Dr Kirill Mackenzie, 1951-2020

Dr Kirill Mackenzie, a long-serving staff member in the School of Mathematics and Statistics, died on 2 May 2020, aged 68. The following obituary was written by his colleague Professor David Jordan for the London Mathematical Society.

Dr Kirill Mackenzie

Kirill was born, as Charles Howard Mackenzie, in Melbourne in November 1951, the only child of Hamish and Elizabeth. His first name was his own later addition.

He was educated in Melbourne, graduating from Monash University in 1973 with a BSc and in1979 with a PhD in differential geometry, under the supervision of Juraj Virsik. Between 1979 and 1986 he held several tutorships, at Monash and the University of Melbourne, and a Queen Elizabeth II Fellowship at the ANU in Canberra. In 1982, midway through this Fellowship, he had a visiting position, for six months, in Sao Paulo, where he gave a series of graduate lectures in Portuguese.

His first book Lie groupoids and Lie algebroids in differential geometry, which included substantial original research, was completed in 1985 and published in the LMS Lecture Notes series in 1987. He moved to the UK in 1986, as a Senior Research Assistant in Durham, working with Philip Higgins on abstract Lie algebroids. Another fruitful collaboration around this time was with Ronnie Brown on double Lie groupoids.

From Durham, he visited two of the pioneers of his subject, Jean Pradines in Toulouse and Alan Weinstein in Berkeley. In Berkeley he also met Ping Xu, then a graduate student, with whom he would subsequently collaborate successfully on Lie bialgebroids and Poisson groupoids. He moved to Sheffield in 1989 to take up a Lectureship and was promoted, in 1999, to a Readership, the position that he held at the time of his death.

Dr Kirill Mackenzie at the poisson geometry conference in Hangzhou, 1999
Dr Kirill Mackenzie at the poisson geometry conference in Hangzhou, 1999 – image courtesy of Dr Iakovos Androulidakis

In the early 1990s, Kirill made several visits to the Institute Henri Poincare, including five weeks at the Centre Emile Borel during which he worked with Yvette Kosmann-Schwarzbach, with  ́whom he would exchange several further research visits. By this time the theory of Lie groupoids and Lie algebroids had been transformed through the emergence, in the work of Weinstein and others, of new examples arising in Poisson and symplectic geometry, including the Lie algebroid structure on the cotangent bundle of a Poisson manifold.

Kirill embraced these developments both in his second book General theory of Lie groupoids and Lie algebroids (2005), again in the LMS Lecture Notes series, and in his research on a Lie theory for double and multiple Lie groupoids and Lie algebroids and its application in Poisson geometry. He referred to this theory as “multiple Lie theory”but Ted Voronov calls it “Mackenzie theory”. A highlight is his paper on double Lie algebroids that was published by Crelle’s Journal in 2011.

Kirill’s many invitations as a plenary speaker included three to the biennial international conferences on Poisson Geometry and five to the annual Workshops on Geometric Methods in Physics at Bielowieza, Poland. He was proud to have given invited series of lectures to young researchers in Kolkata in 2008 and 2012, at the Bialewie ̇za workshops in 2012 and 2013 and in Colombia in 2013.

Dr Kirill Mackenzie

Kirill was a committed teacher with firm views on the curriculum. At Sheffield he introduced several modules including an MMath option on Optics and Symplectic Geometry that was probably unique in the UK. He was keen on project work and, from 2001 to 2006, co-ordinated final year MMath projects in pure mathematics in Sheffield. His PhD students, undergraduate students and personal tutees benefited from and appreciated the time and care that they received from him.

Kirill had some health issues over the years, not least with his eyesight, but his sudden death at a time when he was still active in research and teaching came as a shock. Away from mathematics, he enjoyed music, poetry, art and cooking and was interested in classical civilizations and philosophy. He is survived by his wife Margaret, a pharmacist, whom he met in Melbourne and married in Durham in 1989, and Margaret’s daughter Michaela and son Dan from an earlier marriage. He will be missed and fondly remembered.

Dr Kirill Mackenzie at home
Image courtesy of Dr Iakovos Androulidakis

The School of Mathematics and Statistics has also received the following tributes from those who knew Kirill.

Iakovos Androulidakis

Let me first say why I decided to come to Sheffield and work with Kirill for my PhD. It was 1997 and I was about to finish my MSc in Athens. I sent letters to several UK universities, explaining my training and asking them for information about the possibilities of PhD supervision in Differential Geometry. I received brochures from all of them, from the local secretary. But in Sheffield my letter happened to reach Kirill in person. He took the time to write me a long letter, explaining what his work is about and providing a few references, including his 1987 book. Even before reading through his letter, I thought that he is the only one who showed genuine interest to have me as a PhD student. In fact, this was the main reason why I chose Sheffield... (I could have gone to any university, as I had a full scholarship from Greece.)

