Seminar Calendar
for Model Theory Seminar events the year of Friday, April 21, 2017.

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Questions regarding events or the calendar should be directed to Tori Corkery.
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Friday, April 21, 2017

Model Theory Seminar
4:00 pm   in 345 Altgeld Hall,  Friday, April 21, 2017
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Submitted by erikw.
Matthias Aschenbrenner (UCLA)
The logical complexity of finitely generated commutative rings
Abstract: Since the work of G\"odel we know that the theory of the ring $\mathbb Z$ of integers is very complicated. Using the coding techniques introduced by him, every finitely generated commutative ring can be interpreted in $\mathbb Z$ and therefore has a theory which is no more complicated than that of $\mathbb Z$. It has also been long known that conversely, every infinite finitely generated commutative ring interprets the integers, and hence its theory is at least as complex as that of $\mathbb Z$. However, this mutual interpretability does not fully describe the class of definable sets in such rings. The correct point of view is provided by the concept of bi-interpretability, an equivalence relation on the class of first-order structures which captures what it means for two structures to essentially have the same categories of definable sets and maps. We characterize algebraically those finitely generated rings which are bi-interpretable with $\mathbb Z$. (Joint work with Anatole Kh\'elif, Eudes Naziazeno, and Thomas Scanlon.)

Friday, May 12, 2017

Model Theory Seminar
4:00 pm   in 345 Altgeld Hall,  Friday, May 12, 2017
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Submitted by erikw.
Erik WalsbergO-minimality and the Sub-Riemannian Sphere
Abstract: I will discuss an interesting connection I recently found between Sub-riemannian geometry and o-minimality. In short: sub-riemannian geometers believe that the spheres in real analytic sub-riemannian metrics are definable in some o-minimal expansion of the real field. Furthermore, people in o-minimality are trying to construct the kind of o-minimal expansion that the sub-riemannian geometry are looking for, It seems that the o-minimality community was entirely unaware of this until now. No knowledge of sub-riemannian geometry will be assumed in this talk. Basic knowledge of model theory will be assumed.