Explore the deep connections between L-functions, automorphic spectra, and the conformal bootstrap in this hour-long conference talk that bridges number theory and theoretical physics. Discover how these mathematical frameworks intersect and inform each other, with particular focus on spectral theory and bootstrap methods. Learn about the latest developments in understanding automorphic forms through the lens of conformal field theory techniques, and examine how bootstrap constraints can provide new insights into classical problems in analytic number theory. Gain insights into cutting-edge research that demonstrates the unexpected unity between seemingly disparate areas of mathematics and physics.