Mathematics & Statistics Seminars
Northern Arizona University


The “Friday Afternoon Mathematics Undergraduate Seminar” (FAMUS) is a weekly event consisting of announcements, talks, and faculty interviews. FAMUS takes place most Fridays at 3:00-4:00pm in Room 164 of the Adel Mathematics Building. Typically the first half of FAMUS consists of a talk on a mathematical topic while an interview of a faculty member takes place in the second half. FAMUS is hosted by Jeff Rushall.

Come join us for some entertaining talks! Refreshments always served.

Schedule Spring 2024

Note that talks are listed in reverse chronological order.

The Packing Coloring Problem

Date: May 4, 2024

Speakers: Jeff Rushall (NAU)

Abstract: This problem, first posed in 2002, seeks the minimal number of natural numbers needed to fill an infinite planar grid of squares if the distance between occurrences of the same number is greater than the number itself. [distance measured using the taxicab metric] The problem was resolved just a few months ago by a faculty member + grad student at Carnegie-Mellon. I’ll explain some of the details behind how the problem was solved.

There will be no faculty guest this week. [PDF of Flyer]

Prime Number Spirals: They Might Save Your Life!

Date: April 19, 2024

Speakers: Ian Williams (NAU)

Abstract: In this talk Ian will look at some interesting pictures of prime number configurations (including, not surprisingly, some spirals). Ian anticipates that some bewildered attendees will ask “Uhh…what?” and “Why does it do that?” and he will attempt to answer these questions.

There will be no faculty guest this week. [PDF of Flyer]

Investigating the spread of measles in Arizona and disease surveillance of flu transmission

Date: April 12, 2024

The talks this week are given by a pair of undergraduate students, Alexander Nez and Avery Drennan. They are working on an interdisciplinary project under Dr. Ye Chen that involves two related projects. Here are their official titles and abstracts.

Measles Meta-population Model Dynamics: Developing Realistic Movement Models to Assess Measles Spatial Spread Potential

Speaker: Alexander Nez (NAU)

Abstract: This study develops a stochastic compartmental model to understand measles transmission dynamics among individuals aged 0 to 18 years, utilizing 2019 Census data. The population was divided into seven compartments: Susceptible (S), Exposed (E), Infected (I), Recovered (R), First Vaccine-Prone ($V_{P1}$), First Vaccine-Responsive ($V_{R1}$), and Second Vaccine ($V_2$). We assess the impact of gravity and school commuter movement models on disease spread within the population. The gravity model, influenced by gravity weight $\phi$, predicts movement between census block groups. Conversely, the school commuter matrix, structured around student populations in census block groups and school enrollment data in Maricopa County, uses a Voronoi diagram to create an $n \times n$ commuter matrix. Incorporating school vaccine data, we identify areas of susceptibility, improving our understanding of at-risk populations.  To model measles spread, we use a tau-leaping algorithm that divides the day into parts: 1/3 for school, 1/2 for post-school movement and interaction, and the remaining time at home. This method provides insight into how susceptible individuals, exposed in various locations, can spread the virus within their census block group upon returning home. Our modeling captures the dynamics of disease transmission, offering insights into its trajectory and behavior.

Integrative Forecasting of Flue Transmission: Merging Statistical Regression and Compartmental Models Through Advanced Particle Filtering 

Speaker: Avery Drennan (NAU)

Abstract: Disease surveillance is essential for proactive public health measures, due to its crucial role in making health decisions to respond to evolving disease propagation.  In this study, we develop a new forecasting framework that integrates the strengths of two disease modeling approaches, changepoint regression model and compartmental model, to capture both local trend changes and long-term persistent trends in disease transmission dynamics. For this, we first revise the particle filter algorithm to infer the time-dependent nonstationary transmission rates. To avoid sample degeneracy and impoverishment caused by numerical round-off of the likelihood, our revised particle filter algorithm incorporates a new weight computation and a resampling scheme, simultaneously estimating both time-dependent and static parameters for flu hospitalization data. We then use a penalized likelihood approach to detect multiple changepoints in the inferred time-dependent transmission rates, using a detection technique based on a genetic algorithm to optimize changepoint estimation. With the estimated number of changepoints and their associated time location estimates, we compute local trend changes in the transmission rates. Finally, we reincorporate the forecasted changepoint transmission rates into the SIR model, resulting in enhanced precision in our prediction for flu progression.

