TBA

Motivated by work of Hrushovski on pseudofinite fields with an additive character we investigate the theory ACFA+ which is the model companion of the theory of difference fields with an additive character on the fixed field. Building on results by Hrushovski we can recover it as the characteristic 0-asymptotic theory of the algebraic closure of finite fields with the Frobenius-automorphism and the standard character on the fixed field. We characterise 3-amalgamation in ACFA+. As cosequences we obtain that ACFA+ is a simple theory, an explicit description of the connected component of the Kim-Pillay group and (weak) elimination of imaginaries. If time permits we present some results on higher amalgamation.

Speaker: Mattia Magnabosco (Newton Fellow, Maths)
Title: Synthetic Ricci curvature bounds in sub-Riemannian manifolds
Abstract: In Riemannian manifolds, a uniform bound on the Ricci curvature tensor allows to control the volume growth along the geodesic flow. Building upon this observation, Lott, Sturm and Villani introduced a synthetic notion of curvature-dimension bounds in the non-smooth setting of metric measure spaces. This condition, called CD(K,N), is formulated in terms of the optimal transport interpolation of measures and consists in a convexity property of the Rényi entropy functionals along Wasserstein geodesics. The CD(K,N) condition represents a lower Ricci curvature bound by K and an upper bound on the dimension by N, and it is coherent with the smooth setting, as in a Riemannian manifold it is equivalent to a lower bound on the Ricci curvature tensor. However, the same relation between curvature and CD(K,N) condition does not hold for sub-Riemannian (and sub-Finsler) manifolds. 

Speaker: Rebecca Lewis (Florence Nightingale Bicentenary Fellow, Stats)
Title: High-dimensional statistics
Abstract: Due to the increasing ease with which we collect and store information, modern data sets have grown in size. Whilst these datasets have the potential to yield new insights in a variety of areas, extracting useful information from them can be difficult. In this talk, we will discuss these challenges.

From genetic studies and astrophysics simulations to statistical modelling and AI, scientific computing has enabled amazing discoveries and there is no doubt it will continue to do so. However, the corresponding environmental impact is a growing concern in light of the urgency of the climate crisis, so what can we all do about it? Tackling this issue and making it easier for scientists to engage with sustainable computing is what motivated the Green Algorithms project. Through the prism of the GREENER principles for environmentally sustainable science, we will discuss what we learned along the way, how to estimate the impact of our work and what levers scientists and institutions have to make their research more sustainable. We will also debate what hurdles exist and what is still needed moving forward.