James M. Hughes, William W. Elliott Assistant Research Professor

My research is in low-dimensional contact and symplectic topology. I primarily focus on invariants of Legendrian knots and their exact Lagrangian fillings, particularly those related to cluster theory. I also like to think about different constructions of Legendrian surfaces, especially from a cluster-theoretic perspective.

Office Location:
Office Phone:	(919) 660-2800
Email Address:
Web Page:	https://sites.google.com/view/jmhughes/home/

Teaching (Fall 2024):

• MATH 721.02, LINEAR ALGEBRA & APPLICA Synopsis

  Physics 235, TuTh 10:05 AM-11:20 AM

• MATH 721.03, LINEAR ALGEBRA & APPLICA Synopsis

  Physics 235, TuTh 08:30 AM-09:45 AM

Office Hours:

Fall 2023:

• Tuesdays 2:30-3:30


• Thursdays 3:30-4:30

and by appointment.

Education:

Ph.D.

University of California, Davis

2023

Recent Publications

1. Hughes, J, Weave-realizability for D–type, Algebraic & Geometric Topology, vol. 23 no. 6 (September, 2023), pp. 2735-2776, Mathematical Sciences Publishers [doi]
2. Hughes, J, Lagrangian fillings in $A$-type and their Kálmán loop orbits, Revista Matemática Iberoamericana, vol. 39 no. 5 (July, 2023), pp. 1681-1723, European Mathematical Society - EMS - Publishing House GmbH [doi]