Boris Dubrovin (1950-2019)

By Christian Klein

Boris Dubrovin

It is with great sadness that we announce the passing of Boris Anatolievich Dubrovin on Tuesday, March 19, 2019 at the age of 68, after a long and courageous battle with ALS. He will be sorely missed by family, friends and colleagues, leaving behind an outstanding legacy in the field of mathematical physics.

Boris was born in Moscow on April 6, 1950. In 1972 he obtained a Masters degree in Mathematics at Moscow State University. He continued there as a PhD researcher in Geometry and Topology under the supervision of S.P. Novikov, and defended his thesis on `Spectral theory of finite-gap Sturm-Liouville potentials, and Riemann surfaces' in 1976. He was made an Assistant Professor at his alma mater in 1975, and would remain there until 1993, rising to the ranks of Associate Professor in 1984 after his habilitation at the Leningrad branch of the Steklov Mathematical Institute on `Abelian varieties, theta-functions, and nonlinear equations'. He became a Full Professor in 1988. In 1993 he moved to the International School for Advanced Studies (SISSA) in Trieste, Italy, where he was a Distinguished Professor of Mathematical Physics until his passing.

Boris was a leading figure in mathematical physics with a strong background in geometry. Along with colleagues such as S.P. Novikov, A.R. Its, V.B. Matveev, P. van Moerbeke, he developed the theory of algebro-geometric solutions to integrable partial differential equations. He is best known for the introduction of Frobenius manifolds, now part of the AMS Subject Classification 2000 (53D45). These manifolds are of crucial importance in quantum cohomology and string theory, but also in other fields of mathematics such as singularity theory.

He always had a profound interest in dynamical systems in a broad sense, and he successfully used his geometric insight to address questions out of reach for traditional approaches. In his later career he studied the important question of whether certain characteristics of completely integrable systems can be found in deformations of such systems which are only integrable to a certain order of some small parameter ε. This allowed him to establish what is now known as Dubrovin's conjecture, that critical phenomena for a wide class of Hamiltonian regularizations of the Hopf equation are loosely speaking the same as for the thoroughly studied Korteweg-de Vries equation.

Boris's early achievements were overshadowed by the Cold War, as many articles of the Russian school at the time were not known in the west. In spite of this, his results in mathematics were highly regarded from the start of his career. In 1976, together with A.R. Its and I.M. Krichever, he was awarded the prestigious prize of the Moscow Mathematical Society for his contributions to the field of algebro-geometric solutions to integrable equations. He gave an  invited talk at the International Congress of Mathematical Physicists in Swansea (1988), a plenary talk at the European Congress of Mathematicians in Budapest (1996), an invited talk at the International Congress of Mathematicians in Berlin (1998), and a plenary talk at the International Congress of Mathematical Physicists in Rio de Janeiro (2006). He was also very successful in obtaining scientific funding, particularly at the European level, where he was at the heart of various European networks. His biggest success in this context was certainly one of the first prestigious advanced investigator grants of the European Research Council for his Frobenius manifolds and PDEs project. This was one of just three ERC grants in mathematics in the first edition of this program. He also got one of the few megagrants in mathematics by the Russian government intended to repatriate excellent Russian scientists and used this to found the N. Bogolyubov institute at Moscow State University.

In addition to being an outstanding researcher, Boris was also committed to pedagogy. His review article Theta functions and non-linear equations in Russian Mathematical Surveys 1981, shortly after research papers on the topic first appeared in print, opened this field to a wide audience and remains a standard reference work. The three volumes he wrote with A.T. Fomenko and S.P. Novikov of Modern Geometry — Methods and Applicationsare still used around the world as graduate textbooks in modern geometry.

Boris always enjoyed interacting with students and supervised 25 PhD students and 15 postdoctoral researchers over the course of his career. He encouraged students and visitors to give talks in so-called learning seminars where topics were presented in a down-to-earth manner. He actively attended seminars, even when they were outside his main scope of interest, and engaged in lively discussions.

His last years were marred by his battle with ALS. It was heartbreaking to see that Boris, who had never needed a microphone no matter how big the lecture hall, lost his voice first. His courage and tenacity in finding ways to work and exchange with his colleagues despite his failing health were characteristic of a great personality. Boris is survived by his wife Irina and his daughters Dasha and Lisa.

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