Anatoly Razumovskii

Anatoly Razumovskii is VP for Research at the Institute for Advanced Dynamic Uncertainty, and one of the most extensively trained mathematical scientists in the institution's history. He holds a PhD (kandidat nauk) and a DSc (doktor nauk) — the DSc being the higher Russian doctorate, awarded not for a single thesis but for a sustained body of independent research constituting an original contribution to science of a calibre substantially beyond the PhD. He completed his PhD at Rostov State University (Department of Mathematics and Mechanics), where his doctoral research developed a systematic theory of singular perturbation methods for boundary value problems governed by nonlinear differential equations in structural and continuum mechanics. His thesis established sharp asymptotic expansion theorems for solutions of singularly perturbed elliptic systems in elastic bodies, characterising the boundary layer structure in Sobolev norm topologies and proving convergence rates that, for the first time, captured the geometry-dependent corrections to the outer expansion arising from curvature of the domain boundary. The results resolved a class of open problems in the asymptotic analysis of thin elastic shells under combined loading, and established Razumovskii's reputation as a mathematician of the first order within the Russian mechanics community.

Following his doctorate, Razumovskii pursued his DSc at the Institute of Mechanics of Lomonosov Moscow State University (НИИ механики МГУ), one of the pre-eminent centres for mathematical mechanics in the world, in a programme that spanned the better part of a decade. His DSc monograph developed a variational theory for the optimal control of infinite-dimensional dynamical systems governed by partial differential equations — a line of work that required him to build substantial new machinery in functional analysis, including resolvent estimates for non-self-adjoint second-order operators in Banach spaces, spectral stability results under singular perturbations of the domain, and a treatment of Hamilton–Jacobi–Bellman equations on infinite-dimensional state spaces that predated much of the Western literature on viscosity solutions in Hilbert spaces. The monograph produced a series of fundamental results connecting the classical variational principles of analytical mechanics with the modern theory of stochastic optimal control: it demonstrated, in particular, that the Pontryagin maximum principle for infinite-dimensional systems can be derived as a limiting case of a class of minimax variational problems, and that the value function of the limiting problem satisfies a degenerate HJB equation whose viscosity solutions can be characterised by a family of resolvent identities.

Razumovskii's research sits at the boundary of two mathematical traditions that rarely meet at the level of depth he commands. From the Russian school of mathematical physics he inherited an insistence on the precise functional-analytic formulation of every problem — well-posedness in the appropriate Sobolev or Banach space topology, resolvent estimates, spectral theory of degenerate operators — and from his engagement with optimal control and stochastic analysis he developed the ability to deploy this machinery in settings where the state space is infinite-dimensional and the dynamics are governed by stochastic PDEs. This combination is rare. Most mathematicians who work in stochastic control operate in finite-dimensional or mildly infinite-dimensional settings; most analysts who work on degenerate operators do not engage with the probabilistic structure of the problems. Razumovskii does both, and does both completely. His results on the spectral analysis of degenerate second-order operators in Hilbert function spaces, on Hamilton–Jacobi theory on infinite-dimensional state spaces, and on the rigorous foundations of mean field control for distributed parameter systems represent contributions that are not merely technically demanding but conceptually foundational — they establish the objects that others work with.

At IADU, Razumovskii serves as VP for Research, the role responsible for the scientific governance of the institution, its relationships with peer organisations, and the structural coherence of its research programme across all five divisions. He chairs the Scientific Advisory Board, sets the publication standards to which all IADU output is held, and provides the analytic oversight that ensures the institution's applied and policy-facing work is grounded in the same mathematical rigour as its theoretical research. His own ongoing research focuses on the spectral theory of mean field operators arising in large-population stochastic control problems, the construction of weak solution frameworks for HJB equations on Wasserstein space, and the asymptotic analysis of optimal control problems in which the state space dimension grows with the population size — questions that connect his earliest work on singular perturbation theory to the contemporary frontier of mean field game analysis.