### Overview

**Date:** October 16, 2022

**Place:** Wellesley College

### Schedule

10:00am | Coffee, Tea & Snacks |

10:30am | Filippo Calderoni (Rutgers) |

11:30am | Isabella Scott (University of Chicago) |

12pm | Lunch |

1:30pm | Chris Conidis (College of Staten Island – CUNY) |

2:30pm | Teerawat Thewmorakot (University of Connecticut) |

3pm | End of day |

### Abstracts

#### Filippo Calderoni (Rutgers)

##### Borel structures on the space of left-orderings

In this talk we will discuss some results on left-orderable groups and their interplay with descriptive set theory. We will see how Borel classification can be used to analyze the space of left-orderings of a given countable group modulo the conjugacy relation. In particular, we will discuss many examples of groups whose space of left-orderings module the conjugacy relation is not standard. Moreover, if \(G\) is a nonabelian free group, then the conjugacy relation on its space of left-orders \(\mathrm{LO}(G)\) is a universal countable Borel equivalence relation. This is joint work with A. Clay.

#### Isabella Scott (University of Chicago)

##### Effective constructions of existentially closed groups

Existentially closed groups are at the intersection of model theory, computability theory, and algebra. Questions of complexity can be asked in many directions. We will review earlier constructions from the literature and elucidate their computability theoretic power, as well as propose new constructions of existentially closed groups with interesting computability theoretic properties.

#### Chris Conidis (College of Staten Island – CUNY)

##### The computability of Artin-Rees and Krull Intersection

We will explore the computational content of two related algebraic theorems, namely the Artin-Rees Lemma and Krull Intersection Theorem. In particular we will show that, while the strengths of these theorems coincide for individual rings, they become distinct in the uniform context.

#### Teerawat Thewmorakot (University of Connecticut)

##### Embedding Problems for Finite Computable Metric Spaces

A computable metric space is a Polish metric space (M,d) together with a dense sequence (p_i) of points in M such that d(p_i,p_j) is a computable real uniformly in i,j. In this talk, we consider the following embedding problem: for a fixed finite computable

metric space X, given an arbitrary computable metric space M, determine if X can be embedded into M.

### Travel Support

Limited funding is provided from the NSF to support participation by students and others to NERDS. If interested, please email Russell Miller.

### Vaccination Mandate

All visitors to Wellesley’s campus must be vaccinated. Visitors must fill out an online form prior to arrival.