Overview

Date: October 5, 2025
Place: University of Connecticut

Location details: The meeting will be in Monteith Hall on UConn’s campus in Storrs.

Parking details: Unless explicitly marked as reserved, all lots are free on the weekends. In garages, regular rates apply.

The on-campus visitor parking uses the PayByPhone app, see https://park.uconn.edu/pay-by-phone/. The easiest place to park with this app is the South Parking garage, next to Gampel Pavilion. It is about a 5-7 minute walk from the parking garage to Monteith. There are also some PayByPhone spots in B lot, located behind Buckley Hall, near Storrs Center. You can access various maps of these locations at https://maps.uconn.edu/.

Off-campus parking is available at the Downtown Storrs Parking Garage, located at 33 Royce Circle, see https://ct-mansfield.civicplus.com/DocumentCenter/View/2629/20181207_downtownstorrs_parkingmap. Parking is free for the first two hours in this lot. This lot does not use a mobile app. You take a ticket upon entering and pay with a credit card if you stay longer than two hours. It is about a 7-10 minute walk from the parking garage to Monteith.

Schedule

Time	Speaker	Location
10:00 – 10:30 a.m.	Coffee & Snacks	Monteith 214
10:30 a.m. – 11:30 a.m.	Mostafa Mirai (The Taft School)	Monteith 214
11:30 – 12 p.m.	Andrew DeLapo (University of Connecticut)	Monteith 214
12:00 – 2 p.m.	Lunch	(on your own)
2 – 3 p.m.	Daniel Turetsky (Victoria University of Wellington)	Monteith 214
3 – 4 p.m.	Tyler Markkanen (Springfield College)	Monteith 214

Speakers & Abstracts

Mostafa Mirabi (The Taft School)

Sunflowerable Structures

A sunflower is a set system where any two pairs of distinct elements have a common intersection. The existence of large sunflowers in set systems has important implications in set theory and one of the most important results regarding sunflowers is that any uncountable collection of finite sets contains an uncountable sunflower.

In this talk we will consider generalizations of this result to “structured sunflowers.” Specifically if M is a structure we say it is “sunflowerable” if, whenever M’ is isomorphic to M and every element of M’ is a set of size n (for some fixed n) then there is a substructure of M’ which is both a sunflower and isomorphic to M’. We will give conditions which imply a structure is sunflowerable. This will allow us to give a complete classification of the countable sunflowerable linear orderings as well as show that the Rado graph is sunflowerable.

This is joint work with Nate Ackerman and Mary Leah Karker.

Andrew DeLapo (University of Connecticut)

Computable Categoricity for CSC Spaces

Computable categoricity — the uniqueness of structures up to computable isomorphism — has been studied for a wide variety of combinatorial and algebraic structures. In this talk, I will introduce how questions of computable categoricity can be phrased for certain types of countable, second-countable (CSC) topological spaces. In this context, we are interested in the existence or non-existence of certain computable homeomorphisms between two homeomorphic CSC spaces. We will investigate this question for the indiscrete, discrete, initial segment, and cofinite topologies on the natural numbers.

Daniel Turetsky (Victoria University of Wellington)

Particular Lightface and Boldface Complexities Somewhat Above $\Sigma^1_1$

What is the complexity of Muchnik reducibility? At first glance it’s $\Pi^1_2$, but maybe we can do better? A(\Pi^1_1) is a natural complexity class, sitting above $\Sigma^1_1$ but within $\Delta^1_2$, which I’ll discuss. Muchnik reducibility and another reducibility based on particular embeddings of linear orders both look to sit at this level, and I’ll present partial results for this.

Tyler Markkanen (Springfield College)

Deciding the Density of Computable and C.E. Sets

How hard is it to determine whether an infinite set of natural numbers has asymptotic density 1? Although density provides an intuitive way to measure the size of a set, the decision problems it raises are surprisingly intricate. In this talk, I will present recent joint work with Stephen Flood, Matthew Jura, and Oscar Levin that classifies the complexity of deciding whether a computable or c.e. set has a specified density. I will sketch some of our core constructions — showing, for instance, that the index set of c.e. sets with upper density 1 is $\Pi^0_2$-complete — and then describe the modifications needed to handle a set’s lower density, raising the complexity to the $\Pi^0_4$ level. Similar gaps in complexity arise when comparing the decision problems for sets with density 0 vs. those with density 1, as well as for computable vs. c.e. sets. I will conclude with a potential application to equitable colorings, namely our plans to extend the Hajnal-Szemerédi Theorem to computable graphs.

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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