[2] Mayboroda's research concerns harmonic analysis geometric measure theory and partial differential equations, including boundary value problems for elliptic partial differential equations.
[3] In particular, her work has provided a new mathematical approach to Anderson localization, a phenomenon in physics in which waves are confined to a local region rather than propagating throughout a medium, and has enjoyed wide ranging applications in condensed matter physics, cold atoms systems, research and engineering of organic and nonorganic semiconductor materials and devices.
[1] In 2013, she became the inaugural winner of the Sadosky Research Prize in Analysis of the Association for Women in Mathematics.
[8] She was an invited speaker at the 2018 International Congress of Mathematicians, speaking in the section on Analysis and Operator Algebras.
[9] She became the 2023 National Blavatnik Laureate in Physical Sciences & Engineering, given to an outstanding scientist under the age of 42.