The Graduate Program in Mathematics and Applications of PSL University is offering scholarships for students willing to enroll in the PSL Master of Mathematics (M1 or M2) for 2025-2026.
The teaching language is English and the program is based on the research team in mathematics at CEREMADE (Paris Dauphine-PSL), at DMA (Ecole Normale Supérieure - PSL), at Ecole des Mines Paris-PSL, at Paris Observatory-PSL, at the EHESS, and at Collège de France.
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Two Stipendiary Lecturers in Mathematics at Exeter College
Postdoctoral Research Associate in Infectious Disease Modelling
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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.