I did an undergrad in math with a little research in number theory and recognized parts — eg, I myself worked through the proof for odd regular primes and that 37 is irregular, breaking the general case.

Wiles-Taylor-Wiles was the original proof by Andrew Wiles, and its corrections.

Galois representations is about vectors over Galois extensions, which are essentially adding roots to regular numbers (rationals, integers, etc). That ties into the Langlands program, which is a big area in number theory (that I don’t know much about).

Together with flat deformations and Frey curve, I think they’re talking about a topic in algebraic geometry as applied to number theory.

I also recognize the name Eisenstein from my time as an undergrad, though two decades out and not working in the field I’ve forgotten what his work on ideals implied here. Ideals are a well-known topic though, a sort of structure inside a ring (set with + and *) that is closed under operations — like evens in the integers are the 2Z ideal.

So I’d describe it as “sensible with an undergrad background”.