Mathematicians have studied elliptic curves for decades, owing to their beautiful abstract structure, powerful applications in number theory and algebraic geometry, and practical relevance in cryptography. It is surprising, therefore, that the so-called murmuration phenomenon was first observed in 2022.

Murmurations can be observed through studying databases of arithmetic and automorphic objects, rather than through studying individual objects. The availability of such databases facilitates the application of machine learning (ML) and other data scientific tools. Indeed, murmuration was first discovered by simply taking averages of certain elliptic curve datasets, and it has been shown that various invariants of arithmetic objects can be learned successfully through standard ML techniques such as logistic regression, random forest and neural networks with high (often greater than 95%) accuracy in classification. This approach opens up many possible directions for other ML experiments, their interpretation, and, subsequently, new understanding. In this workshop, we will explore murmuration structures for other arithmetic and automorphic objects, explore the utility of other tools from ML, and seek to establish conjectures, heuristics, and, where possible, rigorous mathematical explanations.

This workshop will provide the opportunity to gather together a wide array of perspectives on elliptic curves, and other number theoretic objects, in the hope of developing structural theorems and applications of this new discovery to outstanding questions in arithmetic. The topic of this workshop also offers a timely opportunity to find directions along which we may further explore this new paradigm of research.

This workshop is partially funded by a Simons Foundation Targeted Grant to Institutes.