Logic Seminar

Please note that the list below only shows forthcoming events, which may not include regular events that have not yet been entered for the forthcoming term. Please see the past events page for a list of all seminar series that the department has on offer.

Past events in this series
21 November 2019
Gabriel Conant

I will present joint work with A. Pillay on the theory of NIP formulas in arbitrary groups, which exhibit a local formulation of the notion of finitely satisfiable generics (as defined by Hrushovski, Peterzil, and Pillay). This setting generalizes ``local stable group theory" (i.e., the study of stable formulas in groups) and also the case of arbitrary NIP formulas in pseudofinite groups. Time permitting, I will mention an application of these results in additive combinatorics.

5 December 2019
Nicolas Daans

   It is a long-standing open problem whether the ring of integers Z has an existential first-order definition in Q, the field of rational numbers. A few years ago, Jochen Koenigsmann proved that Z has a universal first-order definition in Q, building on earlier work by Bjorn Poonen. This result was later generalised to number fields by Jennifer Park and to global function fields of odd characteristic by Kirsten Eisentr√§ger and Travis Morrison, who used classical machinery from number theory and class field theory related to the behaviour of quaternion algebras over global and local fields.

   In this talk, I will sketch a variation on the techniques used to obtain the aforementioned results. It allows for a relatively short and uniform treatment of global fields of all characteristics that is significantly less dependent on class field theory. Instead, a central role is played by Hilbert's Reciprocity Law for quaternion algebras. I will conclude with an example of a non-global set-up where the existence of a reciprocity law similarly yields universal definitions of certain subrings.

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