Alexei Poltoratski

Alexei Poltoratski is a Professor in the Department of Mathematics at the University of Wisconsin, Madison. His research focuses on Harmonic and Complex Analysis and Spectral Problems, with significant contributions to operator theory and mathematical physics.

Research Interests: Poltoratski's work bridges harmonic analysis, complex analysis, and spectral theory, addressing fundamental questions in the uncertainty principle, completeness of exponential systems, and measures' determinacy. His studies also involve Toeplitz kernels, reflectionless operators, and pseudocontinuation phenomena.

Publications Trends: His recent articles (2015–2021) emphasize nonlinear Fourier analysis, spectral gaps, and applications of Toeplitz operators. Preprints from 2021 explore pointwise convergence and classification of measures, while earlier works (2013–2017) tackle polynomial approximation, rank-one perturbations, and Hilbert transforms.

Collaborations: He has partnered with prominent mathematicians including N. Makarov, C. Remling, E. Abakumov, and M. Mitkovski on projects spanning spectral measures, Cauchy integrals, and meromorphic functions.