Are you allowed to learn Torah silently during the chazzan's repetition of Shmonah Esrei?
(This is a case where you are davening with that minyan.)
From the Kitzur Shulchan Aruch:
ואפילו ללמוד אסור בשעה שהשליח צבור חוזר התפלה
"And even learning is forbidden when the Chazzan repeats Shemoneh Esrei.
From Daily Jewish Law
One should not learn Torah during the repetition of the amidah. There are a few concerns:
At least 10 men must pay attention to every word of the amidah;
All of those who are present are obligated to pay attention to the end of each berachah and answer Amen;
Even if there are ten who pay attention to every word, and even if the one who is learning is careful to pay attention sufficiently to answer Amen, others may misunderstand and assume that all learning is permitted.
(Rav Moshe Feinstein, Igrot Moshe Orach Chaim 4:19)
The Rama Mipano says (Shut Rama Mipano 102:8) that those that learn durin'g Hazarat HaSha"s have something to rely on. However, Hacham Yishak Yosef Shalit"a writes that "Yesh LeHimana" one should refrain from doing so (Yesh Lehimana doesn't mean that's an Isur rather not recommended).
Certainly not during kedushah and birkat kohanim. During the rest of chazarat hashatz, I am not sure, but I know that it is forbidden even to think hirhurei divrei torah during kedushah (which is part of chazarat hashatz) because at that time a person's mind should be focused on holiness alone.