Interview with Robert Rossarie
Date: 10:30 29/09/2022
This is an interview with Robert Roussarie. He is mainly known for his 
contribution to Hilbert's sixteenth problem and ciclicity of polygons. 
The interview will be around the following questions: 

1. Please tell us about your first mathematical experiences: They were fostered by which people and who were your first mathematics teachers?

2. What is your first feeling of discovery in mathematics?

3. You started your career in  topology and foliations in real manifolds. Tell us about this and how you started to slowly move to limit cycles and Hilbert's 16 problem.  

4.Tell us about the project of finiteness of cyclicity for planar differential equations. How it started?

5. What do you think about many claims that they have solved the Hilbert 16th problem? Why this problem has so many wrong proofs?

6. Have you tried to understand Ecalle and Ilyashenko's proof of the first part of Hilbert 16th problem?

7. What is your vision for the final solution of uniform bound for limit cycles? Which tools must be developed yet?

8. Many interesting differential equations which come from nature have real numbers as time parameter! What is a complex time for you?

9.  What is your favorite planar differential equations and why?

10. You have been in Brazil many times. How your connection with Brazil started?

11.  If you were to start a new career, what you would choose in mathematics or even science or art?














7. Do you think any arithmetic will be involved? For instance, studying polynomial vector fields by doing modulo primes? What do you think of studying polynomial differential equations in a purely algebraic-geometric framework with less dynamics involved?

8. After the comlexification of planar differential equations under the name holomorphic foliations, many other problems and conjectures 
such as the minimal set problem have arisen, and now there are many people working on these problems without interests on limit cycles. 
What do you think about this process of getting away from the origin of mathematical  objects? 

9. Many interesting differential equations which come from nature have real numbers as time parameter! What is a complex time for you?