This lecture covers three intriguing examples of interactions between physics and geometry: (i) the use of mirror symmetry in a conformal field theory to enumerate rational curves on a quintic, (ii) the Kontsevich matrix model that led to a solution of a conjecture of Witten, and (iii) the Jones-Witten knot invariant and Chern-Simons quantum field theory. The lecture is preceded by an interview with Singer, in which he discusses some of the historical background of these topics and reminisces a bit about how he got interested in mathematics and science. Providing insight on one of the hottest topics in mathematics, as well as a personal look at one of the leaders in the field, this DVD would be of interest to students and researchers in mathematics, physics, and the history of science.