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Research Frontiers in Harmonic Analysis on Lie Groups

Investigates Fourier analysis, representation theory, and spectral decomposition on non-commutative locally compact groups.

Representation Theory and Spectral Gaps on Non-Amenable Groups
Wavelets and Frames on Homogeneous Spaces
Heat Kernel Asymptotics and Functional Inequalities
Multipliers and Fourier Restriction on Curved Geometries
Quantum Groups and Noncommutative Harmonic Analysis
Oscillatory Integrals on Nilpotent Lie Algebras
Uncertainty Principles Beyond Abelian Settings
Ramanujan Graphs and Spectral Expanders on Groups
Convolution Operators and Approximation Properties
Harmonic Analysis on Symmetric Spaces and Rigidity

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