FMA - Filipino Martial Arts. I (mostly) practise a style called Doce Pares, my teacher is Ermar Alexander, who teaches Supreme Grandmaster Diony Canete's Multi-Style system.
Doce Pares as I learn it looks like this:
Doce Pares as I practise it looks like this:
As you can see I've got quite a way to go.
HEMA - Historical European Martial Arts. I'm very new to HEMA, but I already love it dearly. I'll defer here to Wikipedia's definition: "Historical European martial arts (HEMA) refers to martial arts of European origin, particularly using arts formerly practised, but having since died out or evolved into very different forms."
The particular styles I'm studying are the longsword techniques of Fiore De Liberi and the 19th century Infantry Officer's Sabre techniques of John Musgrave Waite as taught by Matt Easton at Schola Gladiatoria.
I'll update this post as I go along or if anyone needs clarification.