Carol Greene is ready for her closeup. In the tradition of Paula Cooper and Marian Goodman, she has built a stable of artists at Greene Naftali whose work is conceptually rigorous and visually rich. Among them are Rachel Harrison, Paul Chan, Michael Krebber, the Bernadette Corporation, Gelitin and Guyton/Walker, figures who don’t so much reflect culture as define it. Dedicated and tough-minded, Greene doesn’t shy away from difficult stuff: a 2010 Bjarne Melgaard show featured man-on-horse porn. Nor fun: her after parties go all night, attracting people from Kim Gordon of Sonic Youth to experimental theatre director Richard Maxwell. Perhaps unique in New York, she is as respected by uptown collectors and museum curators as she is by the creative denizens of downtown. She is in it for the long run, and she’ll likely define it, too.