Hilbert's 16th Problem and O-Minimality - Lecture 1

Explore the intricacies of Hilbert's 16th problem and o-minimality in this comprehensive lecture from the Graduate Course on Transseries and Asymptotic Analysis. Delve into key concepts such as the topology of cycles, limit cycles, and the Rolex Dilemma as presented by Patrick Speissegger from McMaster University. Gain insights into the complement of a cycle, the rolling property, and its corollary. Examine a detailed example that illustrates these complex mathematical ideas. This in-depth presentation, part of the Fields Institute's series, offers a rigorous exploration of advanced mathematical concepts for graduate-level students and researchers in the field.

Intro
The topology of the cycle
Complement of a cycle
Limit cycle
Deluxe problem
Rolex Dilemma
Example
Rolling property
corollary