The great man theory of history is back in vogue: the idea that it is individuals not wider forces that shape the world, both by their own actions and the way they influence others. In music, Beethoven has long been a member of the club. Here's why (it starts very quietly).
Conducted by Paavo Järvi with the Deutsche Kammerphilharmonie Bremen
Join us for a one-day, in-person conference hosted by the Mathematical, Physical and Life Sciences (MPLS) Division, bringing together researchers, technicians, and research enablers to explore how artificial intelligence is shaping scientific inquiry - and the ethical questions that arise.
This event is a showcase for cutting-edge research across the MPLS Division, with opportunities for interdisciplinary exchange, networking, and collaboration.
Oxford Cancer will be visiting the MI on Tuesday 28th October, with a stand outside L1. They will be promoting their DPhil in Cancer Programme, demonstrating how mathematics can be used to solve real world problems, and how mathematics can power interdisciplinary careers.
For more information about Oxford Cancer, please drop by their stand on Tuesday, and visit their website: https://www.cancer.ox.ac.uk/
A DPhil position is available in the Infectious Disease Modelling research group in the Oxford Maths Institute (https://www.maths.ox.ac.uk/groups/mathematical-biology/infectious-disease-modelling).
11:00
Incidence Bounds in Valued Fields with Finite Residue Field
Abstract
Elekes and Szabó established non-trivial incidence bounds for binary algebraic relations in characteristic 0, generalizing the Szemerédi-Trotter theorem for point-line-incidence. This was later generalized to binary relations defined in reducts of so-called distal structures in a result of Chernikov, Peterzil and Starchenko. For fields of positive characteristic, such bounds fail to hold in general. Bays and Martin apply the bounds for distal structures in the context of valued fields to derive incidence bounds in the sense of Szemerédi-Trotter in fields admitting valuations with finite residue field, such as F_p(t). We show that this result can be made uniform in the size of the finite residue field, by making precise in some sense the intuition that ACVF is distal relative to the residue field. In this talk, I will introduce the relevant notions from incidence combinatorics and distality, before outlining a proof of the uniform-in-p result.