Overview

Date: March 7, 2026
Place: Springfield College

Location details: The talks will be in Brown Cooper Health Sciences Center Room 117 (Building 25 on the attached map). The entrance is on the Wilbraham Avenue side of the building.

Lunch will be provided at Cheney Dining Hall, thanks to Springfield College. Parking is available in Lots 4, 9A, and 9. More information, including driving directions, is available at https://springfield.edu/about/campus-maps.

Schedule

10:30–11:00	Coffee
11:00–11:30	Jeremias Valenzuela Morales
11:30–12:30	Charlie McCoy
12:30-2:00	Lunch at Cheney Dining Hall
2:00–3:00	Cecelia Higgins
3:00–4:00	Jenna Zomback

Abstract

Cecelia Higgins (Rutgers University)

Title: Complexity of finite Borel asymptotic dimension

Abstract: A Borel graph is hyperfinite if it can be written as a countable increasing union of Borel graphs with finite components. It is a major open problem in descriptive set theory to determine the complexity of the set of hyperfinite Borel graphs. In a recent paper, Conley, Jackson, Marks, Seward, and Tucker-Drob introduce the notion of Borel asymptotic dimension, a definable version of Gromov’s classical notion of asymptotic dimension, which strengthens hyperfiniteness and implies several nice Borel combinatorial properties. We show that the set of locally finite Borel graphs having finite asymptotic dimension in $\Sigma^1_2$-complete. This is joint work with Jan Grebik.

Charlie McCoy (University of Portland)

Title: Computable $\Pi^0_2$ Scott sentences

Abstract: By a foundation result of Scott, each countable structure for a countable language $L$ is described up to isomorphism by an $L_{\omega_1, \omega}$ sentence, called a Scott sentence. Montalban gave a nice characterization of the structures $\mathcal{A}$ (for a fixed computable language) that have a $\Pi_{\alpha+1}$ Scott sentence; namely, the orbit of each tuple $\overline{a}$ is defined by a $\Sigma_{\alpha}$ formula.

Computable infinitary formulas and sentences involve c.e. disjunctions and conjunctions and therefore have significant relevance to notions within computable model theory.

In earlier work with Alvir, we produced a structure with a $\Pi_2$ Scott sentence, but no such computable sentence. Here we will explore the class of structures, among those with a $\Pi_2$ Scott sentence, that have a computable $\Pi_2$ Scott sentence. In general, we have been able to identify some sufficient conditions that are not necessary, and some necessary conditions that are not sufficient. The only characterizations we have obtained that are both necessary and sufficient still involve comparisons with all other countable structures. There is a deeper reason for this apparent failure: we prove that there is no “nice” characterization of this class, for its index set is, in fact, $\Pi^1_1$ complete. This last result was proved independently by Alvir, Csima, and Harrison-Trainor.

Jeremías Valenzuela Morales (George Washington University)

Title: Controlling the jump in lattice embeddings

Abstract: In this talk, we will explore the viability of using different bookkeeping methods when constructing embeddings of finite jump upper semilattices into the Turing degrees.

Jenna Zomback (Amherst College)

Title: Chaining in measurable dynamics

Abstract: A group action on a probability space is called ergodic if every invariant, measurable set is null or conull. In joint work with Anush Tserunyan, we introduce a new combinatorial strengthening of ergodicity which we call chaining. In this talk, we will place chaining in the existing hierarchies of properties related to ergodicity for measure preserving actions and for nonsingular (measure-class preserving) actions.

Travel Support

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

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