Mr Alexander Cliffe

I am a final year DPhil student in the OxPDE research group at the maths department in Oxford. My research concerns the well-posedness of the Euler equations for compressible gas dynamics, and related equations. In particular, I am investigating the interaction between multiple shock waves in compressible gasses. Some keywords in my research area are hyperbolic conservation laws, 2D Riemann problems, free boundary problems, mixed hyperbolic-elliptic type PDE, and shock reflection phenomena.

Teaching

At St Peter’s College, I teach a range of applied maths courses including M5 Fourier Series and PDE, A1 DE1, A6 DE2, ASO Integral Transforms, and ASO Calculus of Variations. I have also taught numerous courses in the maths department including B4.3 Distribution Theory, B5.6 Nonlinear Systems, B6.1 Numerical Solutions of DEs 1, and C4.6 Fixed Point Methods for Nonlinear PDE.

General interests

Outside of mathematics, I have a general interest in physics, and have been involved with the UK IOAA team as a tutor since 2019, and as a team leader at IOAA22 in Georgia. I enjoy playing many sports, including hockey for the University Men’s 2s, squash, golf, and power lifting.

Major publications

G-Q. Chen, A. Cliffe, F. Huang, S. Liu, and Q. Wang. Global solutions of the two-dimensional Riemann problem for four-shock interactions for the Euler equations for potential flow, in preparation.