Modern statistical tasks require the use of both computationally efficient and statistically accurate methods. But, can we always find a computationally efficient method that achieves the information-theoretic optimal statistical guarantees? If not, is this an artifact of our techniques, or a potentially fundamental source of computational hardness?
In this course, we will survey state-of-the-art results from a new and growing mathematical research area that lies at the intersection of high dimensional statistics and theoretical computer science, and studies the presence of such ``computational-statistical trade-offs''. Along the way, we will also touch on some intriguing connections with statistical physics.