Projects for the 2016 Math REU Program
(Vertex Operator Algebras and partition identities) Mentor: Jim Lepowsky, Matthew Russell, Bud Coulson. Participants: Terence Coelho, Jongwon Kim. In this project, new proofs of partition identities of Rogers-Ramanujan type, and relations with the theory of vertex operator algebras, will be developed.
(Schubert calculus) Mentor: Anders Buch. Participants: Chin-Nuo Lee, Arthur Wang. The project will study the relations between Weyl groups and the geometry of generalized flag manifolds, with the aim of proving a conjecture related to curve neighbourhoods of Schubert varieties.
(Non-displaceable Lagrangians) Mentor: Chris Woodward, Doug Schultz. Participants: George Jeffreys, Daniel Gallagher. The project will study the extent to which Lagrangian tori in moduli spaces of polygons are displaceable, using the technique of McDuff.
(Complex analysis) Mentor: X. Huang. Participant: Eliot Glazer. The project will investigate when the cannonic metric over a hyperbolic Riemann surface coincides with its Bergman metric. (A well-known conjecture predicts that this happens if and only if the Riemann surface is holomorphically equivalent to the unit disk in the Gauss plane.)
(Persistence of grayscale images) Mentor: Rachel Levanger. Participant: Thomas Murrills. We are investigating ways to make the correspondence between sublevel and superlevel persistence of grayscale images more rigorous. Our work will be used to strengthen an ongoing investigation of topological methods for characterizing pattern formation in turbulent fluid flows.
The department plans a similar range of projects in 2017. Typically projects are assigned depending on the applicants and funding available and are decided in February-March of each year. Interested applicants should apply through DIMACS, through their .