Louis Gass

In this presentation, we will explain the Kac-Rice formula, which gives a convenient expression for the expectation and variance of the number of zeros of a regular Gaussian stochastic process. We will apply the Kac-Rice formula to the model of Gaussian trigonometric polynomials and prove the exact asymptotic of the expectation and variance of the number of zeros for this model. If the time allows it, we will discuss a generalization of this model to Riemannian manifolds.