Almost two years ago, Gina Gibney, the director of the Gibney Dance Company, received a gift of $2 million so that she could reinvent her 29-year-old company. Most dance troupes in New York City perform repertory created by their founding choreographer, but Gibney decided it was time to change that paradigm. Why not take in the global dance scene and build an international repertory, much as the Nederlands Dans Theater does? Now, the newly-calibrated Gibney Company debuts at the Joyce with three premieres. Among the commissioned choreographers are Sonya Tayeh, who won the Tony for Best Choreography for Moulin Rouge! The Musical; Alan Lucian Øyen, a Norwegian who recently created a work for Tanztheater Wuppertal; and Rena Butler, the company’s inaugural choreographic associate (her premiere, Lusus Naturae, invokes the film icon King Kong). Brava to Gibney. —L.J.