The articles in this collection are a sampling of some of the research presented during the conference Stochastic Analysis and Related Topics, held in May of 2015 at Purdue University in honor of the 60th birthday of Rodrigo Bañuelos. A wide variety of topics in probability theory is covered in these proceedings, including heat kernel estimates, Malliavin calculus, rough paths differential equations, Lévy processes, Brownian motion on manifolds, and spin glasses, among other topics.

Preface.- Positive-homogeneous operators, heat kernel estimates and the Legendre-Fenchel transform.- Strong stability of heat Kernels of non-symmetric stable-like operators.- Multiplicative functional for the heat equation on manifolds with boundary.- Connections between the Dirichlet and the Neumann problem for continuous and integrable boundary data.- Decomposition and limit theorems for a class of self-similar Gaussian processes.- On a priori estimates for rough PDES.- Lévy systems and moment formulas for mixed Poisson integrals.- Conformal transforms and Doob's h-processes on Heisenberg Groups.- On the Macroscopic Fractal Geometry of Some Random Sets.- Critical behavior of mean-field XY and related models.