Tomorrow, this year’s Fields medals were awarded*. The four recipients of this prestigious quadrennial accolade have made profound advancements in their respective areas of mathematics, specifically:
- Artur Avila has revolutionised the study of dynamical systems, proving many hitherto open conjectures in the field. This is exciting from both a pure perspective, augmenting our understanding of the ergodic theory of various systems; and from an applied point of view, giving a deeper insight into the behaviour of chaotic systems such as phase transitions.
- Manjul Bhargava‘s research massively generalises Gauss’s composition law, as well as enabling one to enumerate rings of finite rank with a particular discriminant. This has subtle connections to the theory of algebraic curves, including new bounds on the average rank of elliptic curves.
- Martin Hairer made extremely notable discoveries about stochastic partial differential equations, which generalise PDEs by including the effects of random noise. In doing so, he…
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