
Isaac Wind Newell
Address
Mathematical Institute
University of Oxford
Andrew Wiles Building
Radcliffe Observatory Quarter
Woodstock Road
Oxford
OX2 6GG
- B4.3 Distribution Theory (Michaelmas 2022), TA
- B4.4 Fourier Analysis (Hilary 2023), TA
- Clarendon Scholarship (2022-2026)
- Mathematical Institute Studentship (2022-2026)
- Hoare Prize in Mathematics and Computer Science (2022)
- Penultimate Year Prize, Oriel College (2021)
- LMS Undergraduate Research Bursary (2021)
- N. Boullé, I. Newell, P. E. Farrell, and P. G. Kevrekidis, Two-Component 3D Atomic Bose-Einstein Condensates Support Complex Stable Patterns, submitted, 2022.
I am interested in nonlinear partial differential equations arising in differential geometry, in particular the problem of isometric embeddings of Riemannian manifolds in Euclidean space. The PDE system at hand is the Gauss-Codazzi system, whose type, in the case of surfaces, depends on the sign of the Gauss curvature. There are many open questions concerning existence of isometric embeddings, particularly when the curvature is negative (giving a hyperbolic system) or can change sign (giving a mixed-type system).