At the kick-off party for the reopening of the New York Public Library for the Performing Arts, Liza Minelli, newly engaged to David Gest, was spotted with lifelong jazz coach Luigi, who also coached mom Judy Garland. “I’m working with Liza to get her back in shape,” Luigi told The Sheet. “She takes my classes every day and has been working with me since she was 16.” On the committee to reopen the library at Lincoln Center this fall: Lauren Bacall, Kevin Spacey, Audra McDonald, Phillip Glass, and Paul Taylor.