Mathematics Colloquium

Understanding the statistical properties of rough high-dimensional landscapes and of the dynamics within them is central to a large set of disparate fields, including statistical physics, computer science, statistics and biology. Theoretical physics methods developed to study spin-glasses, as well as new results obtained in probability theory, play a central role in this context. In this talk I will present the main results on this topic, focusing on recent progress and the new emerging questions and applications, in particular in machine learning and theoretical ecology, which provide common challenges to physicists and mathematicians.