Abstract: Simple hypothesis testing is a fundamental problem in statistics, and it is well-known that its sample complexity is characterized by the Hellinger distance between the two candidate distributions. In this talk, we discuss the problem of simple hypothesis testing under communication constraints, wherein each sample is mapped to a message from a finite set of messages before being revealed to the statistician. We show that it is possible to map samples to messages such that the sample complexity is only an extra logarithmic factor larger than the non-constrained setting. Our proofs rely on a reverse data processing inequality and a reverse Markov's inequality, which might be of independent interest. This is joint work with Ankit Pensia and Po-Ling Loh.