Joshua P. Swanson

Joshua P. Swanson is an RTPC Assistant Professor of Mathematics at the University of Southern California (USC). Previously, he held a Stefan E. Warshawski Visiting Assistant Professorship at the University of California, San Diego (UCSD). He earned his PhD in Mathematics from the University of Washington under advisor Sara Billey, focusing on major index statistics and asymptotics. His research spans algebraic combinatorics with an emphasis on web bases for quantum group representations, plabic graphs, invariant theory, and analytic combinatorics.

Education:

• PhD in Mathematics, University of Washington (2018)
• Bachelor's degree (implied, details not specified)

Research Interests: Algebraic combinatorics, quantum group representations, plabic graphs, Coxeter groups, q-analogues, limit laws, and supercoinvariant algebras. He co-organizes workshops such as ICERM's Topical Workshop on Webs in Algebra, Geometry, Topology, and Combinatorics (2025).

Publications: Over 20 peer-reviewed articles in top journals including Algebraic Combinatorics, European Journal of Combinatorics, and Advances in Mathematics. Recent work focuses on web bases, q-Stirling numbers, and harmonic differential forms.

Awards:

• NSF Grant DMS-2348843 ($180,000)
• AMS-Simons Travel Grant ($5,000)
• Personal prize from Doron Zeilberger ($300)
• McKibben & Merner Fellowship ($10,000)

Teaching: Taught over 20 courses at USC and UCSD, including Probability Theory (Math 407), Linear Algebra (Math 225), and Combinatorics (Math 184). Active in mentoring undergraduate researchers via USC's SURF program.

Professional Engagement: Co-organizes seminars like the USC Combinatorics Seminar and serves on conference committees for FPSAC and CanaDAM. Maintains active collaborations with researchers such as Christian Gaetz, Oliver Pechenik, and Jessica Striker.