Explore the evolution of dispersal in spatially heterogeneous environments through a 45-minute lecture by Adrian Lam from Ohio State University. Delve into the diffusion-competition system formulated by Dockery et al. in 1998, examining their conjecture about the competitive exclusion of faster-diffusing species. Investigate the continuum version of this problem developed by Perthame and Souganidis in 2016, which introduces a selection-mutation model structured by both space and diffusion rate. Learn about recent progress in both problems, including the application of the principal Floquet bundle concept for parabolic equations. Gain insights into the rare mutation limit of time-dependent solutions and its relation to Hamilton-Jacobi equations with constraints.