Twenty-two years old, just graduated from Columbia University and about to enter his first meaningful romantic relationship, Barack Obama charmed a young Australian woman at a Christmas party in 1983. Sitting on an orange bean bag in the sixth-floor East Village apartment in New York City, Mr. Obama and Genevieve Cook, who was three years older, swapped stories about their overlapping stays in Jakarta, where he spent time as a boy. “They talked nonstop, moving from one subject to another, sharing an intense and immediate affinity, enthralled by the randomness of their meeting and how much they had in common.