Department Colloquium

It is conjectured that many models of statistical mechanics have a rich, fractal-like behaviour at and near their points of phase transition, with power-law scaling governed by critical exponents that are expected to depend on the dimension but not on the small-scale details of the model such as…

Abstract: This talk presents recent work on understanding certain solutions of PDE by combining modern mathematics with classical analysis. Machine learning, particularly Physics-Informed Neural Networks (PINNs), is being applied to discover new solutions to nonlinear PDEs with high accuracy. A…

I will explain a proof of the BCFW triangulation conjecture which states that the cells appearing in the Britto–Cachazo–Feng–Witten (BCFW) recursion triangulate the amplituhedron (in full generality at all loop levels). The key ingredient is a relation to …

Abstract: Over the past year, Aristotle, a new system combining formal methods and language modeling, has achieved gold-medal level performance at the IMO, solved open conjectures, and opened up a strange new way of working with math. This talk will explain the technology behind Aristotle and…

Abstract: Many physical systems with chaotic microscopic dynamics display remarkably regular macroscopic behavior. For example, gases made of many interacting particles are well described, at large scales, by familiar hydrodynamic equations such as those of Euler or Navier–Stokes. These systems…

Abstract: Once convexity, duality and volume appear on stage, the Mahler Conjectures are inevitable. These conjectures predict the extremizers of the volume of a convex body times the volume of its dual. They date from the 1930's and are still largely open.

This ``…

Abstract: In many fluid phenomena, experiments and simulations are generating more and more high-resolution time series data, and these pose a problem of great potential usefulness: how can we extract significant, low-dimensional invariants that capture the complexity of any pattern which flows…