Model theory, algebra, and differential equations

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The project concerns applying ideas from model theory, a branch of mathematical logic, to the classification of differential equations. Model theory studies structures and definable sets. A structure in this sense is roughly speaking an underlying set or universe together with some collection of distinguished sets of n-tuples from the set, for varying n. Many parts or objects of mathematics can be fruitfully studied as structures. Differential equations, on the other hand, are equations which describe the rate of change, for example, of some quantity, and they lie behind all of modern science and much of modern technology. The project involves roughly viewing the set of solutions of a differential equation as a structure in the sense of model theory, and attempting to classify or understand such equations via the tools of model theory.