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Logic Seminar - Leo Jimenez

Ohio State Garden of Constants
October 8, 2024
1:50 pm - 2:45 pm
Dulles Hall 024

Leo Jimenez
The Ohio State University

Title
Internality of autonomous differential equations

Abstract
When solving a differential equation, one sometimes finds that solutions can be expressed using a finite number of fixed, particular solutions, and some complex numbers. As an example, the set of solutions of a linear differential equation is a finite-dimensional complex vector space. A model-theoretic incarnation of this phenomenon is internality to the constants in a differentially closed field of characteristic zero. In this talk, I will define what this means, and discuss some recent progress, joint with Christine Eagles, on finding concrete methods to determine whether or not the solution set of a differential equation is internal. A corollary of our method also gives a criteria for solutions to be Liouvillian: I will show a concrete application to Lotka-Volterra systems.

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