Moments of moments of the characteristic polynomials of random orthogonal and symplectic matrices
Claeys, T
Forkel, J
Keating, J
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
volume 479
(22 Feb 2023)
Geometric analysis enables biological insight from complex non-identifiable models using simple surrogates
Browning, A
Simpson, M
PLoS Computational Biology
volume 19
issue 1
(20 Jan 2023)
Inspired by jumping insects, Oxford Mathematicians have helped develop a miniature robot capable of leaping more than 40 times its body length - equivalent to a human jumping up to the 20th floor of a building. The innovation could be a major step forward in developing miniature robots for a wide range of applications.
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The computational complexity of knot genus in a fixed 3-manifold
Lackenby, M
Yazdi, M
Proceedings of the London Mathematical Society
volume 126
issue 3
837-879
(01 Mar 2023)
A category-theoretic proof of the ergodic decomposition theorem
Moss, S
Perrone, P
Ergodic Theory and Dynamical Systems
volume 43
issue 12
4166-4192
(15 Feb 2023)
Measuring Unruh radiation from accelerated electrons
Gregori, G
Marocco, G
Sarkar, S
Bingham, R
Wang, C
(17 Jan 2023)
Analysis and modeling of client order flow in limit order markets
Cont, R
Cucuringu, M
Glukhov, V
Prenzel, F
Quantitative Finance
volume 23
issue 2
187-205
(16 Jan 2023)
In memoriam: Marco Avellaneda (1955-2022)
Cont, R
Mathematical Finance
volume 33
issue 1
3-15
(10 Jan 2023)
Thu, 26 Jan 2023
17:00
17:00
L3
Decidability of the class of all the rings $\mathbb{Z}/m\mathbb{Z}$: A Problem of Ax
Jamshid Derakhshan
(University of Oxford)
Abstract
In his pioneering and celebrated 1968 paper on the elementary theory of finite fields Ax asked if the theory of the class of all the finite rings $\mathbb{Z}/m\mathbb{Z}$, for all $m>1$, is decidable. In that paper, Ax proved that the existential theory of this class is decidable via his result that the theory of the class of all the rings $\mathbb{Z}/p^n\mathbb{Z}$ (with $p$ and $n$ varying) is decidable. This used Chebotarev’s Density Theorem and model theory of pseudo-finite fields.
I will talk about a recent solution jointly with Angus Macintyre of Ax’s Problem using model theory of the ring of adeles of the rational numbers.