President Trump cast his effort to broker peace in Ukraine in existential terms.

© Doug Mills/The New York Times

President Volodymyr Zelensky of Ukraine and other European leaders have learned a thing or two about negotiating, Trump-style. So has Vladimir Putin.

© Doug Mills/The New York Times

President Volodymyr Zelensky of Ukraine and other European leaders have learned a thing or two about negotiating, Trump-style. So has Vladimir Putin.

© Doug Mills/The New York Times

President Trump held forth about the nature of show business and his own tortured relationship with celebrity.

© Tierney L. Cross/The New York Times

The president has taken a strong interest in the Kennedy Center’s affairs ever since naming himself chairman in February, when he restocked its traditionally bipartisan board with loyalists.

© Tierney L. Cross/The New York Times