Research areas: Analysis, Probability and Statistics
I mainly work on development of methods of high-dimensional and infinite-dimensional noncommutative analysis for problems arising in mathematical physics, noncommutative geometry, applied matrix analysis, and, more recently, statistical estimation.
MSE bounds for estimators of matrix functions, Linear Algebra and its Applications, 609 (2021), 231-252
Multilinear Operator Integrals: Theory and Applications (with A. Tomskova), Lecture Notes in Mathematics, 2250, Springer, 2019, XI+192 pp
Multilinear Schur multipliers and applications to operator Taylor remainders (with D. Potapov, F. Sukochev, A. Tomskova), Advances in Mathematics, 320 (2017), 1063-1098
Estimates and trace formulas for unitary and resolvent comparable perturbations, Advances in Mathematics, 311 (2017), 481-509
Spectral shift function of higher order (with D. Potapov, F. Sukochev), Inventiones Mathematicae, 193 (2013), no. 3, 501-538