Fractal Uncertainty Principle and Spectral Gaps

Related lectures (29)

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Explores the spectrum of hyperbolic surfaces, focusing on Fuchsian groups and their actions.

Explores Wedderburn's theorem, group algebras, and Maschke's theorem in the context of finite dimensional simple algebras and their endomorphisms.

Delves into the Fractal Uncertainty Principle for the Fourier transform and spectral gaps, including specialized cases for Cantor sets.

Explains Cantor's theorem comparing cardinalities of different number sets.

Covers countable and uncountable sets, sequences, summation, and Cantor's Diagonalization proof.

Explores flat groups of automorphisms and their properties, including minimization functions and invariance under specific conditions.

Explores the Riemann zeta function, its properties, applications, and analogies in number theory and algebraic geometry.

Explores the Laplacian, Riemannian metric, and invariant operators in hyperbolic surfaces.

Explores mapping functions, surjections, injective and surjective functions, and bijective functions.