Research Interests: Approximation and representation of multivariate functions by various classes of practically useful functions. These classes, in particular, include ridge functions (plane waves), radial functions, feedforward neural networks and linear superpositions. He is also interested in studying approximation properties of sums of abstract function algebras.

Research Interests: Low-dimensional topology, Symplectic/contact topology, Gauge theory, Algebraic geometry, group theory, and topological data science

Research Interests: Functional Analysis, Functional-differential equations, Spectral Theory

Research Interests: Boundary Values of Analytic Functions, Singular Integral Operators, Ridge Functions

Research Interests: Noncommutative analysis, operator algebras, multi-variable operator theory, topological homology, noncommutative holomorphic functional calculus, noncommutative algebraic geometry, quantum information theory

Research Interests: Geometric mechanics

Research Interests: Theoretical and mathematical physics, with main interests in string theory, supersymmetric gauge theories, and integrable models. He is also interested in mathematical topics such as special functions, low-dimensional topology, divergent series, etc.

Research Interests: Functional Analysis, Operator Theory

Research Interests: Spectral Theory, Inverse Problems

Research Interests: Functional Analysis, Spectral Theory, Geometry of Banach Spaces

Research Interests: Inverse Problems, Scattering Theory

Research Interests: Nonlinear Partial Differential Equations; Attractors of Evolution Equations

Research Interests: Functional Analysis, Operator Theory

Research Interests: Spectral Theory, Mathematical Physics, Operator Theory