Actually, at some point, Kirill mentioned exactly that: since I had money of my own, I could have gone to just any university. I told him that I never cared much about famous universities, etc. The most important thing in my choice was to work with someone who, first and foremost, wants to work with me.

Kirill was a very kind person, very warm, caring and "humane", very much in the sense that people from my part of the world (Eastern Mediterranean) are used to. I remember the first time I travelled to Sheffield, in May 1997, before starting my PhD: It was actually the first time I ever left my country; Being completely inexperienced, I didn't plan the trip very well: I flew to London and upon arrival I had to find my way to St Pancras to take the train for Sheffield. So basically I was travelling the entire day, arriving at Sheffield around midnight. Kirill had sent me instructions to my accommodation (a bed and breakfast near Ranmoor), and we had an appointment in his office the next morning. As I left Athens, I expected that upon arrival in Sheffield, I'd find my own way to the accommodation, also to the university the next day. In fact, this looked like a daunting task to me at the time. More than that, until then, I had just spoken to Kirill on the phone one time. I didn't know what he looked like (no Skype back in 1997), so I was very much in the dark with this endeavour. And of course Kirill didn't know what I looked like either.

Well, when I arrived at Sheffield train station, after midnight as I said, a man wearing a black jacket approached me, holding a book with the familiar blue colour used by LMS Lecture Notes Series. I was extremely tired and sleepy to make the connection, so I momentarily dismissed him, rushing to the taxi row. He said "oh, I'm sorry". I immediately recognised his voice, which I had heard only on the phone until then. I turned and looked again at the book, it was his 1987 book; I said "Professor Mackenzie"? We both smiled and he greeted me with a warm hug. He offered to carry my luggage, which I found very warm, given that he was a famous mathematician and I was just a student. Out of respect I said "thank you, I'm OK with it". He drove me to the accommodation, while showing me how to reach the university the next day. As you understand, this was a great relief for me, from several respects. The most important thing was the feeling that this man genuinely cares for me at a personal level.

Later that year, when I settled down in Sheffield and started collaborating with Kirill, I always addressed him as "Professor Mackenzie". I was used to this kind of respect and distance from my undergraduate years. After a few weeks, in one of our meetings, he said "...there is something else, it's OK to call me Kirill if you want...". I explained that I find it very hard, because I have the utmost respect for him, and in Greece we're trained to speak to professors in the plural. He replied "...but please call me Kirill, otherwise people will think that I'm torturing you"! We both laughed at this, and this way I relaxed and enjoyed the friendly feeling that he had created.

Last, I want to say that Kirill was an extremely cultivated person, well beyond mathematics. His knowledge of classical music was huge. Yesterday I heard from Hovik Khumdaverdian that his favourite piece was the last fugue (fugue 24) from the first book of well tempered clavier of Bach. It seems that he repeatedly told Hovik that he would like this fugue to be played at his funeral.

Kirill also liked art very much, I think Vermeer was his favourite painter. And Kubrick is his favourite film director. I gave him a few CDs with films by Theo Angelopoulos as a gift, whom he knew but perhaps hadn't seen films of before. He immediately appreciated his work and recognised the deep symbolisms involved. He also read a lot of poetry, in fact I was very surprised that he had studied Cavafy's work in detail; he was able to recite Ithaca among other poems by Kavafy.

He also had a very wide and deep knowledge of the ancient world, and well beyond that. It was through Kirill that I got acquainted with the work of Runciman on the Byzantine Empire. In 2014 I invited him to Athens for the national Geometry Congress we have every 2 years over here. This was his first time in Greece. It was a very sunny day when we went up to the Acropolis hill, together with my wife Maria who is an archaeologist, and then to the nearby Acropolis museum. Kirill was very moved, he recited Plutarch and admired the beauty of the ancient sculpture and architecture. I must say that I am very glad that I managed to show Kirill, my good teacher, the Acropolis.

Last, let me say that, apart from kindness and generosity, Kirill was also gifted with modesty. He treated all people with politeness and respect, and knew his stature in mathematics compared with the stature of other people.

Kirill was very fond of his cats and liked to cook. He could make very good "spanakopita" (spinach pie), which was very widespread in Australia, due to the Greek community there. But my favourite dish by Kirill was definitely his pumpkin soup!

Dr Kirill Mackenzie at the Acropolis in 2013
Dr Kirill Mackenzie at the Acropolis in 2013 – image courtesy of Dr Iakovos Androulidakis
Magdalini Flori

I remember him describing his postdoc in Latin America (I think it was in Brazil, I'm not 100% sure), where he had prepared seminar-lectures in Portuguese, and he was able to deliver the lectures in the said language. He knew French, was fluent in writing and reading it, not so much in speaking it, and he was quite proud of his Portuguese!

