REU Site : Appalachian Mathematics and Physics Site
About the REU site
The Department of Mathematics and Physics at Marshall University is proud to host the REU Site: Appalachian Mathematics and Physics Site, an 8-week summer undergraduate research program that will run during Summer 2026. This program focuses on providing research opportunities in mathematics and physics to undergraduate students. Participants will receive a $5,600 stipend, paid housing in the campus dormitories, and a meal plan for the duration of the program.
Dates, eligibility, and deadlines
Dates of REU: Finalized dates will be announced soon! Expect the dates to be through most of June and July!
Who is eligible?: As per the NSF rules, only US Citizens or Permanent Residents without a bachelor's degree may participate.
Deadline to apply: Deadline for full consideration of your application is 1 March 2026. We will continue to accept applications after that date until all participants are selected.
Location
Participants will be housed in a dormitory at Marshall University and be provided a campus meal plan. Housing and the meal plan is 100% paid for by the grant (i.e. it does not come out of the stipend!).
Marshall University was recognized as an R2 research institution in 2019. The faculty in the Department of Mathematics and Physics have a history of involvement in REUs, having hosted an NSA-funded REU in combinatorics in 2016 and being involved in a computational REU that ran in 2010--2014. Marshall University runs a Summer Undergraduate Research Experience (SURE) program and was recently awarded a different REU program in civil and environmental engineering.
All participants will have access to classroom space and computational hardware as-needed, and physics participants will have access to the necessary laboratory equipment to conduct their research. Participants will live in the dormitories of Marshall University and will be provided with a meal plan for the duration of the program. The dormitories are approximately a five minute walk from the two buildings in which research will occur. Marshall University has two libraries that can provide academic resources for participants, as well as additional collaboration spaces. The Memorial Student Center serves as a center point of campus with a welcoming foyer as well as nationally-franchised fast food and coffee shops.
Marshall University is located in Huntington, the second largest city in West Virginia. Its downtown area connects to the western edge of campus, and the city and its surrounding towns are host to numerous artistic and musical events each summer. Local transportation options exist for participants without a car. The Tri-State Transit Authority provides a bus service that connects the university to to local recreation, shopping locations, and restaurants in Huntington. Greyhound provides bus services to other nearby cities such as Charleston, WV and Ashland, KY. Huntington also hosts an Amtrak station with service to distant cities such as Chicago, Cincinnati, Philadelphia, and New York City.
West Virginia hosts numerous public recreation areas -- for example Beech Fork State park lies ten miles to the south of Huntington while the New River Gorge National Park, the United States' newest national park, lies near Fayetteville, WV, about a two hour drive from Huntington.
Contact for questions
Please contact
Dr. Tom Cuchta at
cuchta@marshall.edu with any questions about the program.
How to apply
Please fill out the application form
here. You will be asked a series of questions and be asked to arrange for at least one letter of recommendation to be emailed. If you have any questions or concerns with the application, then please direct them to Dr. Tom Cuchta at
cuchta@marshall.edu
Projects
One of the pivotal theoretical challenges faced by Multi-Messenger Astrophysics (MMA) is the accurate modeling of the effect of tides on the gravitational waves (GW) during binary neutron star (BNS) mergers and the mechanisms behind their electromagnetic counterparts, such as the emission of Fast Radio Burst (FRB) during the pre-merger and Gamma Ray Bursts (GRB) after the merger. We will address these three challenges while simultaneously nurturing the next generation of MMA researchers. This is achieved by engaging undergraduate students in the development of innovative techniques to demystify BNS mergers and their counterparts. By combining rigorous training with efforts in developing innovative approaches to the unresolved theoretical problems related to understanding BNS mergers, we ensure that future researchers are equipped to bridge the gap between observational data and theoretical predictions. Three well-defined projects can be explored:
- Project 1: Analytical modeling of the influence of tides on the gravitational wave signal during BNS mergers
- Project 2: The role of the magnetic field in the emission of Fast Radio Bursts during BNS mergers
- Project 3: Analytical modeling of Gamma Ray Bursts
Our analytical models are appropriate for undergraduates, requiring no knowledge of General Relativity, advanced mathematical methods or computer software. We will develop our software in Python, guided by a user-friendly Jupyter Notebook, or using Mathematica computational platform.
