Seminar Talk, WSU, Pullman, WA
Abstract: Eigenvectors of graph-associated matrices like the Laplacian, adjacency, and variations of them often appear in graph-based applications. From spectral clustering of data to spectral-based redistricting algorithms, eigenvectors prove to be a useful tool.
Conference Talk, WNAR IBS 2026, Pullman, WA
Abstract: Tuning machinery for optimal output is a major step in catalysis setup. Each iteration costs practitioners money and time even with thorough understanding of the physical processes involved. With standard modeling techniques, computational costs suffer from the same downfall. To alleviate this step in the process, we deal with discrete approximations of filters and train neural networks to generate similar structures to estimate tuning parameters. We will discuss how we use Graph VAEs to generate bounds for tuning parameters as well as the statistical foundation of this technique.
Seminar Talk, WSU, Pullman, WA
Abstract: In this talk, we will focus on the intersection of graph theory, algebra, and probability theory. Recent research in spectral graph theory and its applications have highlighted the utility of probabilistic approaches. We will take time to cover some interesting methods to motivate research questions. There will be a live-code demonstration that showcases implementation of these methods and what computation in mathematics research can look like. We will discuss eigenvector approximation, clustering, and reconstructibility of graphs. Focusing largely on spectral graph theory, the interdisciplinary nature of the talk will offer fun perspective into intuitive problems.
Guest Lecture, WSU, Pullman, WA
Abstract: An invited talk to discuss higher-level concepts in graph theory to undergraduate graph theory students. We discuss the Law of Large Numbers, Markov Chain Monte Carlo, and how we use them for graph-based data science problems. Including a fun LLN visual!
Colloquium, WSU, Pullman, WA
Abstract: A friendly talk on the mathematics behind gerrymandering and probability theory for a physics-oriented colloquium audience.
Guest Lecture, WSU, Pullman, WA
Abstract: For the “Mathematical Snapshots” class at WSU, a series of guest lectures introduce undergraduates to the researchers in mathematics. We walk through our personal mathematics journey and discuss where this journey has led us.
Guest Lecture, Graph Theory, Pullman, WA
Abstract: As Math 453 comes to a close, I have been invited to give a special topics lecture on spectral graph theory. We will discuss relevant concepts of spectral graph theory and graph partitioning. Then, we will review some open research problems regarding pertubations of the eigensystem and spectral clustering. After a demonstration of Markov Chain Monte Carlo (MCMC), we will discuss applying the process to spectral partitioning problems and redistricting.
Guest Lecture, Advanced Linear Algebra, Pullman, WA
Abstract: As Math 420 reaches its close, I have been asked to give a talk on Markov Chain Monte Carlo (MCMC) and its applications. We will review some probability theory basics through an in-class excercise revealing the intuition of the Weak Law of Large Numebers. Afterward, we will have a demonstration in real time of MCMC’s approximation of a given distribution. After diving into the history of this revolutionary approach, we will end with applications to redistricting and crytography.
Seminar Talk, WSU, Pullman, WA
Abstract: We will discuss the concept of Benjamini-Schramm convergence and its motivation. After discussion of properties of unimodularity in graphs, we discuss its importance in limits of random graphs. We will cover both pointed and rooted graphs and discuss the relationship between both through bias of random variables.
Colloquium, California State University East Bay, Hayward, CA
Abstract: Per my former department’s request, we begin by reviewing my mathematical journey up to where I am today. We then explore the basics of Gerrymandering as a concept and redistricting as a mathematical application. Using graph thoeretic ideas, we define the redistricting methods used in practice. Then, we cover current research in spectral graph theory using eigenvectors of graphs as a tool for this application. Offering many paths for further exploration, we extend an invite to partake in math’s applications to redistricting, networks, and data.
Seminar Talk, WSU, Pullman, WA
Abstract: In this talk, we will explore the mutually beneficial relationship between probability theory and spectral graph theory. At their intersection lie lots of perplexing puzzles and fresh features. Through ample example, we will showcase their established significant symbiotic synergy. Moreover, we will meander through many musings and mysteries.
Presentation at Conference, Joint Mathematics Meeting, Seattle, WA
Abstract: Eigenspaces of linear operators associated with graphs have well known applications in the context of graph partitioning. In this talk, I will use combinatorial methods to evaluate the relationship between eigenvector entries and adjacency structure, particularly in constructing graphs with prescribed eigenvectors. As examples, I will characterize eigenspaces for well-studied graph families including Johnson graphs and perform a similar analysis for graph products. In addition to these combinatorial results, this approach also has applications to dimensionality reduction, a natural problem in data science.
Seminar Talk, WSU, Pullman, WA
Abstract: Many well established graph partitioning methods are determined by eigenvectors of matrices associated with the underlying graph. In this talk, we will explore the combinatorial intuition and computational methods involved in reconstructing a graph from subsets of such a partitioning. This will naturally lead us to characterize desirable attributes of graphs in this context and we will also uncover an application to information security.
Presentation at Conference, University of Calgary, Calgary, AB, Canada, Calgary, AB, CA
Abstract: The sum of the moduli of the adjacency spectra of a graph, the adjacency energy, has been shown to connect linear algebra and the electron energy of molecules. This talk will cover a conjectured lower bound relating the energy of a graph and the size of its largest independent set. A solution for graphs with proportionally large independent sets will be shown and the consequences explored.
Seminar Talk, WSU, Pullman, WA
Abstract: Spectral graph theory (SGT) has various scientific applications, ranging from network optimization to quantum error correction. This presentation will explore the combinatorial realm of SGT by exploring its implications through several proofs of famous counting problems. By investigating methods, this talk aims to illustrate the intersection of combinatorics and spectral graph theory, offering insights into their synergistic relationship.