Explore the concept of minimal exponents in singularities through this lecture by Harvard's Mihnea Popa. Delve into the relationship between minimal exponents and log canonical thresholds, and discover their connections to Igusa zeta functions. Examine the topic through the lens of D-modules, Hodge theory, and birational geometry. Learn about differential identities, roots of Bernstein-Sato polynomials, Lichtin's question, localization, Hodge ideals, and properties of minimal exponents. Conclude with a discussion on open problems in this field of mathematical research.