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ORCID: 0000-0001-9324-4626
ResearcherID: Q-2703-2016
Scopus AuthorID: 57190497169
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Ashley Charles Lightfoot

1 October 1987 – 31 August 2019

We, HSE University Faculty of Mathematics (Moscow), send our deepest sympathies to the family of Ash Lightfoot, a devoted mathematician and a man of heart. We will remember Ash as one of the most active colleagues. Who was always there in his office, with his door wide open - willing and eager to communicate with people. Often helping students understand mathematical concepts. Organizing scientific events. Offering extra-curricular possibilities, research projects for graduate, undergraduate and even high-school students.

Ash Lightfoot was a bright mathematician working on extremely challenging problems, namely, higher dimensional generalizations of knot theory. He is an author of prominent results in this field. Ash was employed as a research fellow in the HSE Faculty of Mathematics since September 2016 till February 2019; after that he accepted a professorship at KAIST, South Korea.


Remembering Ash Lightfoot

Ash Lightfoot stayed in Moscow from the Fall of 2016 to February 2019, while he had a postdoc position at the Higher School of Economics.

I got to know Ash in February 2017. I was forwarded a copy of his email in which he introduced himself, and then I looked at Ash’s papers on the arXiv. I quickly got interested in his work and invited him to speak at our seminar, that is, Geometric Topology Seminar at the Steklov Mathematical Institute. Then Ash delivered to us 5 talks on one of his papers, essentially, his dissertation. In fact, this was one of the longest continuous series of talks at our seminar. Ash’s talks were visibly appreciated by the audience, but it took some effort to keep up with him, because it required a lot of 4-dimensional imagination, and also being on good terms with algebra. By the end only one audience member survived, namely, me. Around the same time I suggested to Ash speaking at two topology seminars at Moscow State University, and I contacted their organizers to arrange his talks there. So then he also spoke once at each of these seminars, the Postnikov Seminar in Algebraic Topology and Manturov’s seminar in Knot Theory.

In August of the same year, Ash suggested to me that we move our Geometric Topology Seminar to the HSE. Upon some reflection I liked this idea, because the Steklov Institute hosts only limited educational activities, which makes it difficult for students to attend the seminar and even to discover its existence. Then I convinced the other seminar organizers, Yevgeny Shchepin and Piotr Akhmetiev, to move it to the HSE and to make Ash responsible for all the organizational matters related to the HSE. This worked out nicely. After resettlement our seminar did attract a number of new students, especially, master students and graduate students. And Ash turned out to be an excellent organizer. He made an arrangement that the participants of our seminar can enter the building without obtaining a permit in advance. He provided hot tea and cookies at each seminar meeting, even though he rarely enjoyed them himself. He organized a few meetings of the seminar himself when I was busy. Particularly, in February 2018 I broke my arm while skiing, and at the same time Ash burnt his leg with hot water, but he was recovering faster than me, and in March he ran a series of introductory talks for students on the subject of his research. I should mention that Ash was also coorganizing with Chris Brav another, more elementary seminar on 3-manifolds targeted at undergraduates, but I don’t know much about it.

Ash has also been active as a volunteer teacher of mathematics to school kids in Moscow. In February and March 2017 he worked (for free) at a math circle at the Moscow State 57th School. This has long been a special school, traditionally contributing a large proportion of mathematical olympiad winners in Russia and also of Moscow-born professional mathematicians (including myself). But their junior math circle, for kids as young as 9 to 11, was a new thing. It so happened that my wife Katya was also 1 teaching at that same math circle. Actually, both she and Ash were recruited there via the mailing list of the Math Department of the HSE. As I learned from my wife, Ash had difficulties in communication with the principal teacher of the math circle, because she was not sufficiently fluent in English to communicate directly with Ash, but nevertheless she wanted him to discuss the material with her through intermediaries, in some detail before each meeting. Apparently Ash found this to be too burdensome and left the circle.

When I learned of this story, in April 2017, I suggested to Ash trying a different venue for teaching school kids, and I contacted Alexandr Spivak, a prominent teacher and organizer of math circles in Moscow. While the approach of the 57th School has some similarity to what is called the Moore method in the United States, the style of Spivak’s circles is closer to traditional university tutorials. And it seems that this more conventional approach resonated better with Ash. In the next several months Ash gave many lectures at Spivak’s circle, in which he managed to explain, among other things, some basic topology of surfaces to kids as young as 11 to 14. The 40 videos of these lectures are available at Spivak’s channel on Youtube.

By the way, no single video remains of Ash’s 10 talks at our seminar, unfortunately, but their abstracts are available at the seminar webpage.

I shared with Ash his passion for link maps, although for Ash this was the main area of work, and for me one of 20, which I had to balance with the other ones. I gave several talks at the seminar with the main goal of explaining to Ash my results on link maps (two times in July 2017 and two times in December 2018, shortly before Ash’s departure to Korea). But on a personal level we did not get very close. In his first year in Moscow, Ash was actively learning Russian, but I was not of much help, unfortunately. It was also visible that he was experiencing some chronic health issues, and I asked him a few times if he needs help with doctors. He always said no, and unfortunately I did not insist too much on it. Perhaps I would be more useful in this respect if I did not avoid seeing doctors myself with my issues for many years.

I last wrote to Ash on August 26, 2019, asking him for advice on arranging passage to the building for seminar participants, with a couple of side comments on mathematics. He replied on the same day in much detail, and his message seemed pretty lively and energetic. Certainly he did not mention any health issues. I did not suspect that something could go so wrong.

It is still hard for me to believe that Ash is no longer with us.

Sergey Melikhov
August 23, 2020



  • 2018

    Four Dimensional Topology (Осака). Presentation: Link homotopy in 4-space via chart descriptions

  • 2017

    Узлы и теория представлений (Москва). Presentation: The triviality of a certain second-order invariant of link homotopy

  • Семинар по геометрической топологии (Москва). Presentation: The triviality of a certain secondary invariant of link homotopy in dimension 4

  • Алгебраическая топология и её приложения. Семинар им. М. М. Постникова (Москва). Presentation: Detecting Whitney disks for link maps in dimension four

  • Дни геометрии в Новосибирске 2017 (Новосибирск). Presentation: Vassiliev invariants and link homotopy in dimension four

  • 2016
    Характеристические классы и теория пересечений (Москва). Presentation: Link homotopy in dimension four

Welcome Aboard: Post-Doc Introductions

Every year, HSE hires post-doctoral researchers from all over the world. And in 2017-18, more than 30 of them started work at laboratories and research centres in a large range of fields and specializations. The HSE Lookis pleased to introduce this year’s international researchers, so that you can learn more about your colleagues and find out about opportunities for potential collaboration.