Recommended prerequisites: Differential equations, electricity and magnetism, mathematical analysis, experience with programming
Problems in algebraic graph theory (advisor: Dr. Sudipta Mallik)
This project involves graph theory and linear algebra. Many properties of a graph can be described by linear algebraic properties such as rank and eigenvalues of a matrix associated with the graph. There are plenty of applications of this line of research such as Google PageRank. Participants will first learn basic results from algebraic graph theory: adjacency, incidence, Laplacian matrices and their applications to walks, bipartiteness, connectedness, spanning trees, chromatic number of a graph. Then they will investigate various open problems such as construction of linear codes from hypergraphs and the Moore-Penrose inverse of a matrix associated with a graph or signed graph. This project will require generating examples of graphs and corresponding matrices using SageMath (a python-based open-source software). The ultimate goal is to write an article with the findings in this project and publish it in a research journal.
Required prerequisite: college level linear algebra and graph theory
Computation of analytic capacity (advisor: Dr. Stephen Deterding)
A function is said to be analytic on a domain if it is differentiable at every point of the domain. An entire function is a function that is differentiable at every point in the complex plane. Unlike the real variable case, a bounded entire function must be a constant. The analytic capacity of a set is a measure of how large a bounded function that is analytic outside the set can become. Sets with zero analytic capacity are removable in the following sense: every function that is analytic outside a set with zero analytic capacity can be extended to an entire function. For a set that is not removable, the analytic capacity provides a measure of how close it comes to being removable. It also plays an important role in the study of rational approximation in the complex plane.
Analytic capacity can be directly computed for simple sets, such as a disk, but for a more complicated set, even something as simple as the union of three disjoint disks, its analytic capacity must be approximated by numerical methods. Recently, a new technique has been developed to determine the analytic capacity of a set by using numerical methods to solve the Kerzman-Stein boundary integral equation from which the analytic capacity can be determined directly.
Participants will learn the basics of this algorithm and how to program it in MATLAB. They will run programs to approximate the analytic capacity of
sets for which this value is not known. Since these sets may contain features such as non-smooth boundaries, some modification of the algorithms may be
required for them to produce the correct answers. They may also investigate how to determine the exact value of analytic capacity using complex analysis
methods if time permits.
Recommended prerequisites: a course in complex analysis is recommended; programming experience is helpful but not required
Combinatorial and algebraic properties of numerical semigroup rings (advisor: Dr. Aleksandra Sobieska)
A numerical semigroup is a subset of the natural numbers obtained by taking all the nonnegative integer combinations of some set. For example, using 3 and 7, we can generate the numerical semigroup {0,3,6,7,10,12,13,14,15,…}. Numerical semigroups appear anywhere that objects arise as combinations of specific numbers, both in advanced math and in the mundane – coins, stamps, football scores, and chicken nuggets.
To a numerical semigroup, one can associate a special ring called the numerical semigroup ring. The algebraic properties of the numerical semigroup ring are often closely related to the combinatorial properties of the semigroup. This project will focus on using minimal free resolutions – a way of encoding the algebraic structure of a ring into several matrices with polynomial entries – to quantify the algebraic properties of the ring, and look to connect these algebraic properties to the combinatorics of the semigroup.
Required Prerequisite: linear algebra; Recommended prerequisites: abstract algebra and some programming experience
Filtration of textile dyes (advisor: Dr. Sean McBride)
The purpose of this project will be to collect data for several new dyes during the functionalization process of porous polycarbonate filters, referred to as hysteresis data. During the functionalization process, the concentration of dyes run through the filter is increased from $50 \mu{M}$ up to $1000 \mu{M}$ and then back down to $50 \mu{M}$. If there was no hysteresis in the data during this cycle, then the rejection as a function of concentration for increasing and decreasing concentration would be the same and we would see no functionalization of the filter. However, for some anionic azo dyes, we see a large hysteretic behavior after ramping up and decreasing the concentration of the dyes run through the filter. The end goal of this research is to determine what variables or environmental conditions are responsible for this hysteric behavior for certain azo dyes. Once this is known, such attributes or combination of environmental parameters can be engineered in later research, leading to advanced dye removal systems.
Recommended prerequisite: basic laboratory skills
The opinions, findings, and conclusions or recommendations expressed are those of the involved faculty and do not necessarily reflect the views of the National Science Foundation.