Colloquium Series

Speaker/Affiliation: Doug Blue, University of Pittsburgh

Title: Compactness, incompactness, and determinacy

Abstract: Compactness phenomena are ubiquitous in mathematics. In set theory, the study of compactness focuses on the tension between combinatorial "square" principles and reflection principles, such as large cardinal and forcing axioms. While it has long been conjectured that the failure of square principles at a singular strong limit cardinal requires powerful large cardinal hypotheses, this talk presents joint work with Paul Larson and Grigor Sargsyan to the effect that a "totally compact" universe of sets carries a much lower consistency strength cost than previously thought. Our results suggest that a longstanding conjecture---that forcing axioms require the consistency of a supercompact cardinal---is false.

Date/Time/Location: Tuesday March 17, 2026 from 3:00-3:50pm in Upham 275

Speaker/Affiliation: Thomas Lamkin, University of California, San Diego

Title: Point Modules of Non-Connected Graded Algebras

Abstract: Artin-Schelter (AS) regular algebras constitute one of the most interesting families of noncommutative algebras. Part of their significance is geometric: by studying the moduli space of "point modules" of 3-dimensional AS regular algebras, Artin, Tate, and Van den Bergh were able to prove that such algebras are Noetherian. Since then, point modules have been investigated for a variety of connected graded algebras, yet there is comparatively little study in the non-connected graded setting. In this talk, we discuss how to generalize the notion of point modules to non-connected algebras. Moreover, we provide evidence for a conjecture that, under mild hypotheses, the non-connected analogues of AS-regular algebras have "good geometry".

Date/Time/Location: Tuesday March 3, 2026 from 3:00-3:50pm in Upham 275

Speaker/Affiliation: Axel Brandt, John Carroll University

Title:Chasing and Running on Graphs

Abstract: What's the first thing that a character from a movie does if they're on the run from the law? Ditch their cell phone in order to avoid being tracked using GPS. Even if they have a dumb phone without GPS, their position can be triangulated using signal strength to the closest
cell towers as a measure of distance. In this talk, we'll explore triangulating a runner's location on a graph, where distances behave somewhat differently.

Date/Time/Location: Thursday, Oct 30, 2025 from 3:00-3:50 pm in UPH 127

Speaker/Affiliation: Grace McCourt, Iowa State University

Title: Problems in Ramsey theory

Abstract: The Ramsey number R(s,t) is the minimum integer n such that any graph on n vertices must either contain a clique of size s or an independent set of size t. This can also be viewed as the minimum integer n such that any red-blue coloring of the edges of K_n results in either a red K_s or a blue K_t. Ramsey numbers and their generalizations are extensively studied in extremal graph theory. In this talk, I will present results on a few variations on Ramsey numbers, including Ramsey-Turan numbers, online ordered Ramsey numbers, and Kneser Ramsey numbers.

This work is joint with Balogh, Chen, and Murley; Heath, King, Sheats, and Wisby; and Heath, Parker, Schwieder, and Zerbib.

Date/Time/Location: Tuesday October 14, 2025 from 3:00-3:50 pm in UPH 127

Speaker/Affiliation: Lawrence C. Washington, University of Maryland

Title: Sums of Primes

Abstract: The sum of the primes up to x is asymptotic to the number of primes up to x^2, namely pi(x^2). However, the sum tends to be less than pi(x^2).

We quantify this and give an equivalent form of the Riemann Hypothesis.

Date/Time/Location: Thurs Sep 18, 2025 from 3:00-3:50 pm in UPH 127