Juanita Pinzón Caicedo
Ph.D., Indiana University, Bloomington, 2014
B.S., Universidad de Los Andes, Bogotá, Columbia 2008
Topology deals with global or large-scale structures of objects. Geometric topology is the study of manifolds and its ultimate goal is the classification of manifolds within a certain framework (topological, piecewise linear, smooth, simply-connected, symplectic, etc.). Objects of dimensions one and two are completely classified, and in dimensions five and above, questions about smoothness can be translated into questions about homotopy type. In dimensions three and four classification is in many cases elusive, and so topologists develop analytic and algebraic invariants that detect the differences between manifolds. I specialize in --manifolds and knot concordance, that is, the study of knots from the perspective of the surfaces they bound in the 4-ball. In the past I have used developments in gauge theory and Floer homologies to advance the study of concordance. I have also used the recently developed theory of trisections to establish relationships between smooth topology in dimensions 3 and 4, with contact and symplectic geometry.
- Nickolas A Castro, David T Gay, and Juanita Pinzon-Caicedo. “Diagrams for Relative Trisections”. In: Pacific Journal of Mathematics 294.2 (2018), pp. 275–305. url: https://doi.org/10.2140/pjm.2018.294.275.
- Nickolas A. Castro, David T. Gay, and Juanita Pinzón-Caicedo. “Trisections of 4–manifolds with Boundary”. In: Proceedings of the National Academy of Sciences 115.43 (2018), pp. 10861–10868. url: http://www.pnas.org/content/115/43/10861.
- Yoshihiro Fukumoto, Paul Kirk, and Juanita Pinzón-Caicedo. “Traceless SU(2) representations of 2-stranded tangles”. In: Math. Proc. Cambridge Philos. Soc. 162.1 (2017), pp. 101–129. issn: 0305-0041. url: https://doi.org/10.1017/S0305004116000360.
- Matthew Hedden and Juanita Pinzón-Caicedo. “Satellites of Infinite Rank in the Smooth Concordance Group”. In: Submitted (2018). url: https://arxiv.org/abs/1809.04186.
- Juanita Pinzón-Caicedo. “Independence of Iterated Whitehead Doubles”. In: Proc. Amer. Math. Soc. (2018). url: https://doi.org/10.1090/proc/14261.
- Juanita Pinzón-Caicedo. “Independence of satellites of torus knots in the smooth concordance group”. In: Geom. Topol. 21.6 (2017), pp. 3191–3211. issn: 1465-3060. url: https://doi.org/10.2140/gt.2017.21.3191.