Glover attended Cornell University for his bachelor's degree, where classes taught by Leonard Gross, Kiyosi Itô, and Frank Spitzer sparked his interest in probability theory.

[1] In 1977, he obtained a master's degree in mathematics from the University of California, San Diego,[2] where he also completed his Ph.D. in 1978 under the supervision of Michael Sharpe.

Glover then served as the associate dean for faculty affairs for the College of Liberal Arts and Sciences.

[6] He served as provost until July 2023, when he stepped down from the position to become senior advisor to the University of Florida's incoming president, Ben Sasse.

[10] Glover notified faculty, staff, and students that he would be resigning from the University of Arizona on August 13th via email.