The talks will typically take place on Tuesdays at 4:00-5:00pm in Adel Room 164. Please contact Nandor Sieben if you would like to give a talk or have a question about the colloquium.

**Speaker:** Dana Ernst
**Title:** Sabbatical report

**Abstract:**
I’ll spend the first several minutes summarizing my sabbatical experience and then dive into one of the projects I worked on. In particular, I’ll discuss some recent results my collaborators and I obtained concerning the structure of impartial games and rulesets, as well as the structure preserving maps between them. In some sense this work can be thought of as formalizing and extending some folklore from combinatorial game theory. This work was initiated at the Combinatorial Game Theory Colloquium in the Azores that I attended in January, and is joint work with Bojan Bašić, Paul Ellis, Danijela Popović, and Nándor Sieben.

**Speaker:** Jim Swift
**Title:** Synchrony and Anti-Synchrony in Coupled Cell Networks

**Abstract:**
The internal state of a cell in a coupled cell network is often described by an element of a vector space. Synchrony or anti-synchrony occurs when some of the cells are in the same or the opposite state. Of special interest are the evenly tagged anti-synchrony subspaces in which the number of cells in a certain state is equal to the number of cells in the opposite state.
We apply these results to systems of coupled van der Pol oscillators, and coupled Lorenz equations.

This is joint work with Eddie Nijholt and Nándor Sieben

**Speaker:** Robert Buscaglia
**Title:** Activities in Data Science and Statistical Applications

**Abstract:**
The discussion will include a survey of projects from the Buscaglia group conducted during the 2022-2023
academic year. This includes results from collaborative projects with Forestry, Biology, Biochemistry, and
Medicine. Important results will be discussed stemming from standard statistical methods, including
linear modeling and generalized linear modeling, along with some non-traditional techniques such as
Functional Data Analysis. Supervised and unsupervised machine learning methodologies and results will
also be introduced. Key published findings, updates on current publications, and grant progress and
upcoming submissions will be discussed for each major project. The presentation will include results from
work completed with two NAU DoMS students (one undergraduate research, one graduate research) and
the final product for the Hooper Undergraduate Research Award completed by Avery Bell, a BS Data
Science student. A small review of the projects conducted in the Data Science capstone will also be
presented.

**Speaker:** Kayode Isaac Oshinubi (SICCS)
**Title:** Predicting the changes and transition between endemic and epidemic phases of an infectious disease outbreak in some countries

**Abstract:**
The objective of this study is to develop a robust method for predicting the changes and transition between endemic and epidemic phases of an infectious disease, using COVID-19 outbreak as an example.

We define indicators for detecting changes and transitions between endemic and epidemic phases using seven scalars calculated from daily reported news cases: variation coefficient, entropy, dominant/subdominant spectral ratio, skewness, kurtosis, uniformity index, and normality index. The indicators chosen are related to the form of the empirical distribution of new cases seen over a fourteen-day period chosen to smooth out the influence of weekends when fewer new cases are registered.

We used the Principal Component Analysis (PCA) to create a score from the seven proposed indicators that allows an acceptable level of forecasting performance by providing a realistic retro-predicted date for the rupture of the stationary endemic model corresponding to the entry into the epidemic exponential growth phase. The first principal component (a linear combination of the seven indicators) explains a considerable portion of the observed variance and can thus be used as a predictor of the event studied (in this case, the presence of an epidemic wave). This score is used to forecast the limits of the several phases of the COVID-19 outbreak in various nations following endemic and epidemic transitions and changes.

We were able to build a new forecasting strategy for predicting an epidemic wave that comes after an infectious disease’s endemic stationary period. This research offers a valuable tool for early epidemic detection, aiding in effective public health responses.

**Speaker:** Nandor Sieben
**Title:** Sabbatical report

**Abstract:**
Summary of sabbatical activties. Short topics include Opt Art and the comparison of ping pong players, students, and teachers.
The major topic is impartial hypergraph games. These consists of two building games and
two removing games played on a finite hypergraph. In each game two
players take turns selecting vertices of the hypergraph until the set of jointly selected vertices satisfies a condition
related to the edges of the hypergraph. The winner is the last player able to move. The building achievement game
ends as soon as the set of selected vertices contains an edge. In the building avoidance game the players are not
allowed to select a set that contains an edge. The removing achievement game ends as soon as the complement
of the set of selected vertices no longer contains an edge. In the removing avoidance game the players are not
allowed to select a set whose complement does not contain an edge.

**Speaker:** Michele Torielli
**Title:** Lefschetz properties and hyperplane arrangements

**Abstract:**
In this talk, we will discuss what it means for a graded ring to have the weak Lefchetz property (WLP) or the strong Lefschetz property (SLP). We will then see which other properties a ring with the WLP or SLP has, and discuss the case of 1 dimensional complete intersection and of the Jacobian algebra of a hyperplane arrangement. This is based on a joint work with S. Marchesi and E. Palezzato.