There will be no faculty guest this week. [PDF of Flyer]

Intro to neural networks and mathematical foundation of Generative Pre-trained Transformer (GPT)

Date: April 5, 2024

Speaker: Misha Baltushkin (NAU)

Abstract: We will define and play around with some simple neural networks. We will investigate the structure of a neural network, talk about the forward propagation process and discuss the “learning process” (back-propagation) that a network undergoes. We will cover some examples of activation functions and explore what they are used for. In the other half of the talk we will discuss the foundation of a transformer model and briefly discuss how it works and why it is so powerful.

There will be no faculty guest this week. [PDF of Flyer]

New Results on Sylver Coinage

Date: March 29, 2024

Speakers: James Warner and Morgan Boyers (NAU undergraduate mathematics majors)

Abstract: James and Morgan will explain some background information on Sylver coinage and then present some new results on Sylver coinage that they have found together with research partners Natalie Burton and Tara Zurick. The highlight: when 4 and any odd integer $x > 5$ have been played, they have turned Sylver coinage into Tic-Tac-Toe (i.e., they will never lose). If you want to know more, come to FAMUS on Friday!

There will be no faculty guest this week. [PDF of Flyer]

The Calissons Problem

Date: March 22, 2024

Speakers: Jeff Rushall (NAU)

Abstract: This topic addresses a funky problem that French bakers have dealt with for centuries. Namely, when they put calissons (delightful little diamond-shaped cookies) into hexagonal boxes, an amazing geometric pattern was noticed. What was this pattern? And why was this pattern? And what do calissons taste like? Well, come to FAMUS on Friday, and all these questions will be answered.

There will be no faculty guest this week. [PDF of Flyer]

The Urinal Problem

Date: March 1, 2024

Speakers: Jeff Rushall (NAU)

Abstract: This topic addresses the following important question: when a person enters an empty bathroom with multiple urinals, which urinal should be selected to maximize this person’s chances of having complete privacy if others enter the bathroom? [note: a math paper was actually published on this problem a few years back] I will analyze the problem - as well as explain what urinals look like, how they are used, etc., for those in the audience who perhaps do not know much about urinals - with the help of many pictures of urinals I have taken over the years.

The faculty guests will be a few soon-to-be-graduating grad students who will discuss their experiences in our grad programs and their future plans. [PDF of Flyer]

Undergraduate Research Projects for 2024-2025

Date: February 23, 2024

Speakers: Jeff Rushall (NAU)

Abstract: In this talk, I will provide the audience with a near-complete list of all undergrad research projects overseen by our faculty for AY 2024-2025. Some are funded, some are not. Some involve individual students, some involve groups. There are 6-9 faculty involved. This is a great chance for students to see all potential undergrad research topics for the upcoming year.

The faculty guest will be Amy Rangel. [PDF of Flyer]

Euler Characteristics

Date: February 16, 2024

Speakers: Misha Baltushkin (NAU)

Abstract: I will explain this graph theoretic invariant, show lots of examples, discuss the history of this famous number, etc. This is a great topic for newbies at FAMUS, so please don’t be shy about attending.

The faculty guest will be Ye Chen. [PDF of Flyer]

A report on the Nebraska Women’s Conference Tara Zurick and Natalie Burton

Date: February 2, 2024

Speakers: Natalie Burton and Tara Zurick (NAU undergraduates)

Abstract: Natalie and Tara will discuss what happened at the conference, how they got there, show lots of pictures, tell us how their presentation went, and explain the impact NCUWM had on their futures.

The faculty guest will be Michele Torielli. Note: This FAMUS will held in Adel 163 and will end at 3:55PM to allow folks to attend the math ed candidate talk in Adel 164. [PDF of Flyer]

New Results on Sylver Coinage

Date: January 19, 2024

Speakers: Natalie Burton and Tara Zurick (NAU undergraduates)

Abstract: Sylver coinage is a game played on the natural numbers; if you want to know the game rules, come to FAMUS! Natalie and Tara, along with fellow undergrads James Warner and Morgan Boyers, have been working together for about 5 months trying to prove some Sylver coinage “claims” made by (among others) John Conway and Richard Guy. And they have been successful; come and see just how much they have proven!

The faculty guest is Mikhail Baltushkin. [PDF of Flyer]