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A list of all the posts and pages found on the site. For you robots out there, there is an XML version available for digesting as well.
Pages
Posts
Intro to the Asymmetric Simple Exclusion Process (ASEP) & Bethe Ansatz Pt. 2
Published:
In this post I continue the discussion from this post on the ASEP and introduce the ‘Coordinate Bethe Ansatz’ approach to finding an explicit solution to the forward equation in the case of two particles. In part 1, we derived the following forward equation for the probability function of the ASEP,
Towards the One-Point Function for the XXZ Spin-1/2 Chain on the Ring
Published:
Some observables from the XXZ spin-1/2 chain have shown KPZ behavior, but it is not entirely clear if the model lies within the KPZ universality class. Of particular interest for us is the one-point function, for which we aim to get an exact expression that is amenable to asymptotic analysis. This content and informal discussion is based on joint work with Axel Saenz Rodriguez.
The Six-Vertex Model & XXZ Quantum Spin Chain part 2
Published:
Here we introduce the transfer matrix of the six-vertex model and show a mathematical relationship it has with the hamiltonian of the XXZ quantum spin chain (aka Heisenberg-Ising hamiltonian). This is a follow up to my previous blog post which you can find here. The work that follows is essentially that of section 10.14 in R.J. Baxter’s book “Exactly Solved Models in Statistical Mechanics” adapted to the more specific case of the six-vertex model and XXZ spin chain (compared to the more general XYZ spin chain and eight-vertex model).
An unexpected relationship: the mathematical ties of a model for a square sheet of ice and one-dimensional magnetism
Published:
What does a model for the possible orientations of hydrogen and oxygen atoms on a sheet of ice have to do with a toy model for magnetism on a chain? Although the original aim for both of these models were describing different things, molecular structure of ice and magnetism, they are intimately related via their mathematical construction. In particular, the operators that govern the dynamics of each model commute, and thus share the same eigenvectors.
Intro to the Asymmetric Simple Exclusion Process (ASEP) Pt. 1
Published:
A brief introduction to the asymmetric simple exclusion process (ASEP) and the forward equation for the dynamics.
publications
Understanding spin waves in 2D magnets: A combined experimental, computational, and mathematical theory approach
Published in SpringerNature MRS Advances, 2025
We present our work towards developing a comprehensive approach to understanding spin-wave (SW) dispersion in 2D van der Waals (vdW) magnets, combining steady-state and time-resolved spectroscopy with electronic structure calculations and mathematical modeling of SW propagation.
Recommended citation: Aislinn, P.J., Winchell, A.J., Lambertson, E.R. et al. Understanding spin waves in 2D magnets: A combined experimental, computational, and mathematical theory approach. MRS Advances (2025).
Download Paper
talks
Intro to the Asymmetric Simple Exclusion Process
Published:
An informal introduction to the asymmetric simple exclusion process (ASEP) given in the graduate student seminar in the department of mathematics at Oregon State University.
Intro to the Bethe Ansatz for ASEP
Published:
An informal introduction to the Bethe Ansatz for the asymmetric simple exclusion process (ASEP) for the graduate student seminar in the department of mathematics at Oregon State University.
Coordinate-Energy Transformation and One-Point Function for the XXZ Spin-1/2 Chain
Published:
I gave an 8 minute talk at the IP3 conference (Interplay between interacting particle systems and integrable probability) at Université Angers on joint work with Axel Saenz and Eric Corwin recently posted on arXiv. You can find the slides from the talk here
teaching
ELITE PD
Professional Development Program, Oregon State University, Mathematics, 2025
Since 2022, I have received training from the Engaged Learning, Inclusive Teaching, and Equity Professional Development program. This is a joint effort from researchers (funded by the NSF) at Oregon State University, Virginia Commenwealth University, and San Diego State University to address concerns in the training that graduate students in mathematics receive. In particular, graduate students typically receive a large amount of training as researchers compared to very little training as educators. However, the majority of these students end up in teaching-heavy roles. Moreover, undergraduate mathematics education is commonly not engaging, inclusive, and equitable. You can find additional info here.
Graduate Assistantship Teaching Appointments
Teaching Appointments, Oregon State University, Mathematics, 2025
This is a collection of my teaching appointments as a graduate assistant in the department of mathematics at Oregon State University. They are sorted in descending order by academic year & term (terms are called by their respective season, i.e. fall, winter, spring, summer). Terms that do not have an associated teaching assignment are terms which I had a research appointment. 4xx/5xx numbered courses are cross-listed undergraduate/graduate courses meaning undergraduate and graduate students are enrolled.