CORDIS Project
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This proposal investigates the spectral gap in mathematics, physics, and computer science, focusing on hyperbolic surfaces and unitary representations. It aims to explore the ubiquity and optimality of spectral gaps and develop new integration formulas for representation varieties.
Spectral gap is a fundamental concept in mathematics, physics, and computer science as it governs the exponential rate at which a process converges towards its stationary state.
It informs the spectral lines of hydrogen, how we shuffle cards, the behavior of semiconductors, and web search algorithms.
Moreover, some of the most prominent issues of contemporary mathematics, including the Ramanujan-Petersson conjecture and the Yang-Mills mass gap, revolve around spectral gap.This proposal seeks to…
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