Mathematics & Statistics Seminars
Northern Arizona University

Fall 2025 Department Colloquium

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.


Stochastic Modeling of Infectious Disease Dynamics

Date: September 2, 2025

Speakers: Ye Chen (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.


Structure of braid graphs for reduced words in Coxeter groups

Date: September 9, 2025

Speakers: Dana C. Ernst (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.


TBD

Date: September 16, 2025

Speakers: Mike Falk (NAU)

Abstract: TBD


TBA

Date: September 23, 2025

Speakers:

Abstract:


TBA

Date: September 30, 2025

Speakers:

Abstract:


Date: October 7, 2025

Speakers: Jim Swift (NAU)

Abstract: TBA


Date: October 7, 2025

Speakers: Outside visitor

Abstract: TBA


TBA

Date: October 21, 2025

Speakers:

Abstract:


TBA

Date: October 28, 2025

Speakers: Shafiu Jibrin (NAU)

Abstract: TBA


TBA

Date: November 4, 2025

Speakers: Mikhail Baltushkin (NAU)

Abstract: TBA


No colloquium, Verteran’s day

Date: November 11, 2025


TBA

Date: November 18, 2025

Speakers: Angie Hodge (NAU)

Abstract: TBA


TBA

Date: November 25, 2025

Speakers:

Abstract:


TBA

Date: December 2, 2025

Speakers: Minah Kim

Abstract: