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 1/20 at 4:00-4:50
Speakers: Jaechoul Lee, Associate Professor, NAU
Abstract: The “curse of dimensionality” presents a formidable barrier in modern data applications: as the complexity of a system grows, the cost of acquiring, monitoring, and processing data often scales prohibitively. However, we can frequently overcome this challenge by exploiting the “intrinsic low-dimensional geometry” of the data, i.e., the observation that high-dimensional signals often reside on compact manifolds characterized by sparsity or low-rank dependencies.
This talk is an invitation to explore the rich mathematical landscape underlying critical engineering challenges, such as efficient signal acquisition, network monitoring, and distributed learning. We will begin by revisiting the classical framework of sparse recovery and group testing, examining how we can identify active components in a signal using a minimal number of measurements. I will discuss our results on order-optimal algorithms that achieve reconstruction with sample complexity linear in the sparsity level and sub-linear decoding time.
From these geometric foundations, we will pivot to the domain of distributed learning. Specifically, our recent result on federated learning using zero-order optimization will illustrate how tools like the Johnson-Lindenstrauss (JL) transform allow us to estimate high-dimensional gradients from compressed queries while preserving geometric structure and robustness. We will also look at emerging frontiers, such as the application of low-rank structure in network traffic analysis and LLM fine-tuning, offering a glimpse into the future of scalable, efficient, and trustworthy systems.
Date: Tuesday 1/27 at 4:00-4:50
Speakers: Nandor Sieben, Professor, NAU
Abstract: In theory the winning strategy of a combinatorial game can be found by a simple process analyzing the digraph of positions. In practice this is often impossible because the game digraph is too large. Folding the game digraph identifies positions that are essentially the same. Folding constructs a quotient game that is easier to analyze since it has fewer positions. The theory allows for the four isomorphism theorems known from Universal Algebra. Clever foldings make it possible to analyze many interesting games like “Totative” and “Sliding Coins”. Joint work with Baltushkin and Ernst.
Date: Tuesday 2/3 at 4:00-4:50
Speakers: TBA
Abstract: TBA
Date: Wednesday 2/11 at 4:00-4:50
Speakers: Mayank Bakshi, Assistant Professor, NAU
Abstract: The “curse of dimensionality” presents a formidable barrier in modern data applications: as the complexity of a system grows, the cost of acquiring, monitoring, and processing data often scales prohibitively. However, we can frequently overcome this challenge by exploiting the “intrinsic low-dimensional geometry” of the data, i.e., the observation that high-dimensional signals often reside on compact manifolds characterized by sparsity or low-rank dependencies.
This talk is an invitation to explore the rich mathematical landscape underlying critical engineering challenges, such as efficient signal acquisition, network monitoring, and distributed learning. We will begin by revisiting the classical framework of sparse recovery and group testing, examining how we can identify active components in a signal using a minimal number of measurements. I will discuss our results on order-optimal algorithms that achieve reconstruction with sample complexity linear in the sparsity level and sub-linear decoding time.
From these geometric foundations, we will pivot to the domain of distributed learning. Specifically, our recent result on federated learning using zero-order optimization will illustrate how tools like the Johnson-Lindenstrauss (JL) transform allow us to estimate high-dimensional gradients from compressed queries while preserving geometric structure and robustness. We will also look at emerging frontiers, such as the application of low-rank structure in network traffic analysis and LLM fine-tuning, offering a glimpse into the future of scalable, efficient, and trustworthy systems.
Date: Tuesday 2/17 at 4:00-4:50
Speakers: Sam Harris, Assistant Professor, NAU
Abstract: Entanglement is a crucial resource in quantum information science and is required for many tasks involving quantum computers. In 2003, van Dam and Hayden devised an approximate method for two parties (Alice and Bob), which takes a certain entangled state and uses it to produce a new entangled state “alongside” the first one, while nearly preserving the first state. Such a process has come to be known as embezzlement of entanglement. In the setting where this process is exact (and not approximate), it is known that such protocols can only occur in infinite-dimensional, “commuting operator” frameworks. In this talk, we exhibit something stronger: Alice and Bob’s operations needed to perform embezzlement are unique in a certain sense, and generate unique observable algebras. We explore this “self-testing” phenomenon and describe what observable algebras one obtains.
