Russian Mathematical Surveys, 2025, Volume 80, Issue 3, Pages 531–532 DOI: https://doi.org/10.4213/rm10244e (Mi rm10244)

DOI: https://doi.org/10.4213/rm10244e

Bibliographic databases:

Zoom inZoom out

Viktor Sergevich Guba, a remarkable mathematician, brilliant representative of the Moscow algebraic school, doctor of physical and mathematical sciences, and professor at Vologda State University, passed away on 7 December 2023.

He was born on 21 August 1962, in the town of Sokol, Vologda Oblast’, in teachers’ family. His father Sergei Grigor’evich Guba worked in Vologda Pedagogical Institute since the mid-1970s. His numerous papers on popularization of mathematics and the methodology of teaching mathematics can be found in the electronic library Matematicheskoe Obrazovanie (Mathematical Education).^1[x]1https://www.mathedu.ru/indexes/authors/guba$\_$s$\_$g/ His mother Irina Alekseevna taught the Russian language and literature in a high school.

After graduating from high school in 1979, Viktor Guba enrolled in the Faculty of Mechanics and Mathematics at Lomonosov Moscow State University, where after his second year there he decided to major in algebra, namely, group theory. A. Yu. Ol’shanskii was his scientific advisor.

In 1984 he graduated from the university and submitted a paper based on his Master thesis to Izvestiya Akademii Nauk, Seriya Matematichaskaya^2[x]2Translated into English at that time as Mathematics of the USSR – Izvestiya., one of the central mathematics journals. This paper, “A finitely generated complete group”, of more than 40 pages, was published a couple of years later with a quite short abstract:

“An example of a 2-generated complete group (different from the identity) with unique extraction of roots is constructed. An example is indicated, in passing, of a non-cyclic 2-generated group in which every element is conjugate to some power of a fixed element. It is proved that there are continuum many non-isomorphic such examples. The proof is based on a method developed in several papers of A. Yu. Ol’shanskii.”

Note that the first sentence mentions a result solving Problem 1.1 in the famous Kourovka notebook. By the time Guba wrote his paper, this problem had waited 20 years for a solution.

Unfortunately, for some reasons unrelated to mathematics Guba was not among the students selected for postgraduate studies. He began to work in Vologda Pedagogical University, but in the spring of 1985 he returned to Moscow University for internship. On a research seminar there he heard about a problem which he solved almost instantly, and he published the solution in one of his best known papers, whose title also describes concisely the main result: “Equivalence of infinite systems of equations in free groups and semigroups to finite subsystems”. This short, but fundamental paper was published in the journal Matematicheskie Zametki^3[x]3Translated into English as Mathematical Notes. in 1986.

After defending his Ph.D. thesis in 1989, Guba returned to Vologda, and, with the exception of the periods of his trips abroad for joint research work, he worked in Vologda University till his last days.

Guba’s visits to the USA resulted in many years of his fruitful cooperation with M. V. Sapir. Apart from a number of well-known papers, they wrote the book Diagram groups, published in 1997 in the series “Memoirs of American Mathematical Society”. As a development of the theory of such groups, Guba and Sapir published in 1999 the paper “On subgroups of R. Thompson’s group $F$ and other diagram groups” in the journal Matematicheskii Sbornik.^4[x]4Translated into English as Sbornik: Mathematics.

About that time Guba became interested in the famous problem of the amenability of R. Thompson’s group $F$. This problem is still open, and nine days before his death Viktor Guba, who was gravely ill and was open about this, discussed his latest advances towards the solution of this problem in a brief telephone conversation with one of these authors.

In the early 2000s he proved that the group $F$ has quadratic growth. His paper “The Dehn function of Richard Thompson’s group $F$ is quadratic” was published in Inventiones Mathematicae in 2006. In 2022 the journal Uspekhi Matematicheskich Nauk^5[x]5Translated into English as Russian Mathematical Surveys published the large survey “R. Thompson’s group $F$ and the amenability problem” by V. S. Guba.

That paper features not just the depth of mathematicsl content: it is a pleasure to read as piece of literary work. This reflects Guba’s high culture as a a lover and connoisseur of literature, classical music, and cinema. His friends and colleagues enjoyed conversations with him on these subjects.

This humanitarian side of Guba’s personality manifested itself brightly in his talent to present mathematical topics concisely, clearly, and colourfully before experts in mathematics and high school students alike. We can find some examples in the remarkable lecture course on the Banach–Tarski paradox, written with S. M. Lvovski and published in 2016 by the Moscow Center for Continuous Mathematical Education, and in many of Guba’s notes published on the LiveJournal Internet portal, under his own name and under the pseudonym of falcao.^6[x]6https://falcao.livejournal.com/category/наука, https://ru-math.livejournal.com/?poster=falcao.

Viktor Sergeevich Guba left a bright mark in mathematics and in the memory of his friends and colleagues. His results are an ornament to the modern group theory.

Citation in format AMSBIB

\Bibitem{TaiTar25}
\by I.~A.~Taimanov, K.~K.~Tarasevich-Nikolaev
\paper Viktor Sergeevich Guba (obituary)
\jour Russian Math. Surveys
\yr 2025
\vol 80
\issue 3
\pages 531--532
\mathnet{http://mi.mathnet.ru/eng/rm10244}
\crossref{https://doi.org/10.4213/rm10244e}
\mathscinet{https://mathscinet.ams.org/mathscinet-getitem?mr=4961289}
\adsnasa{https://adsabs.harvard.edu/cgi-bin/bib_query?2025RuMaS..80..531T}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=001620411700004}