J. Elisenda Grigsby
department of mathematics
Ph.D. University of California, Berkeley
Honors and Awards
- National Science Foundation postdoctoral fellow, Columbia University
- Board of directors, Girl’s Angle (www.girlsangle.org)
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)?
- 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