معرفی
Noah Williams is a tenured Associate Professor in the Department of Mathematical Sciences at Appalachian State University, part of the College of Arts and Sciences. He has completed seven years of service as of fall 2025, actively contributing to both teaching and research in probability and its applications.
Research Interests: Dr. Williams specializes in probability theory, particularly focusing on random polynomials and random matrices. His work investigates the asymptotic behavior of roots and critical points, pairing phenomena, and eigenvalue statistics. He also explores combinatorial problems arising in genome rearrangement, applying probabilistic and discrete methods to model evolutionary distance.
Recent Research Trends: His recent publications reveal a strong focus on the interplay between complex analysis and probability, especially in the context of random polynomials. He frequently collaborates with Sean O'Rourke, producing rigorous results on the Gauss-Lucas theorem and local root-critical point pairing. A secondary thread involves discrete-to-continuous transitions in arithmetic progressions and genome evolution models under operations like DCJ and deletion-insertion.
- No scientific awards or honors are mentioned in the available text.
Teaching & Academic Service: Dr. Williams teaches a wide range of courses including Calculus I, Techniques of Proof, Linear Algebra, and graduate-level Computational Probability. He previously served in multiple instructional roles at the University of Colorado Boulder, including Instructor of Record, Assistant Coordinator for large calculus sections, and Lead Graduate Teacher for pedagogical training. His teaching philosophy incorporates Inquiry-Based Learning (IBL), supported by resources from established IBL initiatives.
Laboratories & Research Teams: While no formal lab is mentioned, Dr. Williams is part of a collaborative research network, primarily with Sean O'Rourke (University of Colorado Boulder), and has co-authored work with other mathematicians such as T. Greenwood, J. Kariv, A. Brisbin, M. Riehl, and J. Christy. These collaborations suggest an active research group or team in probabilistic combinatorics and random matrix theory.
