Last semester I gave a talk that was a 1-hour condensation of undergrad machine learning. https://video.ias.edu/membsem/2017/1127-SanjeevArora . This semester's talk will be a 1-hour treatment of some research directions in theoretical machine learning, including the generalization mystery (why do deep nets generalize to unseen examples, despite having far more parameters than the number of training examples?) and Generative Adversarial Nets (GANs). This will be a bit more mathematical but still accessible to a general math audience. (A more comprehensive survey of research directions was in this grad seminar: http://www.cs.princeton.edu/courses/archive/fall17/cos597A/)