**Speaker:** Jaechoul Lee
**Title:** An efficient least squares algorithm for periodic time series regression

**Abstract:**
Periodic and autoregressive data like daily temperatures or sales of seasonal products can be seen in periods fluctuating between highs and lows throughout the year. Generalized least squares (GLS) estimators are frequently computed for such periodic data, because these estimators are minimum variance unbiased estimators. However, the GLS solution can require extremely demanding computations when the data is large. We develop an efficient GLS algorithm in several periodic regression settings. The algorithm can substantially simplify GLS computations by compressing large sets of data into smaller sets. This is accomplished by constructing a structured matching matrix for dimension reduction. Simulations show that the new computation methods using our algorithm can drastically reduce the GLS computing time. Our algorithm can be easily adapted to many big data that shows periodic characteristics often pertinent to economics, environmental studies, and engineering practices. This talk should be accessible to any audience with knowledge on simple matrix operations.

**Speaker:** Sam Harris
**Title:** Quantum and algebraic versions of the chromatic number

**Abstract:**
A great deal of attention has been given to quantum versions of the chromatic number for a classical graph in recent years. These quantities arise naturally in quantum information theory as a method for determining whether two spatially separated parties can perform certain tasks with the power of quantum mechanics. In this talk, we’ll look at the algebraic definition of the quantum chromatic number, mostly focusing on examples with 3-colorings. At the end, we’ll see a generalized version of Lovasz’s reduction theorem of the k-coloring problem (k>3) to the 3-coloring problem.

No colloquium.

**Speaker:** Elisa Palezzato
**Title:** CoCoA, Posets and Hyperplane Arrangements

**Abstract:**
In this talk, I will introduce the computer algebra system CoCoA and how to use it to do computations with posets and hyperplane arrangements. I will also talk about Terao’s conjecture for free hyperplane arrangements.

**Speaker:** Angie Hodge-Zickerman (NAU), Cindy York (Northern Illinois University), Barbara Boschmans (NAU)
**Title:** AI in Academia: Collaborative Tool or Academic Shortcut? Navigating the New Frontier in Mathematical Education and Research

**Abstract:**
Generative Artificial Intelligence (AI) has sparked a paradigm shift in educational methodologies. We invite you to an interactive colloquium that explores the multifaceted role of AI in academic settings. In this talk, we will discuss the nature of AI as a pedagogical collaborator instead of just a catalyst for academic dishonesty. We will begin with a brief overview of the current state of generative AI and gauge participants’ stances on the use of AI in the mathematics classroom. Participants will be encouraged to engage with AI firsthand, experiencing its capabilities and limitations. The latter part of the colloquium will be aimed at identifying pertinent research questions that arise at the intersection of AI and mathematical studies. We seek to inspire a collaborative brainstorming session on how we can collectively tailor research agendas to address the implications of AI in curriculum development, teaching methodologies, and the broader scope of academic scholarship.

**Speaker:** Michael J. Falk
**Title:** Subspace arrangements and split ideals

**Abstract:**
We define a closure operator on subspace arrangements using the geometry of the Grassmannian, resulting in an invariant of ideals generated by decomposable elements in exterior algebras, which is itself a subspace arrangement. We generalize the definition of Orlik-Solomon algebra from matroids to arbitrary subspace arrangements, with the Orlik-Solomon algebra of a graph, hyperplane arrangement, or matroid arising from the arrangement of coordinate subspaces corresponding to the circuits. We sketch how this approach, combined with the 2-isomorphism theorem of Vertigan-Whittle, leads to a combinatorial classification of Orlik-Solomon algebras.

No colloquium.

**Speaker:** Jaechoul Lee
**Title:** An efficient least squares algorithm for periodic time series regression

**Abstract:**
Periodic and autoregressive data like daily temperatures or sales of seasonal products can be seen in periods fluctuating between highs and lows throughout the year. Generalized least squares (GLS) estimators are frequently computed for such periodic data, because these estimators are minimum variance unbiased estimators. However, the GLS solution can require extremely demanding computations when the data is large. We develop an efficient GLS algorithm in several periodic regression settings. The algorithm can substantially simplify GLS computations by compressing large sets of data into smaller sets. This is accomplished by constructing a structured matching matrix for dimension reduction. Simulations show that the new computation methods using our algorithm can drastically reduce the GLS computing time. Our algorithm can be easily adapted to many big data that shows periodic characteristics often pertinent to economics, environmental studies, and engineering practices. This talk should be accessible to any audience with knowledge on simple matrix operations.

**Speaker:** Shafiu Jibrin
**Title:**

**Abstract:**

**Speaker:** Jeffrey Hovermill
**Title:**

**Abstract:**