# 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.

Research interests

My research focuses on 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. I am especially interested in the connections between isometric embedding and hyperbolic conservation laws, compensated compactness methods, and geometric rigidity problems. I am jointly supervised by Prof Gui-Qiang Chen and Prof Luc Nguyen.

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)

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