Summer Undergraduate Applied Mathematics Institute
May 27 - July 17, 2026
The Summer Undergraduate Applied Mathematics Institute (SUAMI) is an eight-week summer research program for undergraduate students. The goals of the SUAMI are twofold: (1) to expose students to the nature, culture, and rigors of advanced work and research in the area of applied mathematics; (2) to give the students a taste of the graduate school experience to help them make a more informed decision on whether they should attend graduate school. SUAMI is part of a larger summer program run by the Mellon College of Science at Carnegie Mellon, and SUAMI students will have opportunities to participate in the academic, cultural, and social programs of the larger MCS summer community.
SUAMI 2026 will feature research projects in a variety of research areas including graph theory, liquid crystals, interacting particle systems, and low-dimensional topology. There will be both pure projects and projects motivated by applications. Previous coursework in the area of a project will not be necessary to participate in the project.
Your application should include a statement (at most two pages in length) that explains why you are interested in participating in SUAMI. If you are interested in a particular research area, you should mention that. Please include in this statement a description of any obstacles and/or challenges that you have faced and overcome in your pursuit of studying mathematics.
Applications should also include a CV, a transcript and two letters of recommendation.
A final decision regarding the program format will be made and communicated as soon as possible.
Participating students will receive a stipend, on-campus housing, a meal allowance, and reimbursement for domestic round-trip travel to Pittsburgh.
The application deadline is February 15. Late applications will be considered until all spots in the program are filled.
➤ Wild edges in edge-colored graphs
Mentor: Aleyah Dawkins
Abstract: Consider a graph of your favorite city with vertices representing locations in the city and edges representing a route between them. Suppose that each route can currently only support one mode of transportation. City planners want citizens to have access to every location from any other location using their preferred mode of transportation: walking, driving, bussing, etc. Each mode of transportation corresponds to an edge color. We call an edge wild if any mode of transportation can use the route it represents and so a wild edge belongs to every color class. We consider the minimum number of edges that would need to be wild in order for a person to be able to travel between any two locations in the city using entirely their preferred mode of transportation which corresponds to a spanning tree in every color. Inspired by recent open questions of Anders, Foster-Greenwood, Garcia, and Krawzik, we will work to characterize which edges in a graph must be wild given a particular edge coloring and investigate how this parameter behaves for subgraphs.
➤ Modeling and Simulation of Liquid Crystals with Numerical PDEs
Mentor: Andrew Hicks
Abstract: Liquid crystals (LC's) are a material that has increasingly found many uses in our modern world, most famously in liquid crystal displays. This research will look into the behaviors of LC's through the lens of numerical PDE’s and the finite element method (FEM), using the Landau-de Gennes (LdG) model.
Students will be taught the model, as well as all of the mathematical prerequisites to understanding it. They will write their own code to simulate the LdG model, and will also learn how to use a premade code for more advanced simulations. This will then be used to conduct numerical experiments to study various phenomena about LCs.
➤ Interacting Particle Systems: From Mathematical Physics to Machine Learning
Mentor: Matthew Rosenzweig
Abstract: Interacting particle systems (IPS) provide versatile mathematical descriptions of diverse complex phenomena, including plasma dynamics, flocking and swarming, traffic flow, and chemotaxis. In recent years, IPS ideas have migrated into modern statistics and machine learning. For example, gradient flows of probability measures can be approximated by moving collections of particles and are used to train implicit generative models.
This REU will explore the role of IPS in active areas of machine learning and statistics such as generative sampling and Bayesian inference. The focus will be on the rigorous mathematical analysis of models and their algorithmic implementation from theoretical and computational perspectives, leveraging ideas from the intersection of mathematical physics, partial differential equations, and probability. Students will work as a group on a research project under the mentorship of Prof. Matthew Rosenzweig and a postdoc or graduate student with the goal of making an original contribution publishable in a peer-reviewed journal.
➤ Links, lattices, and rational homology 4-balls
Mentor: Jon Simone
Abstract: The study of knots is an important field within topology. For example, one can use knots to draw blueprints for 4-dimensional manifolds. Hence understanding particular properties of knots (and collections of knots called links) allows us to better understand 4-dimensional objects. During the summer, students will: explore a particular geometric property of knots called sliceness; learn how linear algebra (in the form of lattices) can be used as a tool to understand this geometric property; and see how slice knots can be used to construct special 4-dimensional manifolds called rational homology 4-balls. Throughout the summer, students will also work on an original project related to these ideas.
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