Lê Dũng Tráng has a paper "The Geometry of the Monodromy Theorem" (MR0541020 https://mathscinet.ams.org/mathscinet/article?mr=541020 for reference). It's a nice paper, and in it Lê gives a geometric proof of quasi-unipotence of monodromy.

The ending of the paper contains some interesting suggestions for further work, and I was wondering if anyone has thought them through. I'm most interested in a suggested proof of the rationality of the roots of Bernstein's $b$-polynomial.

**Question.** Since 1978, has anyone found a way to use Lê's carrousels to prove rationality of roots of the $b$-polynomial without appealing to the resolution of singularities, as Lê suggests should be possible? 

(I'm also broadly interested in hearing about any further developments on this work; I'm a student currently trying to learn some of Lê and others' work in this area, although most of my reading so far has been papers from the 70's....)