Where: Math 1311

Speaker: Organizational Meeting () -

Where: Math 1311

Speaker: Douglas Ulrich (UMCP) -

Where: Math 1311

Speaker: Richard Rast (UMCP) -

Where: Math 1311

Speaker: Douglas Ulrich (UMCP) -

Where: Math 1311

Speaker: Chris Laskowski (UMCP) -

Where: Math 1311

Speaker: Ermek Nurkhaidarov (Penn State Mont Alto) -

Where: Math 1311

Speaker: Justin Brody (Goucher College) -

Where: Math 1311

Speaker: Chris Laskowski (UMCP) -

Where: Math 1311

Speaker: Douglas Ulrich (UMCP) -

Where: Math 1311

Speaker: Allen Gehret (UIUC) -

Abstract: For the past few years I have been working on a project to show that the (ordered valued differential) field of logarithmic transseries, $\mathbb{T}_{\log}$, has a good model theory (model completeness, QE, etc). The first part of this project was to show that the \emph{asymptotic couple} (=value group + additional structure induced by the derivation) has a good model theory. After completing this first part, for the past year I have turned my attention to the field $\mathbb{T}_{\log}$ itself. This project is very similar to the recent results of Aschenbrenner, van der Hoeven and van den Dries in showing that the (ordered valued differential) field of logarithmic-exponential transseries, $\mathbb{T}$, has a good model theory. In this talk I will describe recent progress in the direction of proving model completeness for this structure, as well as the general strategy moving forward. I will also draw parallels between the two fields $\mathbb{T}$ and $\mathbb{T}_{\log}$ to illustrate the obstructions in $\mathbb{T}_{\log}$ that are not present in $\mathbb{T}$.

Where: Math 1311

Speaker: Caroline Terry (University of Illinois, Chicago) -

Abstract: What is a ``random" graph? The notion of a logical zero-one law gives us one answer to this question. Suppose that for each $n$, $F(n)$ is a set of graphs with underlying set $\{1,\ldots, n\}$. We say the family $F=\bigcup_{n\in \mathbb{N}} F(n)$ has a zero-one law if for every first-order sentence $\phi$, the proportion of elements in $F(n)$ which satisfy $\phi$ goes to zero or one as $n\rightarrow \infty$. When $F$ has a zero-one law, the set of first-order sentences whose probability tends to one forms a complete first-order theory, which describe a ``random" graph arising from $F$ in a precise way. In this talk we present some new examples of families with zero-one laws, including metric spaces and multigraphs. This is joint work with Dhruv Mubayi.

Where: Math 1311

Speaker: Danul Gunatilleka (UMCP) -

Where: Math 1311

Speaker: Richard Rast (UMCP) -

Where: Math 1308

Speaker: John Baldwin (University of Illinois, Chicago) -

Where: Math 1311

Speaker: Douglas Ulrich (UMCP) -