The talks will typically take place on Tuesdays at 4:00-5:00pm in Adel Room 164. Please contact Ye Chen if you would like to give a talk or have a question about the colloquium.
Date: Tuesday 9/8 at 4:00-4:50
Speakers: Samuel Harris, Assistant Professor, NAU
Abstract: The Smith-Ward problem originates in 1980 and is a problem about matrix ranges in operator theory. Matrix ranges are a tool sometimes used to understand the geometry of a bounded linear operator, while capturing underlying “statistics”. While there has been some progress over the years, the problem remained open in general until earlier this year when Marcel Scherer found a counterexample. In this talk we will strengthen this counterexample and show that a plethora of counterexamples exist that are not overly difficult to construct. Moreover, some counterexamples turn out to have rather exotic properties.
Date: Tuesday 9/15 at 4:00-4:50
Speakers: Angie Hodge-Zickerman, Professor, NAU
Abstract: This talk is adapted from Dr. Angie Hodge-Zickerman’s invited 2026 MAA MathFest Leitzel Lecture and explores the important role confidence plays in learning mathematics. Drawing on lessons learned across a wide range of university mathematics courses and mathematical learning experiences, Angie will share practical ways to help students build mathematical confidence while still engaging in challenging and meaningful mathematics. Participants will consider strategies for normalizing “not knowing yet,” creating opportunities for productive struggle, encouraging mathematical risk-taking, and helping students see themselves as capable mathematical thinkers. The session will invite us to consider how small shifts in our teaching can foster deeper engagement, persistence, and ultimately, greater joy in doing mathematics.
Date: Tuesday 9/22 at 4:00-4:50
Speakers: Jeffrey Covington, Data Scientist, NAU
Abstract: Bayesian filters are foundational algorithms for forecasting and prediction. They are the backbone of operational forecasting systems in many fields such as epidemiology, earth science, econometrics, and robotics, to name a few. This rich and active area of research admits many novel approaches, from dynamical systems to pure machine learning and AI, as well as hybrid strategies. First, we introduce Bayesian filtering including the foundational algorithms of the particle filter and ensemble Kalman filter. Next, we present cutting edge research in epidemiology: real-time week-to-week forecasting of influenza hospitalizations. Finally, we highlight promising areas of research and trends across the field of Bayesian filtering, perhaps inspiring discussion and future research.
Date: Tuesday 9/29 at 4:00-4:50 (Online)
Speakers: Tom Edgar, Assistant Professor, CSU Pueblo
Abstract: The Kevin Bacon game challenges players to find shortest paths from a given performer to Kevin Bacon where connections consist of actors who appeared together in a movie. In this talk, we’ll investigate a single object, the sum-of-bits function, that could perhaps be a contender for the Kevin Bacon role in an analogous game played with mathematics. We’ll see a variety of topics from the undergraduate math curriculum that can be connected via this idea. Exploring bridge objects like this the sum-of-bits function allows us and our students to see that there are often beautiful connections between seemingly separate and independent mathematical areas. Knowing these connections can allow problem-solving techniques in one subfield to help with another.
Date: Tuesday 10/13 at 4:00-4:50
Speakers: Jeffrey Downard, Associate Professor, NAU
Abstract: Modern cosmology gives a highly successful account of the universe once a sufficiently determinate framework of spacetime structure is in place. But what explains the origin of those lawful forms of order? Beginning with the cosmic calendar and the first second of the standard ΛCDM model, I introduce six foundational problems concerning the origins of law, time, spacetime dimension, low entropy, the cosmological constant, and the relation between regularity and randomness.
I then distinguish three broad families of hypotheses: H₁, on which the relevant laws and structures are fundamentally fixed; H₂, on which increasingly determinate forms of order evolve from a comparatively vague field of potentiality; and H₃, on which observable order is selected from different possible universes. The methodological core of the project is a four-ladder framework that tracks geometric, algebraic, numerical, and logical structure. The aim is to make the hidden assumptions in competing cosmological models more explicit. Many H₁ and H₃ approaches develop one or two of these ladders in detail while implicitly presupposing the others. By locating competing models on all four ladders, we can compare them within a common framework and ask which provides the most coherent responses to the six problems.
I will illustrate the approach by sketching an H₂ model in which progressively richer forms of cosmic structure grow to support the spacetime order represented by Einstein’s field equations. I will also briefly indicate how later volumes extend the framework to the co-evolution of relativistic and quantum-field laws and, subsequently, to later forms of nested cosmic order.
Date: Tuesday 10/20 at 4:00-4:50
Speakers: Mike Falk, Professor Emeritus, NAU
Abstract: After some preliminaries about linear subspaces and determinants, and projective spaces, and exterior algebras, I’ll give an overview and status report on a classification of Orlik-Solomon algebras of matroids using the 2-isomorphism theorem for hypergraphs of Vertigan and Whittle. This is joint work in progress, of long vintage, with Geoff Whittle. Matroids as such will not appear in the talk; everything is based on hypergraphs, that is, collections of subsets of finite sets. The argument involves extending definitions and direct sum decomposition results about OS algebras from independence complexes of matroids to arbitrary finite simplicial complexes.
Date: Tuesday 10/27 at 4:00-4:50
Speakers: Dana Ernst, Professor, NAU
Abstract: Open discussion on the impact of AI on research in mathematics, statistics, data science, mathematics education, and other related areas.
Date: Tuesday 11/10 at 4:00-4:50
Speakers: Kiona Ogle, Professor, NAU
Abstract: A suite of long-term vegetation monitoring programs exist across the globe that employ a variety of methods to document occurrence, cover, or abundance of plant species. One example is the US National Park Service (NPS) Inventory and Monitoring (I&M) program, which monitors vegetation attributes in multiple parks across the US. Synthesizing long-term I&M data across diverse ecosystems could strengthen inference on the drivers of vegetation change, but differences in sampling protocols challenge such synthesis. Hence, our objective is to develop statistical approaches for integrating data from multiple sites that employ complementary sampling methods to identify drivers of plant species occurrence. In this talk, I will describe a hierarchical Bayesian framework that we developed that (1) accommodates different sampling methods, (2) accounts for detection error (observer error), (3) is capable of dealing with many (100+) plant species, and (4) simultaneously quantifies drivers of species occurrence. We applied this framework to I&M data obtained under a nested quadrat design and estimated the effects of moisture stress on the probability of occurrence for 192 grass and forb species from five sites within two iconic national parks in the western US. We summarize the types of results generated by this approach and key takeaways learned in the context of detection error rates, variation in occurrence probabilities across species and genera, and complex relationships between occurrence and moisture-related covariates.
Date: Tuesday 11/17 at 4:00-4:50
Speakers: Keegan Line, Graduate student, NAU
Abstract: TBD