Date: Tuesday 2/24 at 4:00-4:50
Speakers: Sabrina Zarza, Michigan State
Abstract: This talk explores how Chicana feminist methodologies offer innovative ways of understanding students’ experiences with mathematics across secondary and postsecondary contexts. Drawing on two interconnected studies, one examining high school students’ sense of belonging in mathematics classrooms and a dissertation study using walking pláticas with Latiné mathematics majors who attended both Hispanic-Serving and Predominantly White Institutions, I illustrate how relational and place-based approaches generate new insights into the structural conditions that shape participation in mathematics. Together, these studies center students’ narratives and embodied experiences as a foundation for theory building about belonging and engagement in mathematics. By foregrounding these perspectives, this work complements existing approaches to studying student experience and extends how researchers and educators understand the sociopolitical context of mathematics learning. The talk concludes by considering implications for mathematics educators, teacher preparation programs, and researchers interested in designing studies that more fully account for students’ lived experiences with mathematics.
Date: Tuesday 3/3 at 4:00-4:50
Speakers: TBA
Abstract: TBA
Date: Tuesday 3/10 at 4:00-4:50
Speakers: TBA
Abstract: TBA
Date: Tuesday 3/17 at 4:00-4:50
Speakers: Lan Zhang, Assistant Professor, NAU
Abstract: Reinforcement learning (RL) has emerged as a powerful framework for addressing cybersecurity challenges from both offensive and defensive perspectives. Traditional signature-based malware detection is inherently reactive, and while modern deep learning approaches have significantly improved detection accuracy, they remain vulnerable to adversarial manipulation. Generating adversarial malware is fundamentally difficult because malicious functionality must be preserved, detectors operate as black boxes, and malware features are discrete rather than continuous — all properties that make conventional gradient-based methods ineffective. RL overcomes these barriers naturally by learning through interaction with the environment, without requiring access to model internals or continuous feature spaces. Beyond attacking detectors, RL can also be applied proactively on the defensive side, enabling intelligent, adaptive responses to sophisticated threats such as lateral movement attacks, where an adversary progressively compromises machines across a network to reach high-value targets.
Date: Tuesday 3/24 at 4:00-4:50, Room 223
Speakers: Nellie Gopaul, Associate Teaching Professor, NAU
Abstract: This talk shares a first look at incorporating music, movement, and structured peer interaction into a statistics classroom. Developed during participation in NAU’s Faculty Wellness Fellows program, classroom activities bridge larger student well-being data with small, intentional changes designed to support student engagement, enjoyment, and connection. A brief interactive component is planned, followed by reflection on how instructional choices can shape students’ experiences in meaningful ways.
Date: Wednesday 3/25 at 4:00-4:50
Speakers: Vincent Martinez, Associate Professor, UNY Graduate Center, CUNY Hunter College
Abstract: Predicting the weather is an old problem and it’s still unsolved in spite of having access to weekly forecasts on our phones. We’ve gotten very good at it over the years though and have developed more principled methods that do away with things like star gazing, watching animals, and folklore. As our technology and understanding advanced, we’ve been able to collect more data about the atmosphere and have a better physical understanding of the physical mechanisms involved. The modern method is to use weather data with partial differential equations that model the weather. This talk will address a fundamental mathematical reason for why the modern method is so successful, but also why it’s still a very difficult thing to do.
Date: Tuesday 3/31 at 4:00-4:50
Speakers: Anders Claesson, Professor, University of Iceland
Abstract: Montmort’s classical hat-check problem asks for the probability that a random permutation has no fixed points; the answer, famously, tends to 1/e. The same limit holds, by an elementary argument, for endofunctions. Cayley permutations sit between these two families and present a harder challenge. A Cayley permutation is a function on {1,…,n} whose image contains every positive integer up to its maximum value; via their fibers, Cayley permutations are in bijection with ballots (ordered set partitions).
In this talk, we use two-sort species to study the functional digraphs of Cayley permutations. We derive differential equations for the generating series of R-recurrent Cayley permutations, a class that includes derangements as a special case. From these equations, we obtain an explicit counting formula for fixed-point-free Cayley permutations involving subfactorials and differences of r-Stirling numbers. We then use this formula to prove that the proportion of Cayley derangements again tends to 1/e, just as for permutations and endofunctions.
This is joint work with Giulio Cerbai (University of Iceland).
