Title: Bridging Mathematics and Life Science: Snapshots From Reaction-Diffusion Equations
Speaker: Xige Yang (Ohio State University)
Abstract: Since Alan Turing's pioneering work in 1952, reaction-diffusion equations (RDEs) have been rapidly attracting scientists and researchers with different background. In my talk, I will give a friendly introduction to RDEs from various points of view. First, I will start with some simple simulations of an RDE, then introduce basic theoretical results of RDEs. Second, due to limitations of theoretical results, numerical methods will be addressed. In particular, a new field called numerical algebraic geometry (i.e. how to solve polynomial systems using a computer) will be introduced in order to find multiple solutions of an RDE, which may well also bring some new insights into applications of classical algebraic geometry. Finally, if time allows, I will briefly show how data science can help to avoid the mathematical difficulties of RDEs by providing an equation-free solution to them.