Research

Irreversible k-Threshold Dynamics

Fort Hays State University Undergraduate Research

My primary mathematical research investigates irreversible k-threshold processes on structured graph families. In these processes, an initial set of vertices is activated, and additional vertices activate once sufficiently many of their neighbors are active. My work studies how graph structure influences the minimum seed set required for complete conversion, along with probabilistic and temporal properties of the propagation process.

This research began at Fort Hays State University under the guidance of Dr. Soumya Bhoumik and Dr. Paul Flesher and developed from corona and double-corona products to generalized base-b corona constructions. The project has resulted in manuscript work, my undergraduate thesis, conference presentations, and computational tools for exploring threshold dynamics.

Roadside Vehicle Tracking & Work-Zone Traffic Simulation

University of Nebraska–Lincoln  REU   ·   Summer 2025

During an interdisciplinary Research Experience for Undergraduates at the University of Nebraska–Lincoln, I contributed to a project investigating roadside vehicle detection, tracking, and traffic simulation for freeway work-zone safety. The broader project combined computer vision with traffic and vehicle simulation to generate realistic vehicle trajectories from roadside-camera data.

My work focused primarily on improving the simulation environment using CARLA and SUMO, including work-zone speed behavior and more realistic truck and traffic conditions.