## Yuri Netrusov, Senior Lecturer and member of the School of Mathematics for nearly 20 years until his retirement in 2019, passed away in March. Misha Rudnev has written an appreciation of Yuri’s deep mathematical work along with a tribute to a friend and former colleague.

On the morning of March 26, Yuri Netrusov was found dead in his Sutton home. His death was sudden and unexpected. He was 61 years old. He is survived by his wife Olga and son Mikhail.

I have known Yuri since 2001 when I came to Bristol. We used to smoke by the School’s old building back door, and he would tell stories almost non-stop. But despite this outgoing demeanour, I have always felt a certain aura of mystery that enveloped his personality.

Yuri came to the UK in 1995 to work with David Edmunds, a prominent UK analyst at the University of Sussex. He was one among a small cohort of his colleagues from St Petersburg, whose move to the UK was somewhat facilitated by Edmunds and others. In 1997 he was awarded a EPSRC Advanced Fellowship, which he took to Bristol in 2000. He stayed in Bristol until 2019, when he voluntarily took early retirement.

He was born in St Petersburg (then Leningrad), where he went to the famous maths-physics school No 239, which had been the alma mater of many outstanding Soviet scientists for generations, in particular those representing the renowned Leningrad School of Mathematical Physics.

Yan Fyodorov, another Leningrad-born British mathematician, who knew Yuri back in the school years remembers that Yuri, possibly owing to a working-class background, appeared “culturally” somewhat different from many of his peers* and kept to his own devices, although his outstanding mathematical abilities were evident to everyone.*

After school Yuri went to Maths-Mech of Leningrad University, which he finished in 1983 and five years later defended his PhD in the Leningrad branch of the Steklov Mathematical Institute.

His mathematical heritage belongs to a number of state-of-the-art areas of function and spectral theory, geometric measure theory and harmonic analysis. He had a special taste for nailing down precise characterisations of fine, exceptional phenomena, arising in function space settings. What made Yuri unambiguously a star, was his soon-after-PhD series of solo papers on characterisation of exceptional sets for different Besov spaces – a challenge formulated earlier by David Adams. This connected to another renowned question of spectral synthesis, which had been famously resolved in the Sobolev space context by Lars Hedberg, who pointed out that the question appeared to be more subtle in the context of Besov and Lizorkin-Triebel spaces. This was indeed the case, and Yuri succeeded in resolving the corresponding problem, based on a very different, somewhat algebraic approach, with ideas going back to classical works of Whitney. These results became a chapter in a well-known book *Function Spaces and Potential Theory *by Adams and Hedberg, which was fully dedicated to *Theorems by Yuri Netrusov. *Yuri worked particularly closely with Hedberg and regarded their subsequent joint study, *An axiomatic approach to function spaces, spectral synthesis and Luzin approximation, *as one of his top works. It is also his most cited work.

Yuri continued research in collaboration with several distinguished UK mathematicians. In a paper with Vladimir Maz’ya he constructed a family of new striking counter-examples in the theory of Sobolev spaces. His works with Yuri Safarov produced remarkable insights into the distribution of the eigenvalues of the Laplace operator. Netrusov and Edmunds settled, negatively, a conjecture on the behaviour of entropy numbers under real interpolation that had been open for some 20 years.

Edmunds recalls, “*Yuri’s mastery of combinatorial techniques was crucial: the techniques developed have stimulated much work on related problems.*

My opinion is that Yuri was an extraordinarily deep and original analyst, with absolutely first-class ability. He had remarkable insight into what was possible; at the core of his proofs there was usually a really beautiful idea.”

Yuri’s choice of fine-drawn mathematical questions may have been an expression of an overall very subtle, and although occasionally exuberant, but generally introspective, ruminative, musing personality. It was as if he was to see things at greater depth than his friends, among whom he was nicknamed *Dedushka* (Grandpa). He could, but would not be too eager to reveal his secrets or show off his erudition, such as an extremely broad and analytic knowledge of history.

He was universally praised for his modesty and kindness. His English, of which Nabokov’s *Pnin *would be a pale shadow, was legendary. Wendy Atkinson, his landlady and lifelong friend in Sussex recalls, among many other fond anecdotes, him telling her that he was “*going to have a snake *(snack)”. His eternal maxim, reflecting on life’s ineluctable absurdity, was – shrugging his enormous shoulders – “such is life”. Only in Yuri’s English it became a verdict. “*LIFE IS SUCH!”*

**A Farewell Ceremony will be held at North East Surrey Crematorium at 4pm on 18th April.**