Charles Rezk

Roles & Affiliations: Charles Rezk is a Professor in the Department of Mathematics at the University of Illinois at Urbana-Champaign. He is affiliated with the College of Liberal Arts & Sciences and holds offices in both the Computing Applications Building and Altgeld Hall. He actively teaches advanced courses such as Homotopy Theory (Math 527) and Higher Category Theory (Math 595).

Research Interests: Rezk specializes in algebraic topology, with a focus on homotopy theory, higher category theory, and infinity categories. His work explores topics like elliptic cohomology, spectral algebra, and model categories. He has contributed to foundational areas such as quasicategories and topological André-Quillen cohomology.

Academic Contributions: Rezk manages the ALGTOP-L algebraic topology mailing list and maintains a comprehensive website with course materials, publications, and resources. His research includes notable papers on free colimit completions in infinity-categories (2025) and spectral algebra models of unstable periodic homotopy theory (2020). He also engages in educational outreach through lecture notes and video courses on finite group representations and abstract algebra.

Professional Activities: Rezk has organized conferences, contributed to editorial boards, and participated in initiatives like the Bousfield Classes conference. His work bridges foundational category theory with applied homotopy theory, influencing both pure and applied mathematical research.