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Lecture #2: Quantitative questions in spectral geometry

Random and Arithmetic Structures in Topology: Introductory Workshop August 25, 2020 - September 11, 2020

September 01, 2020 (09:00 AM PDT - 10:00 AM PDT)
Speaker(s): Lola Thompson (Universiteit Utrecht)
Location: MSRI: Online/Virtual
Primary Mathematics Subject Classification No Primary AMS MSC
Secondary Mathematics Subject Classification No Secondary AMS MSC

uantitative Questions In Spectral Geometry


In 1992, Reid posed the question of whether hyperbolic 3-manifolds with the same geodesic length spectra are necessarily commensurable. While this is known to be true for arithmetic hyperbolic 3-manifolds, the non-arithmetic case is still open. Building towards a negative answer to Reid's question, Futer and Millichap have recently constructed in nitely many pairs of non-commensurable, non-arithmetic hyperbolic 3-manifolds which have the same volume and whose length spectra begin with the same rst n geodesic lengths. In the present lecture, we show that this phenomenon is surprisingly common in the arithmetic setting. This talk is based on joint work with B. Linowitz, D. B. McReynolds, and P. Pollack.

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uantitative Questions In Spectral Geometry

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