Skip to main content

Secondary navigation:

Morrissey College of Arts and Sciences

J. Elisenda Grigsby

department of mathematics

J. Elisenda Grigsby photo

Assistant Professor

Ph.D. University of California, Berkeley
A.B. Cum Laude, Harvard University


Honors and Awards

  • National Science Foundation postdoctoral fellow, Columbia University
  • Board of directors, Girl’s Angle (

I study the topology of 3- and 4-dimensional manifolds, objects whose local structure is modeled on standard Euclidean 3-dimensional (resp., 4-dimensional) space. The field of topology is concerned with those properties of a space that remain unchanged when the space is stretched or pinched without tearing or gluing. In recent years, the study of low-dimensional manifolds has been transformed by an influx of ideas from physics, namely gauge theory and quantum field theory. In essence, one studies a manifold by associating to it some auxiliary space (e.g., the space of solutions to a collection of differential equations) from which topological information about the original space is more easily extracted. My research focuses on using these new tools to address classical questions in low-dimensional topology: for example, when are two knots equivalent (when are two smoothly imbedded circles in 3-dimensional Euclidean space homotopic through smooth imbeddings)?

Selected publications

  • On the colored Jones polynomial, sutured Floer homology, and knot Floer homology, with S. Wehrli, Advances in Mathematics, to appear
  • Grid diagrams for lens spaces and combinatorial knot Floer homology, K. Baker and M. Hedden, Int. Math. Res. Notices (2008), 39 pp.
  • Knot concordance and Heegaard Floer homology invariants in branched covers,
    with D. Ruberman and S. Strle, Geometry and Topology 12 (2008), pp. 2249-2275
  • Knot Floer homology in cyclic branched covers, Algebraic and Geometric Topology, 6 (2006) 1355-1398