Two Stipendiary Lecturers in Mathematics at Exeter College
Postdoctoral Research Associate in Infectious Disease Modelling
Image: Lizzie Siddal - Lovers listening to music
Two Stipendiary Lecturers in Mathematics at Exeter College
Postdoctoral Research Associate in Infectious Disease Modelling
Image: Lizzie Siddal - Lovers listening to music
I am going to start by reviewing axioms of quantum mechanics, which in fact give a description of a Hilbert space. I will argue that the language that Dirac and his followers developed is that of continuous logic and the form of axiomatisation is that of "algebraic logic" in the sense of A. Tarski's cylindric algebras. In fact, Hilbert spaces can be seen as a continuous model theory version of cylindric algebras.
I introduce modal group theory, where one investigates the class of all groups using embeddability as a modal operator. By employing HNN extensions, I demonstrate that the modal language of groups is more expressive than the first-order language of groups. Furthermore, I establish that the theory of true arithmetic, viewed as sets of Gödel numbers, is computably isomorphic to the modal theory of finitely presented groups. Finally, I resolve an open question posed by Sören Berger, Alexander Block, and Benedikt Löwe by proving that the propositional modal validities of groups constitute precisely the modal logic S4.2.
We are currently inviting applications for two Postdoctoral Research Associates (PDRAs) to work with Professor Robin Thompson at the Mathematical Institute, University of Oxford. These are two fixed-term positions for 24 months and 12 months, respectively, funded by a research grant from the Biotechnology and Biological Sciences Research Council (BBSRC). We anticipate the start date for these positions be in January 2026 but earlier or later start dates can be negotiated.
Mathematical models are used to inform decisions across many sectors including climate change, finance, and epidemics. But models are not perfect representations of the real world – they are partial, uncertain and often biased. What, then, does responsible modelling look like? And how can we apply this ethical framework to new AI modelling methods?
Erica Thompson is Associate Professor of Modelling for Decision Making at UCL’s Department of Science, Technology, Engineering and Public Policy (STEaPP), and the author of 'Escape From Model Land' (2022).
Please email @email to register to attend in person.
The lecture will be broadcast on the Oxford Mathematics YouTube Channel on Wednesday 25 June at 5-6pm and any time after (no need to register for the online version).
The Oxford Mathematics Public Lectures are generously supported by XTX Markets.
This talk will be a case study on the recently discovered boundary Carrollian conformal algebra (BCCA) in theoretical physics. It is an infinite-dimensional subalgebra of an abelian extension of the Witt algebra. A striking feature of this is that it is not integer graded; this already puts us in a rather novel setting, since infinite-dimensional Lie algebras almost exclusively appear with integer grading in physics. But this means that there is new ground to be broken in this direction of research. In this talk, I will present some very early results from our attempt at studying the representations of the BCCA. Any thoughts and comments are very welcome as they could be immensely helpful for us to navigate these unfamiliar waters!