**September 1 – 8, 2019**

**Organizers: Jaume Llibre (Barcelona), Dana Schlomiuk (Montréal)**

Polynomial vector fields occur in many areas of applied mathematics such as for example in population dynamics, chemistry, electrical circuits, neural networks, shock waves, laser physics, hydrodynamics, etc. They are also important from the theoretical point of view. Three problems about these systems stated more than one hundred years ago are still open. Theoretical developments in this area of research are bound to shed light on these very hard open problems and have an impact on applications. In recent years a number of new significant results were obtained on families of polynomial vector fields. The goal of this workshop is to focus on these new developments, facilitate scientific exchanges and stimulate further activity in this growing area of research.

Some of the points which will be discussed are the following:

- The algebraic invariant theory of polynomial differential systems.
- Integrability of polynomial differential systems.
- Algorithms for effective computations of algebraic and geometric properties of polynomial vector fields.
- Hilbert’s 16th problem.
- Counting problems on particular solutions of polynomial vector fields.
- Singular perturbations problems occurring in planar slow-fast systems.