Explore a seminar on spectral geometry focusing on linear programming bounds for hyperbolic surfaces. Delve into the typical behavior of two crucial quantities on compact manifolds with Riemannian metrics: the number of primitive closed geodesics of length smaller than T and the error in the Weyl law for counting Laplace eigenvalues smaller than L. Examine the historical context of qualitative behavior understanding and recent quantitative advancements. Learn about the concept of predominance in the space of Riemannian metrics and its implications. Discover stretched exponential upper bounds and logarithmic improvements that hold for a predominant set of metrics. Gain insights from Yaiza Canzani's joint work with J. Galkowski, presented at the University of North Carolina at Chapel Hill.