Alexander Logunov specializes in harmonic analysis, potential theory, and geometric analysis. He works at Princeton University.
Assist. Prof. Logunov received, jointly with Eugenia Malinnikova, the 2017 Clay Research Award for their introduction of novel geometric-combinatorial methods for the study of elliptic eigenvalue problems, leading to the solution of long-standing problems in spectral geometry.
Among other results, he proved an estimate (from above) for Hausdorff measures on the zero sets of Laplace eigenfunctions defined on compact smooth manifolds and an estimate (from below) in harmonic analysis and differential geometry that proved conjectures by Shing-Tung Yau and Nikolai Nadirashvili. In 2018 he received the Salem Prize for his work on these conjectures.