The University's Environmental Sustainability team is hosting its first ever Green Action Week from 20–24 February.

This week is an opportunity to bring together the diverse and extensive sustainability work across Oxford. It aims to enhance networking and exchange of ideas, engage students and staff with research, promote environmental action, raise awareness and celebrate with colleagues. 

We invite applications for a Postdoctoral Research Assistant to undertake research in battery modeling within the Multi-Scale Mathematical Modeling Project of the Faraday Institution, to work with Professor Jon Chapman at the Mathematical Institute, University of Oxford. This is a 2-year fixed term position, until 31 March 2025.

Thu, 02 Feb 2023
17:00
L3

Geometric Stability Theory and the Classification of Unstable Structures

Scott Mutchnik
(University of California, Berkeley)
Abstract

The equivalence of NSOP${}_1$ and NSOP${}_3$, two model-theoretic complexity properties, remains open, and both the classes NSOP${}_1$ and NSOP${}_3$ are more complex than even the simple unstable theories. And yet, it turns out that classical geometric stability theory, in particular the group configuration theorem of Hrushovski (1992), is capable of controlling classification theory on either side of the NSOP${}_1$-SOP${}_3$ dichotomy, via the expansion of stable theories by generic predicates and equivalence relations. This allows us to construct new examples of strictly NSOP${}_1$ theories. We introduce generic expansions corresponding, though universal axioms, to definable relations in the underlying theory, and discuss the existence of model companions for some of these expansions. In the case where the defining relation in the underlying theory $T$ is a ternary relation $R(x, y, z)$ coming from a surface in 3-space, we give a surprising application of the group configuration theorem to classifying the corresponding generic expansion $T^R$. Namely, when $T$ is weakly minimal and eliminates the quantifier $\exists^{\infty}$, $T^R$ is strictly NSOP${}_4$ and TP${}_2$ exactly when $R$ comes from the graph of a type-definable group operation; otherwise, depending on whether the expansion is by a generic predicate or a generic equivalence relation, it is simple or NSOP${}_1$.

Counting graphic sequences via integrated random walks
Balister, P Donderwinkel, S Groenland, C Johnston, T Scott, A (17 Jan 2023) http://arxiv.org/abs/2301.07022v1

The IF Oxford festival explores science and ideas through an exciting mix of presentations and interactive activities. Thousands of visitors come to dozens of venues across the city, and connect online.

The Ratios Conjecture and upper bounds for negative moments of L-functions over function fields
Bui, H Florea, A Keating, J Transactions of the American Mathematical Society volume 376 issue 6 4453-4510 (21 Mar 2023)
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