According to the FirearmsID.com definition, Firearms Identification is "identification of fired bullets, cartridge cases or other ammunition components as having been fired from a specific firearm." This branch deals with identifying firearms that were used in crimes, as well as testing various pieces of firearms if they are working properly. Research can be conducted around how exactly forensics figure out what type of firearm was used in a crime or how they pin down crime details, like where the shot came from and how far away from the victim the shooter was standing.
DNA forensics is a very important branch of forensics that focuses on examining the DNA sequence of victims and perpetrators. Forensics can obtain DNA from bodies or any body part, such as hair, skin or bodily fluids. They don't need a lot of samples to determine the DNA; a hair, a fingernail or a single drop of blood all suffice. Because every person has an unique DNA sequence, they can then use their finding to match to the victims or criminals.
Each person has a set of fingerprints that are completely unique. Forensics always dust crime scenes for fingerprints left behind, because if they can find any samples, they have a sure way of connecting the suspects to the crime or on the other hand, if they are not guilty, discarding them as possible suspects. Interesting topics around this branch of forensic research include the techniques forensics use when looking for fingerprints, the matching procedures and crimes in which fingerprint analysis solved the case.
Forensics don't work only on murder cases and victim identification--they deal with crimes like arson as well. Forensic scientists who work on arson cases will first and foremost be interested in the source of the fire. When they determine that, they can establish if the fire was arson or not, what exactly caused it and how it spread. How forensics figure out where the fire started and specify the type of chemicals that were its source are both good topics for research.