The faculty of the UBC harmonic analysis group work in a wide range of research areas, including classical harmonic analysis, geometric measure theory, microlocal analysis, and additive combinatorics. The research interests of the group are classical and modern harmonic analysis, particularly Kakeya and restriction theory, maximal operators, and singular and oscillatory integrals, with connections and applications to geometric measure theory, additive combinatorics, complex analysis, and partial differential equations.
Info for prospective students
|Partial Differential Equations, Harmonic Analysis, Dynamical Systems
|Harmonic analysis, geometric measure theory and additive combinatorics
|Cone multipliers and local smoothing, Multi-parameter maximal functions, Hilbert transform along polynomial surfaces, Scalar oscillatory integrals, oscillatory integrals with degenerate phases, Estimates for the Bergman kernel.
|Fractal geometry, ergodic theory, real and harmonic analysis
|Fractal geometry and its relationships with harmonic analysis, geometric measure theory, number theory, ergodic theory.
|Mathematical problems related to analog-to-digital conversion, blind source separation, sparse approximations and compressed sensing, and applications in seismic signal processing.
|Incidence geometry, the restriction and Kakeya problems, and sum-product phenomena.