DrSci. Boris N. Khoromskij
Max-Planck-Institute for Mathematics in the Sciences
Inselstr., 22-26, D-04103
Leipzig, Germany
e-mail: bokh{at}mis.mpg.de
In 1968 Boris Khoromskij has finished a special mathematical school No. 18 in Moscow, where the director was the world-known mathematician, member of the Russian Academy of Science, Professor of the Moscow State University Andrey N. Kolmogorov. In 1973 Boris Khoromskij graduated the Mathematics Department of the Moscow State University. Then he worked as a leading scientist at the Mathematics Department of the Joint Institute for Nuclear Research (JINR) in Dubna, Moscow region, where he received his PhD in Mathematics in 1978 and the Doctor of Science degree (habilitation) in 1992. At that time Boris Khoromskij was the Head of the Numerical Methods Group at JINR. Since 1993 Boris Khoromskij has been working in Germany at the WIAS institute in Berlin, and then at Heidelberg University, Stuttgart University and the University of Kiel.
Beginning from 1999 till now Boris Khoromskij is working as a senior scientist at the Max-Planck Institute for Mathematics in the Sciences in Leipzig, Germany (now emeritus). His field of research is mainly concerned to numerical methods for PDEs with the focus on modern tensor numerical methods for multi-dimensional problems in a wide range of applications in scientific computing.
Boris Khoromskij authored 3 books and more than 170 scientific articles. He advised 9 PhD students.
According to Research.com in 2025 Boris Khoromskij has ranking # 56 among the best mathematics scientists in Germany, and ranking # 1046 among the best mathematics scientists in the world.
His h-number in Google Scholar is 51.
The quantized tensor train (QTT) format, which was first introduced by Boris Khoromskij in 2009, see Preprint of the Max-Planck Institute , number 55/2009 provides the logarithmic computational and storage complexity in grid size for accurate approximation of univariate and multidimensional functions on large grids. (The cooresponding journal paper was published with delay in 2011.)
Nowadays the QTT approximation techniques deliver powerful methods for numerical solution of multidimensional problems in large scale scientific computing, computational quantum chemistry, data science, stochastic and UQ simulations, optimal control problems and other applications. Moreover, the QTT tensor algorithms can be viewed as the basic tool for operating with big data in the modern quantum computing.
(Photo from February 2010 at 26th GAMM Seminar in Leipzig on Tensor Approximations and High-Dimensional Problems.)
Books:
B. N. Khoromskij and G. Wittum. Numerical Solution of Elliptic Differential Equations by Reduction to the Interface.
Research monograph, LNCSE, No. 36, Springer-Verlag 2004.
Boris N. Khoromskij
Tensor Numerical Methods in Scientific Computing
Research monograph, De Gruyter, Berlin, 2018.
Radon Series on Computational and Applied Mathematics 19.
Venera Khoromskaia and Boris N. Khoromskij
Tensor Numerical Methods in Quantum Chemistry
Research monograph, De Gruyter, Berlin, 2018.
Current research topics :
Numerical analysis in higher dimensions.
Quantized-TT formats in application to quantum molecular dynamics.
DMRG and QTT methods for multidimensional boundary value, spectral and time-dependent problems.
Tensor methods for stochastic and parametric PDEs.
Tensor-structured methods in electronic structure calculations.
Range-separated (RS) tensor format for summation of long-range electrostatic potentials.
Rank-structured tensor methods for calculation of the Bethe-Salpeter excitation energies.
Tensor numerical methods in geometric and stochastic homogenization for elliptic PDEs.
last modified: November 12, 2025
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