The study of the structuresvof deep-sea vents and of the life around them represents an intersection of which two fields of science

It's probably either of Geology and Oceanography.

Geology is the study of solid earth which deals on rocks while Oceanography simply studies the ocean. For the study of deep-sea vents, it's probably more into geology while the studies of life on the deep sea is part of oceanography. 

This is what i found on google “phytoplankton, tiny organisms that live in the ocean, are autotrophs. some types of bacteria are autotrophs. most autotrophs use a process called photosynthesis to make their food.” i hope this you for what your looking for