I remember the following story: in his line of research, the letter "g" and "G" are used for various different things: a Lie group, its Lie algebra, a Lie groupoid, and so on. He always had distinct ways of writing them when using the same letter for a different entity (calligraphic, gothic style, etc), and when giving blackboard talks, succeeded in doing so. And once, somebody in the audience, asked in an exasperated voice: "Kirill, how can you write "g" in so many ways? My "g" always looks the same!".

Ping Xu

I first met Kirill in the late 1980s when he visited Berkeley where I was a graduate student. I was attracted by and trying to learn about “groupoids” but was very much frustrated by the subject being too abstract. Kirill offered me tremendous help and support in this endeavour.

In 1991, one year after I received my PhD, Kirill hosted the very first scientific visit of my career. Kirill was a great host: he showed me around the town of Sheffield, introduced me to his family, and drove me to see Bolsover Castle. The mathematics we did together led to the publication of three joint papers, which I consider to be the best work of my entire career. In particular, Kirill and I introduced the concept of Lie bialgebroids and studied their integration problem – a parallel of Drinfeld’s theory of Poisson groups and Lie bialgebras. The search for an analogue of Manin triple for Lie bialgebroids led to the development of the theory of Courant algebroids in 1997. The latter provided the foundation for the generalized complex geometry pioneered by Nigel Hitchin and his Oxford school in the early noughties, a development which has attracted the attention of many mathematical physicists throughout the world.

Kirill had a deep perspective on his mathematics, which often gets recognized and increasingly appreciated as time passes. For instance, the theory of double structures he developed in the early 1990's has recently become a very active area of research. I myself realized lately that Kirill’s work on double Lie algebroids provides a unified framework for understanding the two types of Kontsevich—Duflo theorems for Lie algebras and for complex manifolds as the two extreme cases of a much more general phenomenon.

Beyond being a collaborator, Kirill had become a guidance and a close friend of mine. We were in frequent contact; sharing exciting news but often frustrations as well. Indeed, he has always been a driving force for me to overcome many many difficulties in my life and career. Kirill sent me a last email on May 1st at 20:37 London time, just hours before his death. He wrote:

“Things here are much the same as you describe: all lecturing is now done remotely. I am spending an enormous amount of time preparing
podcasts. I wonder what will become of all this work.”

And, as always, did not forget to encourage me by ending this final message with:

“All the best, for keeping going and staying safe,
(and apologies for being so slow to reply)
Kirill”

As I read these words, I could not have imagined that they would turn out to be his last words to me. I was completely shocked when, two days later, I heard of his passing, which I still cannot accept today.

Kirill is deeply missed.

Yvette Kosmann-Schwarzbach

A week ago, I received news that Kirill Mackenzie died in his sleep, the night of the first of May. Last week has been, first and foremost, about trying, with some of his close friends and collaborators, to assure that a proper mathematical tribute be rendered to him in the form of a publication dedicated to his memory, and, only now, memories of our past exchanges, visits, correspondence, phone conversations and, of course, electronic mail messages, are slowly taking shape. In sum, we have been in contact for some thirty years, we have met at many conferences, we wrote a joint article 18 years ago, we have exchanged numerous visits: Kirill to Lille in 1993, to Polytechnique in 1994, Kirill invited to Paris for five weeks at the Borel Center in 1994, a first visit to Sheffield for the Schwarzbachs in 1995 with our teenage Yseult (16) and Joseph (14) (and the guesthouse was poorly heated but the welcome was heartfelt and the discussions lively), Sheffield again in 2000 and in 2007 with Bertram, that included an invitation to the Mackenzie residence for an evening of interesting conversations with Margaret and Kirill, another visit to Sheffield in 2016. There was a matinee together at the Paris Opera for “Werther at 2:30 PM on Sunday 19” [January 2014] which Kirill, the musician, appreciated.

We both attended and lectured in Goettingen in 2011. That was when Kirill shared a light dinner with Bertram and me in our rented little two-story apartment before we started discussing some mathematical problem (which one? he would have remembered). In Lausanne in 2013 (or was it during Poisson 2008?), Kirill visited us in our picturesque rental apartment overlooking the steep steps leading to the cathedral and we discussed some questions of common interest (groupoids? Poisson structures? maybe it was still clear to Kirill even recently and he could have reminded me) while Bertram went up the steps to enjoy a concert in the cathedral.

I could quote from elogious letters of recommendation for Kirill that I wrote on various occasions in order to underline, for instance, that “the importance of [his work] has been growing steadily in the last twenty years” (and this was in 1999!). I could quote from the mathematical letters I received from him, or from the notes that he wrote during several of our discussions, in Sheffield or in Paris, written in his careful, large and regular handwriting, patiently instructing me in the beauties of Lie bialgebroids and in the arcana of multiple structures. But I simply want to remember a mathematician and a great friend.