duncan-david.jpg image

 

Assistant Professor, Pure Math
Year Started at JMU: 2018
duncandl@jmu.edu
Contact Info

Research Description

I am interested in certain partial differential equations and algebraic invariants that arise in gauge theory and Floer theory. Much of my research has focused on the critical points of the Yang–Mills and Chern–Simons functionals, which capture information about the geometry and topology of 3- and 4-manifolds.

Education
  • PhD in Mathematics, 2013, Rutgers University
  • BS in Mathematics, 2006, University of Washington

 

Select Publications

"Triangles & Princesses & Bears, Oh My!" Math Intelligencer (2022). https://doi.org/10.1007/s00283-022-10219-5

"Characterizing immutable sandpiles: A first look." (with W.J. Engelbrecht) Discrete Mathematics, Vol. 345, Issue 1, 2022.

"Critical group structure from the parameters of a strongly regular graph." (with J.E. Ducey, W.J. Engelbrecht, J.V. Madan, E. Piato, C.S. Shatford, A. Vichitbandha) Journal of Combinatorial Theory, Series A, Vol. 180 (2021), 105424.

"The Yang–Mills flow for cylindrical end 4-manifolds." Indiana University Mathematics Journal, Vol. 69, Issue 3, 2020, pp. 1007–1071.

"The Chern–Simons invariants for doubles of compression bodies." Pacific Journal of Mathematics, Vol. 280, 2016, pp. 17–39.

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