During the tenure of this fellowship, Emily Peters investigated the classification of finite-index subfactors. Factors were first studied in the 1940s by John von Neummann, who drew inspiration from quantum mechanics. Fields medalist Vaughan Jones created the field of subfactors in the late 70s/early 80s. Recently the classification of subfactors has been a field of renewed interest, as new techniques have been developed which allow us to see further than we used to. At the same time, new computer programs are being developed to supplement human effort. Classifying subfactors has three components: systematically searching for candidates, constructing the ones that exist, and ruling out the ones that don't. Classifications of subfactors are often in terms of the index of the subfactor, which measures how big it is. Early results classified subfactors with index up to index 4, then 4.73. As an NSF fellow, Peters was part of the team which classified subfactors with index up to 5. She also worked on projects which are now helping to classify subfactors whose index is less than 5.24. Peters was also a developer of the FusionAtlas package of computer programs. These programs help streamline the construction and classification of subfactors. In these projects, there are some steps which are extremely algorithmic, and some steps at which inspiration is required. Computers can and should be doing much of the algorithmic work, and the FusionAtlas aims to streamline these computational problems. In particular, the FusionAtlas is very good at systematically searching for candidates, and has some tools which do important steps in the construction of subfactors. Furthermore, it is easily adaptable so that when new tests to rule out subfactors become available, they can easily be added to the program. As an NSF fellow, Peters also attempted to have a broader impact on mathematical literacy and student mentorship. Her public outreach efforst included talks for undergraduates and general audiences. She also taught six mathematics courses (for middle and high school students) as part of the Boston Math Circle.
