Undergraduate Mentoring
Roberto Rezende-Uehara (Seton Hall) Spring 2025. Independent study. Curves, Surfaces, and Relativity.
Tanmay Patel (Seton Hall) 2024-2025. Senior thesis. Calculus of variations and applications.
Edward Strong (Seton Hall) 2024-2025. Independent study. Algebraic topology and smooth manifolds.
Makenna Greenwalt (Oregon) Spring 2024. Independent study. Topics in Complex Analysis.
Makenna studied advanced topics in complex analysis, such as the Riemann mapping theorem, analytic continuation and Riemann surfaces.
Ethan Ferrer-Perry (Oregon) 2023-2024. Directed reading. Problems in the Calculus of Variations.
Ethan studied the calculus of variations, with an emphasis on isoperimetric problems and the Plateau problem. Topics included the first and second variations, the direct method, geodesics, minimal surfaces, and the classical isoperimetric inequality.
Keagan Brenna (Oregon) Summer 2023. Summer research. Geometry and Dynamics of Fractals.
Through a summer research award, Keagan studied the geometry and dynamics of fractals in the plane. Specifically, he studied those fractals that can be obtained as attractor sets of iterated function systems (IFS). In the case where the IFS consists of affine functions, Keagan conjectured a classification for the attractor sets, and made progress towards its resolution.
Nick Plati (McMaster) 2019-2020. Summer research & Senior thesis. Numerical Investigation of Calibrated Submanifolds of Euclidean Space.
For his senior thesis, Nick studied a special class of minimal surfaces, called calibrated submanifolds. In the presence of symmetry, these submanifolds are (typically non-explicit) solutions to nonlinear ODE systems. Nick studied the intrinsic geometry of these submanifolds, computing their Weyl and scalar curvatures, and posed various conjectures.
Sean Afshar and Matthew Stevens (Stanford) Spring 2018. Directed reading.
As part of Stanford's Directed Reading Program, Sean and Matthew studied the mathematics of magnetic monopoles and the geometry of principal bundles. This included an introduction to manifolds, Lie groups, bundles, and connections, with applications to the Maxwell Equations and the Aharonov-Bohm effect.