Isaac Wind Newell
MMathCompSci (Oxon)
Status
Postgraduate Student
Research groups
Address
Mathematical Institute
University of Oxford
Andrew Wiles Building
Radcliffe Observatory Quarter
Woodstock Road
Oxford
OX2 6GG
University of Oxford
Andrew Wiles Building
Radcliffe Observatory Quarter
Woodstock Road
Oxford
OX2 6GG
Major / recent publications
- N. Boullé, I. Newell, P. E. Farrell, and P. G. Kevrekidis, Two-component three-dimensional atomic Bose-Einstein condensates supporting complex stable patterns, Phys. Rev. A 107 (2023), 012813.
Teaching
- Stanford University Math 53 (Trinity 2024), tutor
- Part A Number Theory (Trinity 2024), tutor
- Prelims Groups and Group Actions (Trinity 2024), tutor
- Continuous Mathematics, CS Dept., (Hilary 2024), tutor
- C4.4 Hyperbolic Equations (Hilary 2024), TA
- Part A Linear Algebra (Michaelmas 2023), St Edmund Hall, tutor
- Prelims Linear Algebra (Michaelmas 2023), Wycliffe Hall, tutor
- B4.2 Functional Analysis (Trinity 2023), tutor
- B4.4 Fourier Analysis (Hilary 2023), TA
- B4.3 Distribution Theory (Michaelmas 2022), TA
Prizes, awards, and scholarships
- 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)
Research interests
I study the isometric embedding of Riemannian manifolds through the medium of nonlinear PDEs: namely, the Gauss-Codazzi-Ricci (GCR) equations. I am especially interested in low-regularity problems: the interpretation, validity, and geometric consequences of the GCR equations for rough embeddings. I also study geometric rigidity problems motived from elasticity theory. Broadly, I am interested in compensated compactness methods for nonlinear PDEs, mixed-type problems, and connections between differential geometry and hyperbolic conservation laws from continuum physics.