Dr. Harold Williams

Assistant Professor

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Biography

Harold Williams is an Assistant Professor at the University of Southern California, specializing in representation theory, geometry, combinatorics, and their applications in theoretical physics and artificial intelligence. He has a robust research portfolio supported by significant grants, including the NSF CAREER grant DMS-2143922. His work involves collaborative research with notable mathematicians and contributions to various mathematical topics such as automating theorem proving, cluster theory, and Q-systems. Williams has published numerous papers in high-impact journals and was previously a postdoctoral researcher at the Center for Quantum Mathematics and Physics at the University of California, Davis, where he was supported by the NSF Postdoctoral Research Fellowship DMS-1502845. Aside from his academic endeavors, he has been actively involved in organizing workshops and conferences in representation theory and noncommutative algebra. His passion for music, particularly classical guitar, complements his analytical skills in mathematics.

Research Interests

Experience

Postdoctoral Researcher

— Present

Center for Quantum Mathematics and Physics • University of California, Davis

Conducted research on quantum mathematics and physics.

Requirements for University of Southern California

Master Program
Requirements
GPA Requirement
Required:3
TOEFL
Listening
Required:20
Reading
Required:20
Writing
Required:20
Speaking
Required:20
Total
Required:90
IELTS
Listening
Required:6
Reading
Required:6
Writing
Required:6
Speaking
Required:6
Overall
Required:6.5
GRE General
Prerequisites
Bachelor's degree in Engineering, Math, or Hard Science
Application Checklist
  • Online application
  • Official transcripts
  • Personal Statement
  • Resume/CV
  • Letters of Recommendation (not required for MS CS, but allowed)
Specialization Notes

GRE is NOT required for Master's applicants for 2025-2026.