معرفی
James M. Hughes serves as the William W. Elliott Assistant Research Professor in the Department of Mathematics at Duke University. He completed his Ph.D. at the University of California, Davis in 2023 and is currently teaching multiple courses including Real Analysis (MATH 431/731) and Advanced Problem Solving (MATH 283S).
His research focuses on low-dimensional contact and symplectic topology, with particular emphasis on invariants of Legendrian knots and their exact Lagrangian fillings. Hughes investigates connections between these geometric structures and cluster theory, exploring different constructions of Legendrian surfaces from cluster-theoretic perspectives. His work bridges abstract mathematical theory with concrete geometric constructions.
Hughes has published two significant papers in 2023 in prestigious mathematics journals. His research demonstrates strong connections between Hamiltonian isotopy classes of decomposable Lagrangian fillings and weave fillings, providing combinatorial criteria for determining orbit sizes of fillings. He employs both geometric and Floer-theoretic approaches in his investigations.
His teaching responsibilities include multiple sections of Real Analysis and Advanced Problem Solving courses. Office hours are held on Tuesdays 2:30-3:30 and Thursdays 3:30-4:30, with additional appointments available as needed.
