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: September 2, 2025
Speakers: Ye Chen, Associate Professor of Mathematics (NAU)
Abstract: Mathematical models of infectious diseases often rely on a key parameter: the transmission rate. In reality, this rate changes over time with seasonality, behavior, and immunity. Capturing its fluctuations is essential for accurate modeling, yet treating it as a constant oversimplifies reality. This talk presents a stochastic SIHR model where the transmission rate follows a Black–Karasinski process, ensuring both positivity and mean reversion for biological realism and long-term stability. The model builds on stochastic differential equations (SDEs) and Itô calculus—mathematical tools pioneered in finance to model volatile systems like stock prices—here adapted to capture the randomness of disease spread. A key theoretical result establishes the existence and uniqueness of a global, positive solution to the system, proved using Lyapunov function. For inference, Particle Markov Chain Monte Carlo (pMCMC) is used to jointly estimate static parameters and latent state trajectories from hospitalization data. Validation on synthetic data and application to Arizona influenza hospitalizations from the 2022–2024 flu seasons yield estimates consistent with CDC reports.
Date: September 9, 2025
Speakers: Dana C. Ernst, Professor of Mathematics (NAU)
Abstract: In this talk, we will discuss the architecture of braid graphs in Coxeter systems. It turns out that every reduced expression has a unique factorization as a product of so-called links, which in turn induces a de- composition of the braid graph into a box product of the braid graphs for each link factor. When the corresponding Coxeter graph avoids certain three-cycles, each braid graph is a median graph (i.e., for every triple of vertices, there is a unique vertex, called the median, that belongs to shortest paths between each pair). One consequence of this result is that every braid graph in Coxeter systems avoiding the banned three-cycles can be isometrically embedded into a hypercube.
Date: September 16, 2025
Speakers: Mike Falk, Professor Emeritus of Mathematics (NAU)
Abstract: I’ll talk about a perspective on and generalization of Orlik-Solomon algebras of matroids that allows the application of the 2-isomorphism theorem of Vertigan and Whittle to study isomorphisms and automorphisms, resulting in a classification theorem and clarification and possible resolution of some old open problems. We will explain the background and main ideas and display the method with examples.
The main characters are: a finite set V with a specified collection of its nonempty subsets, also known as a hypergraph, the exterior algebra over V, consisting of linear combinations of subsets of V endowed with the natural anti-commutative multiplication, and (sub)quotients of the exterior algebra by various ideals. Some knowledge of the definitions of (quotient) vector space, ring, and ideal will be helpful but not necessary.
Date: September 23, 2025
Date: September 30, 2025
Speakers: Abdurrahman Ado (NAU)
Abstract: In this talk, we will discuss on a paper that we have published about a nonlinear deterministic model that incorporates public awareness and treatment to describe the dynamics of HIV/AIDS in an infected population with detectable and undetectable viral load. The model was developed and analyzed, and it undergoes backward bifurcation in which a stable disease-free equilibrium coexists with a stable endemic equilibrium. The most sensitive parameters for the control of the spread of HIV are identified by forward sensitivity index method. Numerical simulations carried out show the behavior of the state variables and the impact of public awareness in controlling the spread of HIV. The results show that public awareness will help in curtailing the spread of HIV infection, and when treatment is applied to infected individuals with detectable viral load can easily suppress their virus to become undetectable so that they cannot transmit HIV through sexual intercourse.
Date: October 7, 2025
Speakers: Jim Swift (NAU)
Abstract: The Sierpinski Gasket is the famous fractal obtained by recursively removing the middle portion of an equilateral triangle. Alternatively, the Sierpinski Gasket is the limit of a sequence of graphs, called Sierpinski pre-gaskets. Each of these pre-gaskets has a graph Laplacian, which converges to a well-defined Laplacian on the Sierpinski Gasket. An important nonlinear Partial Differential Equation on any domain is defined in terms of the Laplacian. We (Neuberger, Sieben, and Swift) use techniques we have developed over several papers to understand some of the patterns of solutions that occur in this equation when the domain is the Sierpinski Gasket.
Date: October 13, 2025 (Monday!)
Speakers: Prasit Bhattacharya, Assistant Professor (NMSU)
Abstract: The Frobenius map, which raises an element to its p-th power, is a fundamental ring endomorphism in characteristic p. This simple algebraic structure has profound implications, serving as the generator for Galois groups of finite fields. In the 1950s, N.E. Steenrod generalized this concept to graded F_p-algebras, a generalization that has since yielded cornerstone results in geometry and algebraic topology.
This talk explores a new, crucial question: Can Steenrod operations be refined to detect hidden symmetries? We will trace the historical development of this question and present a compelling, affirmative answer, demonstrating a novel connection between algebraic operations and geometric symmetry.
Date: October 21, 2025
Speakers: Sheila Miller, Assistant Professor, ASU
Abstract: In this talk we will introduce a family of strong logical axioms called rank-to-rank embeddings and the relationship between these large cardinal embeddings and left distributive algebras. There are many examples of left distributive operations in classical mathematics, including group conjugation and the weighted mean. Those operations are idempotent, however, and hence not free. In the late 1980s Richard Laver showed that the closure of a single rank-to-rank elementary embedding under an application operation generates a free left distributive algebra and demonstrated the linearity of a particular ordering on terms of the free left distributive algebra (given the existence of such embeddings). Patrick Dehornoy subsequently used the braid group on infinitely many generators to show the linearity of that ordering relation within ZFC. The consistency strength of other related theorems is still unknown; it remains possible that a theorem about finite left distributive algebras has large cardinal strength––that is, cannot be proven from the usual axioms of set theory. David Larue later extended that work to demonstrate braid group representations of the free left distributive algebra on n generators, for any natural number n. Still elusive was an algebra of embeddings isomorphic to a free left distributive algebra on more than one generator. We outline an inverse limit construction of such a free, two-generated left distributive algebra of embeddings from a slightly stronger large cardinal assumption than the one used by Laver (joint work with Andrew Brooke-Taylor and Scott Cramer) and state two additional, related results (joint work with Scott Cramer, Meng-Che “Turbo” Ho, and Nam Trang). We conclude with statements of three open problems about left distributive algebras.
Date: October 28, 2025
Speakers: Shafiu Jibrin (NAU)
Abstract: Karlovitz et al. presented a modification of an alternating projection algorithm for finding strictly feasible points for linear matrix inequalities in a 2014 paper. One variation of their modification employs eigenvalue replacement, while another utilizes eigenvalue shift. They showed that eigenvalue shift outperforms eigenvalue replacement in terms of computation time and number of iterations. We propose a new eigenvalue replacement technique and extend their method to include an affine set. Our numerical experiments indicate that the new eigenvalue replacement technique is superior to eigenvalue shift. This is a joint work with my former student, Priscilla Kwofie.
Date: November 4, 2025
Date: November 11, 2025
Date: November 18, 2025
Speakers: Minah Kim (NAU)
Abstract: TBA
Date: November 25, 2025
Speakers: Jeffrey Moore Covington (NAU)
Abstract:
Date: December 2, 2025