Mathematics for genetics
Genetics is a very wide field of knowledge and many different areas of mathematics are being applied to genetics. Here is a probably not exhaustive list of the fields of mathematics that I have encountered in genetics (you will note that the elements of the list are not mutually exclusive)


diffusion equations
differential equations
markov processes
birth-death process
probability theory (a lot of it)
Bayesian probabilities
statistics
Math related to MCMC processes as well as HMC processes
Many fields of theoretical computer science are being applied and I guess theoretical computer science is a field of mathematics.
Graph theory
numerical integration
Analysis of dynamic systems


You say


set theory


Yes of course

group theory


Probably not so much or maybe I jsut don't really know what it is

ordinary and partial differential equations


I think pretty much any field of science applying mathematics will use differential equations.



But of course, not all geneticists are good mathematicians. Each geneticist specialize in a particular subfield. Some of them do a lot of mathematical modelling, others don't do any. Statistics and everything related to data science will always be useful though.