Literally, an epicenter is the point of origin of an earthquake, the part that has the strongest vibrations. Figuratively, especially when applied to culture, an "epicenter" is the center, the focal point, the place with the richest, highest concentration of something, such as culture.
Example: In a recent review of Sapporo University for potential exchange students to Japan, I wrote, "Of course, being removed from the cultural epicenters of Japan means making some compromises. Certain things will probably be more expensive in Hokkaido than they would be in Honshu. Hotels don’t seem to have free Internet, for instance."
To conclude the article, I wrote, "It’s an interesting mixture of nature and people, occupying a different place on the slider than options in Tokyo, Osaka, and Kyoto." Tokyo, Osaka and Kyoto are the cultural epicenters of Japan.
"I'll Let You Kick This One Off"
In idiomatic speech, to "kick off" something is to begin something; that is, to be the first to do something.
Example: In a recent "The Early Show" segment on CBS, two political commentators were being consulted by a CBS hostess about recent political events: (Republican) Ann Coulter, and (Democratic) Tanya Acker. The first question concerned credit for the U.S. withdrawal of combat troops from Iraq for President Obama. The second question concerned what the Associated Press now calls the "NY Mosque" controversy.
Ann Coulter had answered the segment's first question before Tanya. When the hostess posed the second question, she said, "Tanya, I'll let you kick this one off." This meant, Tanya would be permitted to answer first for the second part of the segment. It is in this sense that she was "kicking off" the second part.
(English Idioms takes no political positions, but this is a real-life example of the idiom.)
"Did You Get Him?"
In American action movies, to "get" someone is to successfully kill or make unable to fight an enemy in a gunfight.
This use was a feature of idiomatic speech in the U.S. Army long before ever seeing the movie screen.
Example: In "Cop Out," the goofy African-American sidekick "Paul" (played by Tracy Morgan) to Bruce Willis' character "Jimmy," successfully shoots "a bad guy" in a gunfight within the corridor directly behind the front door of a house owned by a notorious drug dealer.
"Jimmy" (Bruce Willis) asks, "Did you get him?"
"Paul" (Tracy Morgan) replies, "His head ain't on his body no more, does that count?" [Rough paraphrasing. I only saw the movie because a family member rented it.]
This means, the bad guy's head had been "taken off" by the gunshot so yes, that was probably a fatal shot. (Probably?)
Something You Can Live With
Broadly speaking, "something you can live with" is something that is undesirable, but is tolerable and can be withstood. In business, "something you can live with" is a deal that will not result in catastrophic consequences such as bankruptcy.
This idiom is used to describe a painful result that is not "fatal" to a company; if it is not "deadly" or "lethal" to the company's profits, the financial pain can be tolerated.
Example: "Company X made many concessions in its recent deal with the labor union. The deal was something the company could live with. Regardless, a prolonged strike would have been more damaging than the deal that was reached."
Meeting In The Middle
To "meet in the middle" (also: meet mid-way, meet halfway) is, put simply, to compromise during negotiations of some sort.
The context can be political or social, but is often applied to business deals. Each side concedes something in order to reach an agreement that benefits both sides in some way, even if neither side is fully satisfied with the result.
Example: "Company X avoided a long labor dispute with the union representing its workers. The union's demands were very high, but both sides met in the middle and a deal was reached."
➤ Read more idioms and phrases, English grammar and vocabulary at Basic English Grammar And Vocabulary .