Birkhoff conjecture for nearly centrally symmetric domains
V. Kaloshin, E. Koudjinan, K. Zhang, Geometric and Functional Analysis 34 (2024) 1973–2007.

Nearly circular domains which are integrable close to the boundary are ellipses
G. Huang, V. Kaloshin, A. Sorrentino, Geometric and Functional Analysis 28 (2018) 334–392.

Diophantine properties of elements of SO(3)
V. Kaloshin, I. Rodnianski, Geometric And Functional Analysis 11 (2001) 953–970.

Gaussian decay of the magnetic eigenfunctions
L. Erdös, Geometric and Functional Analysis 6 (1996) 231–248.