Modern Coexistence Theory and beyond

A fundamental problem from population biology is finding conditions under which interacting species coexist or go extinct. I will present results that lay the foundation for a general theory of stochastic coexistence. This theory extends and makes rigorous Modern Coexistence Theory and leads to resolving a number of conjectures due to Chesson, Ellner, and Palis. I explain how this theory can be used to show that random environmental fluctuations can rescue species from extinction