This talk is going to be an extended and more technical version of my brief public lecture https://www.ias.edu/ideas/2017/arora-zemel-machine-learning
I will present some of the basic ideas of machine learning, focusing on the mathematical formulations. Then I will take audience questions.
In the lectures I will formulate a conjecture asserting that there is a hidden action of certain motivic cohomology groups on the cohomology of arithmetic groups. One can construct this action, tensored with $\mathbb C$, using differential forms. Also one can construct it, tensored with $\mathbb Q_p$, by using a derived version of the Hecke algebra (or a derived version of the Galois deformation rings).