Christine Eagles, University of Waterloo
Algebraic Independence of solutions to multiple Lotka-Volterra systems
A major problem in recent applications of the model theory of DCF_0 is determining when a given system of algebraic differential equations defines a strongly minimal set. A definable set S is strongly minimal if it is infinite and for any other definable set R (over any set of
parameters), either S\cap R or S\setminus R is finite. In joint work with Yutong Duan and Leo Jimenez, we classify exactly when the solution set to a Lotka-Volterra system is strongly minimal. In the strongly minimal case, we classify all algebraic relations between Lotka-Volterra systems and show that for any distinct solutions x_1,...,x_n (not in the algebraic closure of the base field F), trdeg(x_1, ..., x_m/F) = 2m.
MC 5403