Analysis research in the department includes convex bodies, dynamical systems and ergodic theory, operator algebras, and complex analysis.
Alfonseca's research focuses on the study of the geometry of convex bodies on the Euclidean space, and their asymptotic behaviour as the dimension increases. Her work uses methods from Harmonic and Fourier analysis.
Duncan studies operator algebras associated to directed graphs and dynamical systems. His recent focus is on free products of operator algebras associated to directed graphs, and semicrossed products associated to dynamical systems. The latter is an operator algebra that encodes important elements of the dynamics via algebraic properties.
Littmann's research focuses on approximation problems in complex analysis and applications in analytic number theory and signal processing. His work uses techniques from de Branges' theory of Hilbert spaces of entire functions.