Corvallis, OR 

Joshua Barsky
University of California, Riverside
Title: Connecting the Zeta Function and Prime Numbers
Abstract: In this talk, I will discuss the Riemann Zeta Function $\zeta(s)$ and its surprising connection to prime numbers. We will first look at the significance of this topic before moving into a brief timeline from Leonhard Euler to Bernhard Riemann. After exploring how these concepts were brought together, we will dive into more details like the Zeta Zeros and the prime counting function $\pi(x)$. Finally, we will bring everything together to show how the Riemann Zeta function and prime numbers are connected.

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Eduardo Chamorro
California State University, Stanislaus
Title: Indistinguishability of Directed Cycle Models
Abstract: Linear compartmental models (LCMs) have broad applications in fields such as pharmacokinetics, epidemiology, ecology, and systems engineering, where they are used to describe the movement of substances or information between different compartments. These LCMs consist of an underlying weighted-directed graph, where the weights represent flow rates between compartments, as well as input flow into the system and measurements being taken in some subset of the vertices, or compartments. A central challenge in the study of LCMs is identifying situations where models with distinct graphical structures can represent data equally well. This is called the study of indistinguishability.

Through a graph-theoretic approach, we developed Python code to generate all possible indistinguishable LCMs to a specific model. We then used the information to form conjectures on the connections between model structure and indistinguishability. Drawing from graph theory and abstract algebra, we proved various conjectures about the indistinguishability of certain families of LCMs. The primary objective was to uncover additional graph-theoretic conditions for indistinguishability to enhance the understanding of the structural and algebraic attributes of LCMs that contribute to it. With this information, biologists and modelers can determine when two models will be indistinguishable simply by the graph structure without having to perform complex algebraic computations.

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Kamrul Chowdury
Oregon State University
Title: FDTD Analysis of a Random Isotropic Cold Plasma Model
Abstract: In this talk, we study finite-difference time-domain (FDTD) discretizations for a random isotropic cold plasma model, where uncertainty is introduced through the collision-time parameter. We represent this uncertainty using a polynomial chaos (PC) expansion, which leads to a coupled deterministic PC system. We then discretize the PC system in space and time using the Kashiwa--Fukai (KF) FDTD scheme. We present analytical results on stability, convergence, and dispersion, and we discuss how these results provide insight into the accuracy and reliability of the proposed numerical method.

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Eli DeWitt
Michigan Technological University

Title: Euler’s Pentagonal Number Theorem, An Introduction to Integer Partitions
Abstract: How many ways can you write an integer as an unordered sum of natural numbers? This deceptively simple question is the subject of integer partitions and surprisingly, leads to deep results in combinatorics and analysis. In this presentation, we introduce integer partitions using generating functions and Young-Ferrers diagrams, then build towards Euler's pentagonal number theorem — a striking result that encodes partition counts in the geometry of pentagons.

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Luna Lu
Reed College
Title: How Much Can We Know? An Information-Theoretic View of Kalman Filtering
Abstract: In general, state space models estimate hidden states of a system from noisy observations. Many problems in engineering and mathematical physics apply these tools to better acquire information that stays true to reality. But how much information do our observations contain? Turns out, we can calculate entropy, or degree of uncertainty, for each recursive step in our model, and find approximated bounds to hopefully satisfy these questions. In my talk, I will introduce the Kalman Filter, an algorithm for inference on such models that is linear (or approximately linear) and theoretically optimal, and use its covariance evolution to quantify uncertainty and interpret the filtering process through the lens of information theory. I hope to use this perspective to not just investigate the application of such filters, but also to test the theoretical limits of how much these tools can really accomplish.

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Leanne Merrill
Lane Community College
Title: Crossword Counting Conundrums
Abstract: Did you know that crossword puzzles are rich with mathematical mystery? In this brief talk, we'll discover some of the interesting questions you can ask and answer about crossword puzzles. This inquiry will involve graph theory, combinatorics, geometry, and more. No experience with any of these fields or with crossword puzzles is required to engage with and enjoy this talk!

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Micheal Timmons
Linn-Benton Community College
Title: Kepler Mapper as a tool in permafrost data analysis
Abstract: Kepler Mapper, a python implementation of the mapper algorithm, can be used in order to analyze and visualize high-dimensional data of Alaskan fresh-water pollution due to permafrost melting. These maps show us relationships in pollutants, geographic position, pH, and type of hydrological source. We can look at the distinction between streams with acid-burnt vegetation and with healthy vegetation in their metal and pollutant profile, as well as how the composition of the base underlying rock changes the pollutants present in melt-damaged streams.

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Zejing Wang
Oregon State University
Title: Introduction to Persistence Homology
Abstract: Applied topology has shown surprising power in recent AI research. In particular, persistent homology provides a refined algebraic structure that can be extracted from both discrete and continuous data via computational methods, while it has a theoretic background from algebraic topology. My talk will include a brief introduction to this concept.

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Brandi Whiteman 

Oregon State University

Title: Women's Participation in the Communities of Practice of a Doctoral Mathematics Program: Insights into Persistence
Abstract: Women have been historically underrepresented in the field of mathematics in the United States (US), especially at the doctoral level. Substantial research has been done to identify barriers that women face to earning mathematics PhDs, but fewer studies have investigated factors that contribute to women’s persistence and success. My study relies on Herzig’s (2002) framework for persistence in doctoral mathematics to understand what factors contribute to the persistence and success of six women who are currently enrolled in one mathematics doctoral program in the US. Additionally, I apply an intersectionality lens to analyze their experiences with respect to the multiple systems of power and oppression (e.g., patriarchy and white supremacy) that influence cultural and structural aspects of the academy.

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• Lucas Anderson (OSU) – The Eccentric, Emerging World of Riemannian Diffeology
  

• Joshua Barsky (University of California Riverside)– Zeta and Primes
  

• Eduardo Chamorro (Michigan Technological University) - Indistinguishability of Directed Cycle Models
  

• Ricardo Noe Gerardo Reyes Grimaldo (LBCC) – Unstable Antibody Protection Facilitates Persistence of Foot-and-Mouth Disease in African Buffalo Populations

• Nora Kearsley – Fourier Analysis and its Applications
  

• Luna Lu (Reed) - How Much Can We Know? An Information-Theoretic View of Kalman Filtering
  

• Ella McNeal (OSU) – Student Understanding of Integrals
  

• Tory Friedman TeBockhorst (OSU) – Traveling Wave Behavior in Foot and Mouth Disease
  

• Noah Unger-Schulz (OSU) – Don't Meet Me in the Middle: Abisectionable Metric Spaces