Solving Systems of ODEs via Combinatorial Homological Algebra

Explore a lecture on solving systems of ordinary differential equations (ODEs) using combinatorial homological algebra. Delve into a simple yet non-trivial 2-dimensional model system with continuous piecewise linear nonlinearities and a high-dimensional parameter space. Learn how to efficiently compute a homological representation of dynamics and validate these computations for the differential equation of interest. Discover how a predetermined finite set of computations can capture dynamics across an explicitly defined "all" of parameter space. Gain insights into differential equations, the homological Conley index, Morse decomposition, and the Rook field. This 52-minute talk, presented by Konstantin Mischaikow, covers joint work with several collaborators and includes a Q&A session at the end.

Intro
What is a differential equation
What is the homological conley index
Morse decomposition
Decomposition recap
Strategy
Ramp systems
Theorems
The Rook field
Questions