Partial differential equations (PDEs), often regarded as the language of physics and engineering, encode how quantities such as velocity, temperature, pressure, or concentration evolve in space and time. PDEs provide the mathematical framework through which we model the real world. Yet, even when the governing equations are known, predicting their behaviour can be challenging. Konstantin Riedl investigates.

Computers have long been useful for studying mathematical problems. But recently computer techniques have been used to prove new theorems in geometry, specifically related to the study of gravity through Einstein's theory of General Relativity. This Oxford Mathematics Public Lecture will describe these developments and what they might mean for the future.

Quantum computers achieve a remarkable exponential speedup in integer factorisation (potentially making widely deployed cryptographic schemes vulnerable). Beyond that large-scale applications remain comparatively scarce, and if a fully error-corrected quantum computer were available it is not clear what 'killer app' it would be used for.