The Bottom of the L^2 Spectrum of Higher-rank Locally Symmetric Spaces

Explore the intricacies of the $L^2$ spectrum of higher-rank locally symmetric spaces in this 47-minute lecture by Sam Edwards from Durham University. Delve into the comparison between rank one geometrically finite locally symmetric spaces and higher-rank symmetric spaces without rank one factors. Examine the conditions for the existence of square integrable positive Laplace eigenfunctions in both cases. Gain insights into the connection between square integrability of positive Laplace eigenfunctions and Patterson-Sullivan and Bowen-Margulis-Sullivan measures in the higher-rank setting. Learn about the joint work with Oh and Fraczyk-Lee-Oh that forms the basis of this presentation at the Institut des Hautes Etudes Scientifiques (IHES).