The story of the index theorem ties together the Gang of Four—Atiyah, Bott, Hirzebruch, and Singer—and lies at the intersection of analysis, geometry, and topology. In the first part of the talk I will recount high points in the early developments. Then I turn to subsequent variations and applications. Throughout I emphasize the role of the Dirac operator. This talk is part of a subprogram of the Mathematical Science Literature Lecture series, a Memorial Conference for the founders of index theory: Atiyah, Bott, Hirzebruch and Singer. Talk chair: Cumrun Vafa Registration：https://harvard.zoom.us/webinar/register/3516062319845/WN_9Qb6IBIfQ0ujujfLvue2eA

A professor in the Department of Mathematics at the University of Texas at Austin. He has worked on a variety of problems centering around global issues in geometry and global analysis. His work often relates to questions in theoretical physics (quantum field theory, string theory, and condensed matter theory).