NEW YORK — Several Columbia University professors said this week that the recent resignations of two high-ranking black administrators have shaken their confidence in the institution’s president, Lee C. Bollinger, and reignited concerns among their colleagues about other aspects of his leadership.

Last Saturday, Stanford quarterback Tavita Pritchard was struck in the head by an opponent so violently that his helmet was ripped off, his bare head snapped back and forth and his skull slammed to the ground with a thud.