I've also been told multiple times by multiple sources that women values confidence, competence and leadership. I understand the confidence part in being able to express without embarassment your interest (but still in a socially graceful manner), but I would really like pointers about what area of my life I could engage to become more competent or a leader. In what domains women like competence/leadership?

It would be useful to know what's your job. I've gained a lot of confidence with people in general since I left the Unversity (used to be a physicist) and went to work to a private firm where I have to take responsibility with the customers all the time. In general: practice makes better, find a way to practice interaction with people and you will become better at it. In addition, being good at your job is usually a self-esteem boost, that reflects in your everiday behavior.

My only hobby at the moment are the game of Go and dabbing in math/logics/AI, which, as fascinating as they are, are seldom considered very attractive.

This seems realy limiting, I'm sure there's gonna be more. It doesn't need to be a proper hobby, just something you're interested in. Do you read books? Watch movies? Follow the news? Have some funny story to share? It should be enough to break ice at least. Other than that, sometimes topics are as interesting as you make them be. I've entertained girls talking about particle physics, economics models, Dunbar number and yes, even AI related stuff.