The Geometry and Topology group at the University of Iowa Department of Mathematics brings together faculty with diverse research interests across modern geometry and topology. Our work spans quantum topology, including categorical braid group actions, skein modules, and character varieties (Ben Cooper); differential geometry and geometric analysis, with connections to algebraic geometry and combinatorics (Hao Fang); symplectic geometry, Gromov–Witten theory, Floer homology, and mirror symmetry (Mohammad Farajzadeh-Tehrani); and low‑dimensional topology, contact geometry, and mapping class groups (Keiko Kawamuro). We also pursue interdisciplinary applications of topology, such as modeling DNA knotting and protein folding and applying topological data analysis to complex biological data, bridging pure mathematics with mathematical biology (Isabel Darcy).

Our vibrant present is built upon a deeply rooted historical legacy. Oswald Veblen, an architectural figure in modern geometry and topology, graduated from the University of Iowa in 1900. Edward W. Chittenden established a rigorous culture of point-set topology and trained Deane Montgomery (PhD 1933), who later contributed to the resolution of Hilbert’s fifth problem and served as President of the American Mathematical Society. Steve Armentrout’s long tenure fostered a broad and influential lineage in topology.

Building on this foundation, Tom Branson advanced geometric analysis through his work on conformally invariant differential operators and Q-curvature. We also recognize emeritus Professor Charlie Frohman, whose contributions to skein theory and quantum topology, together with his mentorship, helped shape Iowa’s modern strength in geometric topology.