What are the latest advances in fully homomorphic encryption? First of all, I am interested in cryptosystems based on LWE / RLWE and NTRU problems.
I guess the latest real production grade homomorphic library is Microsoft SEAL, which implements the BFV and the CKKS encryption schemes.
I'm not a big MS fan. There are other options to explore:
HELib implements the BGV scheme with GHS optimizations.
NuFHE implements a GPU reference of fully homomorphic encryption on torus
Also checkout the open group site for homomorphic encryption.