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