We will discuss topological and algebraic aspects of splittings of free groups. In particular we will look at the core of two splittings in terms of CAT(0) cube complexes and systems of surfaces in a doubled handlebody.

In this talk I will discuss some recent constructions of blow-up solutions for a Fujita type problem for power related to the critical Sobolev exponent. Both finite type blow-up (of type II) and infinite time blow-up are considered. This research program is in collaboration with C. Cortazar, M. del Pino and J. Wei.

Hannah Fry takes us on a tour of the good, the bad and the downright ugly of the algorithms that surround us. Are they really an improvement on the humans they are replacing?

Hannah Fry is a lecturer in the Mathematics of Cities at the Centre for Advanced Spatial Analysis at UCL. She is also a well-respected broadcaster and the author of several books including the recently published 'Hello World: How to be Human in the Age of the Machine.'

5.00pm-6.00pm, Mathematical Institute, Oxford

Please email @email to register

Watch live:
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The Oxford Mathematics Public Lectures are generously supported by XTX Markets

Breakthroughs in machine learning have led to impressive results in numerous fields in recent years. I will review some of the best-known results on the computer science side, provide simple ways to think about the associated techniques, discuss possible applications in string theory, and present some applications in string theory where they already exist. One promising direction is using machine learning to generate conjectures that are then proven by humans as theorems. This method, sometimes referred to as intelligible AI, will be exemplified in an enormous ensemble of F-theory geometries that will be featured throughout the talk.

It is a classical theorem of Magnus that the word problem for one-relator groups is solvable; its precise complexity remains unknown. A geometric characterization of the complexity is given by the Dehn function. I will present joint work with Daniel Woodhouse showing that one-relator groups have a rich collection of Dehn functions, including the Brady--Bridson snowflake groups on which our work relies.

We consider a collisionless kinetic equation describing the probability density of particles moving in a one-dimensional domain subject to partly diffusive reflection at the boundary. It was shown in 2017 by Mokhtar-Kharroubi and Rudnicki that for large times such systems either converge to an invariant density or, if no invariant density exists, exhibit a so-called “sweeping phenomenon” in which the mass concentrates near small velocities. This dichotomy is obtained by means of subtle arguments relying on the theory of positive operator semigroups. In this talk I shall review some of these results before discussing how, under suitable assumptions both on the boundary operators (which in particular ensure that an invariant density exists) and on the initial density, one may even obtain estimates on the rate at which the system converges to its equilibrium. This is joint work with Mustapha Mokhtar-Kharroubi (Besançon).

I will explain a new proof of the non-linear stability of the Minkowski spacetime as a solution of the Einstein vacuum equation. The proof relies on an iteration scheme at each step of which one solves a linear wave-type equation globally. The analysis takes place on a suitable compactification of $\mathbb{R}^4$ to a manifold with corners whose boundary hypersurfaces correspond to spacelike, null, and timelike infinity; I will describe how the asymptotic behavior of the metric can be deduced from the structure of simple model operators at these boundaries. This talk is based on joint work with András Vasy.