Please send application materials, including letters of reference, via Mathprograms.org. The deadline for submitting all application materials is March 21st, 11:59 p.m. Applicants must be US citizens or permanent residents, and plan to be enrolled in an undergraduate program in the Fall 2025 semester. 

Program is pending support from the National Security Agency.

Topics to Be Explored 

Modeling and Simulation of Swing Equations in Transient Stability Studies of Power Systems (Guangming Yao, Clarkson University):   This project explores efficient electromagnetic transient (EMT) modeling and simulations for analyzing power system dynamics. Nonlinear differential equations, specifically swing equations, play a critical role in assessing the transient stability of power systems. These equations share similarities with various phenomena in different disciplines. The traditional swing equation is grounded in a fundamental principle of dynamics, where the accelerating torque is the product of the rotor’s moment of inertia and its angular acceleration. Disturbances in power systems, including the location and type of faults, significantly impact transient stability, potentially causing imbalances that lead to a loss of synchronism. Analyzing and solving the swing equation enables operators to evaluate system stability during disturbances and implement protective mechanisms to safeguard the system. Tasks related to swing equations in this project include: Modeling, Analytical or Numerical Solution Techniques, Parameter Estimations, and/or Investigating modeling of multi-machine transient stability. Fundamental concepts in mathematical modeling, computational mathematics and numerical analysis can be introduced at beginning, followed by particular focuses of students’ choices. (A course in differential equations and familiarity with MATLAB or similar software are required).  

Links in embedded graphs (Joel Foisy, SUNY Potsdam):  A spatial embedding of a graph is a way to place a graph in space, so that vertices are points and edges are arcs that meet only at vertices. Mathematicians have studied graphs that are intrinsically linked: that is, in every spatial embedding, there exists a pair of disjoint cycles that form a non-splittable link. Sachs and Conway and Gordon showed that the complete graph on 6 vertices is intrinsically linked. More recently, people have studied graphs that have non-split links with more than 2 components, as well as knotted cycles, in every spatial embedding. We will use tools from graph and knot theory to examine analogs of intrinsic linking for planar graphs. Experience in these areas is not required. (minimum requirement: good experience in at least one proof intensive math class).

*reference available on request.