8:30-9:00 am Continental Breakfast, Name Tags 294

9:00-9:10 am Welcome 294

9:10-10:10 am Keynote Address 294

10:30-11:50 pm Student Talks     296, 298 

11:50-1:00 pm Lunch     * On your own

1:00-2:20 pm Student Talks     296, 298

2:20-2:50 pm Afternoon Snack Break 294

2:50-3:50 pm Student Talks      296, 298 

4:00-4:30 pm Mingle 294

4:30-4:45 pm Award Ceremony & Closing Remarks 294

Conference activities will take place on the second floor of Smith Memorial Student Union. 

*Lunch and dinner will be on your own. Portland State University hosts the Portland Farmers Market in the Park Blocks next to SMSU. See here for more information.

Hannah Kravitz, Portland State University 

Title: Metric graphs: spectral methods, localization, and applications

Abstract: I study structures called ``metric graphs,” which are networks with a distance metric defined on their edges. This creates a 1D structure on which to solve partial differential equations (PDEs), with boundary conditions in the form of coupling conditions at the vertices. This seemingly simple setup (it is in one dimensional after all), leads to many interesting questions like: 

1) What causes waves to get trapped in certain parts of the graph (localization)?

2) Which frequencies can exist on a graph (the eigenvalue problem)?

3) How can the research be applied in areas like optical science and modeling the spread of epidemics? 

4) How can we utilize the graph’s structure to develop efficient computational algorithms? 

Throughout this talk, I will explore these questions and share insights into how metric graphs offer new ways of thinking about wave behavior in a range of contexts.

Bio: Dr. Kravitz is an Assistant Professor of Mathematics at Portland State University. Her research focuses on numerical methods for partial differential equations on metric graphs, as well as applications of network science to epidemiology. This research combines many fields including numerical analysis, computational math and network science, and her work has several applications in public health and optical science.

Prior to graduate school, Dr. Kravitz worked as a data analyst for University of Washington's Institute for Health Metrics & Evaluation, conducting survey programming, census enumeration and data collection logistics, and verification and analysis of incoming data. In the past, she has also worked as an environmental engineer at a consulting firm and a governmental agency, performing air dispersion modeling, geographical data analysis, and environmental permitting.

Room 296 Winners

Lila Goldman (Western Washington University)

Title: Chutes and Ladders as a Markov Process

Abstract: Chutes and Ladders is a very simple board game with little strategy involved. The gameplay is dictated entirely by spinning a spinner and moving one’s game piece accordingly. Because of this, players often want to know, “How long is this going to take?”. As it turns out, we are able to answer that question with certainty because Chutes and Ladders is a fantastic example of a Markov process. In this talk, we will construct a Markov chain and use it to predict potential game lengths of Chutes and Ladders.

Gemma Bertain (University of Puget Sound)

Title: Reduced Trip Permutations of Plabic Graphs

Abstract: The decorated trip permutation of a reduced plabic graph tells us what cell in the Grassmannian the graph parameterizes. This research studies the trip permutations of unreduced plabic graphs and how they change when the graphs are reduced. If the output is a permutation with no fixed points, this tells us what cell in the Grassmannian an unreduced graph parameterizes without actually reducing the graph.

Room 298 Winners

Anna Singley (Los Alamos National Laboratory, University of Portland)

Title: Network Analysis of Collaboration in Mathematics

Abstract: Complex networks can be used to explore a plethora of biological, social, and ecological systems. Visualization of complex data with a network allows for more intuitive analysis and realization of underlying structure in a dataset. Tools from network topology and graph theory allow for a more thorough study of the evolution of a network over time. Using a repository of open access journal articles organized by math subject code (MSC), we can visualize the evolution of a field over with the use of networks. Further, we can conduct a process similar to contact tracing to attempt to study the spread of an idea over a collaborative network - helping us to visualize the evolution of a mathematical subfield.

Shosuke Kiami (University of Washington)

Title: Stochastic Dynamical System

Abstract: In their recent work, Steinerberger-Zeng introduced a class of dynamical systems in the complex plane that take on the form $z_n = z_{n-1} \pm e^{i a_n}$ where $a_n$ is some sequence of reals and the sign of “+/-“ is chosen so as to minimize $|z_n|$. In our work, we study the case where $a_n$ is chosen uniformly at random from $[0, 2\pi)$ which yields a stochastic process with a peculiar looking stationary distribution. This stationary distribution has yet eluded a closed form, however, we prove various properties about the stationary distribution including its asymptotic behavior in higher dimensions.