David Roe

Bio

David Roe is a principal research scientist in the Department of Mathematics at MIT.  He studies computational number theory and arithmetic geometry with a particular focus on p-adic fields, which are analogues of the real numbers with a different notion of distance designed to measure divisibility by a fixed prime number.  He has used p-adic numbers to develop point counting algorithms for varieties over finite fields, to study modular forms of varying level, and to design fast algorithms for computing L-functions associated to hypergeometric motives.  He has also contributed to the study of p-adic numbers themselves, from methods for tracking precision in p-adic computations, to criteria for determining which Galois groups may arise for p-adic extensions, to improved techniques for enumerating p-adic fields of small degree.  The p-adic numbers also played a central role in his journey toward building computational tools for the mathematical community, which began with his work on p-adic computation in SageMath.  Building on this foundation, he has been heavily involved in developing the L-functions and modular forms database (LMFDB), a collection of mathematical objects arising in number theory and arithmetic geometry; he is also one of the founders of researchseminars.org, a site created during the pandemic to connect mathematicians to online research seminars.