# MSCS Seminars Today

## Calendar for Tuesday April 23, 2019

Tuesday April 23, 2019

**Midwest Model Theory Day**

Rigidity and bi-interpretability with Z for higher rank lattices.

Nir Avni (Northwestern)

1:00 PM in 636 SEO

A lattice in a Lie group is a discrete subgroup with finite co-volume. In many contexts, there is a dichotomy between lattices in Lie groups of rank one and lattices in Lie groups of higher rank, where the two classes behave in qualitatively different ways. I will talk about this dichotomy in the context of Model Theory.
This talk is part of Midwest Model Theory Day. http://homepages.math.uic.edu/~freitag/MWMT13

**Midwest Model Theory Day**

Fraisse constructions in the free group

Rizos Sklinos (Stevens Institute)

2:30 PM in 636 SEO

In an influential paper Fraisse obtained the ordered rationals as a limit of finite linear orders through amalgamations. Furthermore his construction implied the (ultra)-homogeneity, the countability and universality of the limit structure. Since then various adaptations of Fraisse's method had given very interesting examples in many mathematical disciplines. The random graph in graph theory and Philip Hall's universally locally finite group in group theory to name a few.
In joint work with Kharlampovich and Myasnikov we look into the possibility of applying Fraisse constructions in classes of groups that played a central role in answering Tarski's question on nonabelian free groups. In particular, we modify Fraisse's method to prove that nonabelian limit groups form a ∀
∀-Fraisse class and finitely generated elementary free groups form an elementary-Fraisse class.
This talk is part of Midwest Model Theory Day, http://homepages.math.uic.edu/~freitag/MWMT13

**Quantum Topology / Hopf Algebra Seminar**

Three Variants of Welded Knot Theory

Jonathan Schneider (UIC)

3:00 PM in 612 SEO

Welded Knot Theory was originally conceived by Rourke & Fenn in terms of (framed) braids,
and was subsequently expanded by Kauffman, Rourke and Fenn into a quotient of Virtual Knot Theory.
Satoh and Rourke have shown that the theory is modeled by toral surfaces or fiberwise-embedded toral
surfaces. The latter model, however, requires a slight refinement of the the- ory, which we call
“Roto-Welded Knot Theory”. This refinement omits the virtual I-move, and thus represents a partial return
to the original braid concept. In this talk I will compare Welded, Roto-Welded,
and Framed Welded Knot Theories. In particular, only Roto-Welded admits a proven complete
topological model.

**Midwest Model Theory Day**

Scott sentence of finitely-generated groups

Turbo Ho (Purdue)

4:00 PM in 636 SEO

Scott showed that for every countable structure A, there is a L_{\omega_1,\omega} sentence, called the Scott sentence, whose countable models are the isomorphic copies of A. The quantifier complexity of a Scott sentence can be thought of as a measure of the complexity of the structure. Knight et al. have studied the Scott sentences of many structures. In particular, Knight and Saraph showed that a finitely-generated structure always has a \Sigma_3 Scott sentence. In this talk, we will focus on finitely-generated groups. On the one hand, most "natural" finitely-generated groups have a d-\Sigma_2 Scott sentence. On the other hand, we give a characterization of finitely-generated structures where the \Sigma_3 Scott sentence is optimal. We then give a construction of a finitely-generated group where the \Sigma_3 Scott sentence is optimal.
This is joint work with Matthew Harrison-Trainor.
This talk is part of Midwest Model Theory Day, http://homepages.math.uic.edu/~freitag/MWMT13