Dr. Joshua Swanson

Assistant Professor

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Biography

Joshua P. Swanson is a Non-Tenure Track Assistant Professor of Mathematics at the University of Southern California (USC). He completed his Ph.D. in Mathematics at the University of Washington in June 2018, under the supervision of Sara Billey, with a thesis titled 'Major Index Statistics: Cyclic Sieving, Branching Rules, Asymptotics'. Prior to his current role, he was a Visiting Assistant Professor at the University of California, San Diego (UCSD). Swanson's research focuses on algebraic combinatorics, particularly on topics such as web bases, quantum groups, and plabic graphs. He has co-organized workshops on various aspects of algebra and combinatorics, including the ICERM Topical Workshop on Webs, Algebra, Geometry, and Topology. He has also been involved in multiple research projects and has published works on combinatorial representation theory. In addition to his teaching responsibilities, Swanson has been awarded grants for his research and is active in mentoring undergraduate students in mathematical research.

Research Interests

Algebraic Combinatorics Webs Quantum Groups Plabic Graphs Invariant Theory Symmetric Functions Coxeter Groups Complex Reflection Groups Higher Coinvariant Algebras Tableau Combinatorics Stirling Numbers Dynamical Algebraic Combinatorics q-Analogues Limit Laws Cumulants Free Lie Algebras

Experience

Non-Tenure Track Assistant Professor

2021-09-01 — Present

University of Southern California • Los Angeles, CA

Teaching and research in mathematics, focusing on algebraic combinatorics and related fields.

Visiting Assistant Professor

2018-09-01 — 2021-06-01

University of California, San Diego • La Jolla, CA

Engaged in teaching and collaborative mathematical research projects.

Awards

#

NSF DMS-2348843 grant

2024-01-01
#

AMS-Simons Travel Grant

2019-01-01

Courses

Math 533: Algebraic Combinatorics Math 432: Applied Probability Math 505a: Applied Probability Math 407: Probability Theory Math 425a: Fundamental Concepts Analysis Math 225: Linear Algebra Differential Equations Math 11: Introductory Probability Statistics Math 126g: Calculus II

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.