Date: Tuesday 4/7 at 4:00-4:50
Speakers: Kayode Oshinubi, Postdoc, NAU
Abstract: Mosquito-borne diseases pose a growing public health challenge, with climate change expected to shift mosquito population dynamics and disease burden. West Nile Virus (WNV), transmitted via migratory birds and Culex mosquitoes, disproportionately affects Maricopa County, Arizona—one of the nation’s highest-burden counties per CDC surveillance data—yet it remains unclear whether incorporating weather and bird dynamics into forecasting frameworks meaningfully improves forecast accuracy. Using a 15-year (2006–2019, 2021) weekly time series of mosquito abundance, infectious mosquito density, and human WNV cases from Maricopa County, we developed and compared four mechanistic ordinary differential equation (ODE) model configurations of varying complexity, ranging from mosquito-human dynamics only to full models incorporating bird reservoir dynamics and weather forcing driven by daily temperature and 30-day accumulated precipitation. The Ensemble Kalman Filter (EnKF) combined with an Ornstein-Uhlenbeck (OU) process was used to estimate three time-varying parameters—baseline mosquito population growth rate, mosquito bite rate, and avian force of infection—alongside static parameters, and to generate probabilistic 1- and 2-week-ahead forecasts with full uncertainty quantification. Model skill was evaluated against a CDC-style baseline using relative Weighted Interval Score (WIS) across 1- and 2-week-ahead horizons, seasons, and years. All model configurations fit the surveillance data reasonably well regardless of whether weather or bird dynamics were included. However, forecast accuracy diverged markedly across targets: the full model incorporating birds and weather outperformed simpler configurations for total mosquito abundance, and models with weather forcing outperformed their weather-free counterparts for infectious mosquito density. For human WNV cases, all models outperformed the baseline, suggesting that human case forecasting is less sensitive to the inclusion of bird and weather data than mosquito-specific targets. Forecast skill was strongest during summer and fall across all models, and ensemble aggregation further stabilized predictions across the decade-long dataset. These findings suggest that weather and bird dynamics are most critical for forecasting mosquito abundance and infection prevalence, while human case forecasting may be achievable with simpler model structures. This weather-adaptive, probabilistic forecasting framework offers actionable near-real-time predictions to support mosquito control and resource allocation, and its generalizability positions it as a scalable One Health tool as climate change continues to reshape the landscape of mosquito-borne disease.
Date: Tuesday 4/21 at 4:00-4:50
Speakers: Allie Pari
Abstract: Any two reduced expressions for an element of a Coxeter group are related by a sequence of commutation and braid moves. Two reduced expressions are called braid equivalent if they are related by a sequence of only braid moves. Braid equivalence is an equivalence relation, and the corresponding equivalence classes are called braid classes. The braid class for a reduced expression can be encoded in a graph, called a braid graph, in a natural way. In a paper by Barnes, Breland, Ernst, and Perry, the authors proved that in a Coxeter system that is simply laced and triangle free (i.e., the corresponding Coxeter graph contains no three-cycles), every braid graph is median. In this thesis, we extend this result and prove that every braid graph in a Coxeter system whose corresponding Coxeter graph contains no three-cycles with the labels 3,3,m (where m is greater than or equal to 3) is median. To that end, we also generalize the theory presented in the aforementioned paper and a paper by Awik, Breland, Cadman, and Ernst. Many of the proofs and theorem statements in this thesis take inspiration from research done by three undergraduate students Atillio, Patrick, and Wilmer, under the guidance of Ernst during the 2024–2025 academic year.
Date: Wednesday 4/22 at 4:00-4:50
Speakers: Maddy Cox
Abstract: The chromatic polynomial of a graph, which counts the number of proper vertex colorings for a certain number of colors, also provides information about combinatorial properties of the graph. This talk will discuss different construction methods for chromatic polynomials and present formulas for chromatic polynomials of common graph families such as cycles, trees, and complete graphs.
There is a surprising connection between graphs and hyperplane arrangements. Chromatic polynomials of graphs can be used to count the number of chambers that a collection of hyperplanes divides a space into. Translating back and forth between a graph and its associated hyperplane arrangement, where edges correspond to hyperplanes, helps us better understand patterns in the chromatic polynomial and the geometric structure of the arrangement.
Date: Tuesday 4/28 at 4:00-4:50
Speakers: Scott Akin
Abstract: Any two reduced expressions for an element in a Coxeter group are related by a sequence of commutation and braid moves. Restricting to braid moves defines equivalence classes called braid classes, which are encoded by braid graphs. Similarly, commutation moves define commutation classes. The relationships between commutation classes are captured by the quotient commutation graph.
In this thesis, we study the connection between braid graphs and quotient commutation graphs in simply-laced Coxeter systems. We introduce the transversal property: a condition where a single braid class for an element contains exactly one representative from every commutation class. We prove that, for certain systems, the quotient commutation graph of an element is isomorphic to the braid graph of one of its reduced expressions if and only if the element has the transversal property. We conclude by providing several families of elements that satisfy this condition.