One of my characters has a Physics Ph.D, and I’m curious what an appropriate dissertation topic would be if she took these subjects:
Quantum (Field) Theory
Statistical Mechanics
Atomic+Optical Physics
Solids
(High Energy) Plasma
(Plasma) Astrophysics
“Observation of Einstein-Podolsky-Rosen Entanglement on Supraquantum Structures by Induction Through Nonlinear Transuranic Crystal of Extremely Long Wavelength (ELW) Pulse from Mode-Locked Source Array.” 
Oh, me too! I’m not up to writing great literature, I just want to tell an entertaining story. And to know what sort of business license you need to bring the dead back to life.
Quantum (Field) Theory: how about something like “Micro-local approach to the Hadamard condition in quantum field theory on curved space-time”? It’s what google scholar suggested, anyway.
Is there a way to intergrate each class into a disseratatio?
The subject wouldn’t be “Solids”, it would be “Condensed Matter Physics”.
Hmmm … solid state physics and astrophysics … maybe the references in this would be up your character’s alley. And guys, BPM 37093 makes a great valentine’s gift! 
Sounds like it’d be very interesting to study that star. I’m asking as a non-scientist, do stars involve plasma physics? How long would her Ph.d take (roughly 15 classes)?
Stars are giant balls of plasma, so studying them definitely requires plasma physics.
Given that set of classes, a good dissertation topic would be something about exotic star corpses, like neutron or quark stars. This fictional student should also probably take a course on relativity at some point. A typical physics Phd takes 5-6 years.
Excellent help! (BTW, is the 5-6 years take doing classwork into account, or is it just writting the disseration)
The 5-6 year estimate would include classwork, but it’s not unusual to take longer to earn a doctorate in physics or astrophysics.