By ERIC ANDERSON (Albany) Times Union Amtrak officials have been crisscrossing the United States in recent months, meeting with state transportation officials in places like Tennessee, Texas and Nevada as they seek to bring train service to some of the nation’s fastest growing population centers. While most of the focus is on new routes in the South and West, New York state and the Capital Region likely would benefit from the effort as well. Amtrak is focusing on developing new “corridors,” routes tying together population centers that are several hundred miles apart and offer frequent train service. Some of the changes would be extensions of existing routes.