Summer Graduate School

Algebraic Theory Of Differential And Difference Equations, Model Theory And Their Applications

The purpose of the summer school will be to introduce graduate students to effective methods in algebraic theories of differential and difference equations with emphasis on their model-theoretic foundations and to demonstrate recent applications of these techniques to studying dynamic models arising in sciences. While these topics comprise a coherent and rich subject, they appear in graduate coursework in at best a piecemeal way, and then only as components of classes for other aims. With this Summer Graduate School, students will learn both the theoretical basis of differential and difference algebra and how to use these methods to solve practical problems. Beyond the lectures, the graduate students will meet daily in problem sessions and will participate in one-on-one mentoring sessions with the lecturers and organizers.

School Structure
Lectures will be held on the following topics:
(1) Effectivity in the algebraic theories of differential and difference equations (lectures by Alexey Ovchinnikov)
(2)  General model theory of differential and difference fields (lectures by David Marker)
(3)  Model theory of log-differential equations (lectures by Anand Pillay)
(4)  Applications to modeling (lectures by Marisa Eisenberg)
Beyond the lectures, the graduate students will meet daily in problem sessions and will participate in one-on-one mentoring sessions with the lecturers and organizers.

Suggested prerequisites

• Graduate-level course in algebra
• The first 4 chapters from “Model Theory, An Introduction” by David Marker
• Chapters 1, 2, and 7 from "An Introduction to Differential Algebra" by Irving Kaplansky
• Chapters 1-5 and 9 from “Ideals, Varieties, and Algorithms” by Cox, Little and O’Shea
• or as an alternative to Cox, Little and O'Shea:  sections
  1.1, 1.2, 1.3, 2.1, 2.2, 3.1, 4.1, 4.2, 4.3, 6.1, 6.2 of "Invitation to Nonlinear Algebra" by Michalek and Sturmfels

For eligibility and how to apply, see the Summer Graduate Schools homepage