field) has many ideals, and of course one is interested in the possibility of universal division, i.e. the nonexistent of zero divisors. I didn’t focus too much on that.

I wound up finding the commutator ideal, and came to appreciate the duality between the simplicity of the notation of an object and the intricate details of its actual natural, be it a quad tree to a lattice, or what have you.

I was very sorry to hear of his passing. Peter Linnell was a kind, helpful person and will surely be greatly missed by the Virginia Tech and Blacksburg community.

Margaret McQuain, VT Math Department Instructor for decades, now retired

I met Peter Linnell in England in the 1970’s when my then-husband, Robert Snider, was on Sabbatical there for a year. Robert got Peter interested in coming to Virginia Tech. When Peter moved here he did not have or want much furniture. We loaned him a card table and chairs. But he needed a lamp. At the time I only had a Cookie Monster lamp that belonged to my daughter and he said he wanted it. We loaned it to him, thinking he would get a decent lamp soon. But he kept it for 20 years and then one day out of the blue he brought it to school to return it! I thought he had gotten rid of it years ago.

It is fair to say that Peter was one of nicest people you could know. He will be sorely missed.

Kelli Karcher, MS in Mathematics under Peter Linnell, VT, 2013; Advanced Instructor, VT Math Department

For those who did not know Dr. Linnell, he first joined the Virginia Tech faculty in 1983. He will be remembered fondly by his students and colleagues as an amazing teacher, a well-respected researcher, and the enthusiastic director of the Virginia Tech Regional Math Competition (for which he wrote questions and organized since 1999). He loved classical music, chess, running, and the Manchester City soccer club. (And that’s Manchester City, not Manchester United!!) He was a sweet and gentle person who was well liked by all who knew him. He was a beautiful human being, and I cannot imagine a day going by where I will not miss him.

We who were his students will always cherish memories of research meetings and trips to the grocery store and algebra class. We remember how he would be unable to recognize the car that transported him every week to the store, but could recall the weather in Blacks- burg on this day 17 years ago and the code for every vegetable at the grocery store. That we chuckle when we remember how he was never angry at anything or any student...the exception to this anger was himself when he lost something like his keys or Hokie pass- port! Upon which occasion you could hear him muttering under his breath. Finally, we will recall his British pronunciations of the Greek letters beta (BEEETAHHH) and theta THEEEEEEtah) and epsilon (epSIIIIIIIIIlon) bringing smiles to our faces.

Sam Eastridge (PhD in Mathematics under Peter Linnell, 2017; currently Assistant Professor of Mathematics, Brevard College)

The news of Dr. Linnell’s death is very sad. I’m sorry to hear it, but I know he has been struggling for a while. The last few emails I sent him he said he was not doing well, but I didn’t realize how bad it had become.

I will certainly look back with incredible fondness on my time with Dr. Linnell. I can certainly say there is no mathematician in the world I tell more stories about than Dr. Linnell. I wonder how much time I spent waiting for him to get those plastic produce bags open, and oh the disappointment when there was no sockeye salmon! I will also never forget that when he broke his collarbone, he proceeded to teach left-handed as if he had done it his entire life. Then, as he recovered, he would stre-e-e-e-etch to reach the top of the board with his right hand. He refused to just start halfway down the board. And who could count the number of times he had to explain to me that my proofs were totally incorrect and I was thinking about everything wrong. And he did this with great kindness!

Peter Linnell was my advisor for my PhD studies, and I considered him a good friend. He was one of a kind, and I can say even more confidently that I can with most people that there will never be another like him. I often played chess with other graduate students on my phone, and all I had to do was hand him the phone and ask which move to make to ensure my victory. He was always up to date on the latest computer world chess championships, and kept me posted on the latest chess games between [the chess-playing computers] Stockfish and Houdini. Dr. Linnell also followed the weather closely, and if you have ever considered talking about the weather “small talk,” you haven’t talked weather with Dr. Linnell.

I often took him on trips to the grocery store as he never got a driver’s license, and he loved talking about his days road biking in the mountains of Europe. He was passionate about his exercise, especially running and biking, and I believe his resting heart rate was around 25 bpm. His teaching style was methodical and surprisingly easy to follow, and I cherish my memories of Abstract Algebra in my second year as a graduate student. As his advisee and as a student in his class, I always felt that he cared about my success and about doing his job to the very best of his ability. I will always be grateful for the time I got to spend with Dr. Linnell, and I will miss him greatly. Thank you, Dr. Linnell.

Peter Haskell, Mathematics Department since 1988, Professor since 2003, Department Head, 2007 to 2018

Many years ago, I asked an expressive undergraduate advisee who was in Peter’s class what she thought of him. She said, ”He’s a trip! But he’s a GOOD teacher.” (This view was shared by many of his colleagues.)

Peter became the Director of the Virginia Tech Regional Math Competition (the VTRMC) in 1999, and under his leadership it achieved phenomenal growth, in both numbers and ge- ographic reach – making the adjective “Regional” an anachronism. He took note of unusual performances, particularly high scores by high school students, and from time to time he’d call my attention to the impressive professional achievements of mathematicians who had first come to his attention through their work on the VTRMC. 

You can read more personal tributes on the Math Department's Facebook page.