Your situation with algebraic geometry is probably more similar to that of humanities graduate students than to that of students of applied math or engineering.

" [...] Contrast this situation with that of academia. Professors of Literature or History or Cultural Studies in their professional life find themselves communicating principally with other professors of Literature or History or Cultural Studies. They also, of course, communicate with students, but students don't really count. Graduate students are studying to be professors themselves and so are already part of the in-crowd. Undergraduate students rarely get a chance to close the feedback loop, especially at the so called "better schools" (I once spoke with a Harvard professor who told me that it is quite easy to get a Harvard undergraduate degree without ever once encountering a tenured member of the faculty inside a classroom; I don't know if this is actually true but it's a delightful piece of slander regardless). They publish in peer reviewed journals, which are not only edited by their peers but published for and mainly read by their peers (if they are read at all). Decisions about their career advancement, tenure, promotion, and so on are made by committees of their fellows. They are supervised by deans and other academic officials who themselves used to be professors of Literature or History or Cultural Studies. They rarely have any reason to talk to anybody but themselves -- occasionally a Professor of Literature will collaborate with a Professor of History, but in academic circles this sort of interdisciplinary work is still considered sufficiently daring and risqué as to be newsworthy.

What you have is rather like birds on the Galapagos islands -- an isolated population with unique selective pressures resulting in evolutionary divergence from the mainland population. There's no reason you should be able to understand what these academics are saying because, for several generations, comprehensibility to outsiders has not been one of the selective criteria to which they've been subjected. What's more, it's not particularly important that they even be terribly comprehensible to each other, since the quality of academic work, particularly in the humanities, is judged primarily on the basis of politics and cleverness. "