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A smooth projective variety is said to satisfy Bott vanishing if $\Omega^j\otimes L$ has no higher cohomology for every $j$ and every ample line bundle $L$. This is a very restrictive property, and there are few non-toric examples known to satisfy it. I will present a new class of examples obtained as smooth GIT quotients of $(P^1)^n$. For this, I will need to use the work by Teleman and Halpern-Leistner about the derived category of a GIT quotient, and explain how this allows us, in some cases, to compute cohomologies directly in an ambient quotient stack.

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