Harmonic Analysis

Harmonic Analysis and Fractal Geometry Seminar

Group overview

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.

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People

Faculty Research Interests
James Colliander Partial Differential Equations, Harmonic Analysis, Dynamical Systems
Izabella Laba Harmonic analysis, geometric measure theory and additive combinatorics
Malabika Pramanik 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.
Pablo Shmerkin Fractal geometry, ergodic theory, real and harmonic analysis
Ozgur Yilmaz Mathematical problems related to analog-to-digital conversion, blind source separation, sparse approximations and compressed sensing, and applications in seismic signal processing.
Joshua Zahl Incidence geometry, the restriction and Kakeya problems, and sum-product phenomena.
Postdoctoral Researchers Research Interests
Tongou (Thomas) Yang Decoupling, restriction and Kakeya problems, fractals and geometric measure theory
Alexia Yavicoli Fractal geometry and its relationships with harmonic analysis, geometric measure theory, number theory, ergodic theory.
Graduate Students Research Interests
Noe Ducharme Applied harmonic analysis, wavelet theory, Fuglede's spectral set conjecture
Caleb Marshall Euclidean Harmonic Analysis, Directional Singular Integrals, Fractal Maximal Averages, Projections of Fractals
Yuveshen Mooroogen