January 10, 2018, 4:00pm-4:50pm, MS 5233
Speaker: Elliot Kaplan (UIUC)
Title: An introduction to $HT$-fields
Abstract: In this talk, I will introduce the class of $HT$-fields. Let $T$ be an o-minimal theory extending the theory of ordered fields and let $K$ be a model of $T$ which is also equipped with a nontrivial derivation $x \mapsto x'$, making it an $H$-field (a particularly nice type of ordered differential field). We require that this derivation interact nicely with the o-minimal structure on $K$. The class of $H$-fields has been thoroughly explored by Aschenbrenner, van den Dries, and van der Hoeven. I will establish some analogues of their results on $H$-fields for the class of $HT$-fields and discuss my ongoing work.
December 7, 2017, 4:00pm-4:50pm, MS 5137 [Talk cancelled due to classes cancelled]
Speaker: Allen Gehret (UCLA)
Title: o-minimal and P-minimal structures
Abstract: In this talk I will survey o-minimal structures, P-minimal structures, and discuss the analogy between the two.
November 30, 2017, 4:00pm-4:50pm, MS 5137
Speaker: Artem Chernikov (UCLA)
Title: Generic expansions of NSOP1 theories, after Kruckman-Ramsey and Jeřábek
Abstract: The class of NSOP1 theories was introduced by Shelah. It provides a proper generalization of the class of simple theories, contains new interesting algebraic and combinatorial examples, and still admits a reasonable theory of independence generalizing forking independence in simple theories. We will discuss recent results of Kruckman-Ramsey and Jeřábek which demonstrate that various generic expansions of a theory preserve the NSOP1 property (e.g., every NSOP1 theory eliminating the infinite quantifier has an NSOP1 expansion with definable Skolem functions).