Ph.D. Students

Former

(By graduation year.)

• Ina Petkova. Ph.D., Columbia University, 2012. Co-advised with P. Ozsváth and D. Thurston
• Thesis: Bordered Heegaard Floer homology, Satellites, and Decategorification.
• Currently an Associate Professor at Dartmouth University.
• Kristen Hendricks. Ph.D., Columbia University, 2013. Co-advised with P. Ozsváth.
• Thesis: Localization and Heegaard Floer Homology.
• Currently an Associate Professor at Rutgers University.
• Jonathan Hales. Ph.D., Stony Brook University, 2013. Co-advised with O. Plamenevskaya.
• Thesis: Exotic Four-Manifolds, Corks, and Heegaard Floer Homology.
• Currently a Software Engineer working at PostEra.ai.
• Corrin Clarkson. Ph.D., Columbia University, 2014.
• Thesis: Three Manifold Mutations Detected by Heegaard Floer Homology.
• Currently the Director of General Education Math Modeling at Indiana University.
• Jonathan Hanselman. Ph.D., Columbia University, 2014.
• Thesis: Bordered Heegaard Floer homology and graph manifolds.
• Currently an Assistant Professor at Princeton University.
• Mike Wong. Ph.D., Columbia University, 2017. Co-advised with P. Ozsváth.
• Thesis: Unoriented skein relations for grid homology and tangle Floer homology.
• Currently an Assistant Professor at the University of Ottawa.
• James Cornish. Ph.D., Columbia University, 2018.
• Thesis: Growth Rate of 3-Manifold Homologies under Branched Covers.
• Currently on the job market.
• Jeffrey Musyt. Ph.D., University of Oregon, 2019.
• Thesis: Equivariant Khovanov homotopy and periodic links.
• Currently an Assistant Professor at Slippery Rock University.
• Keegan Boyle. Ph.D., University of Oregon, 2019.
• Thesis: On symmetries of knots and their surgeries.
• Currently a Postdoctoral Fellow at the University of British Columbia.
• Michael Gartner. Ph.D., University of Oregon, 2019.
• Thesis: Naturality in Heegaard Floer homology.
• Currently a data scientist at AI2.
• Gabriel Montes de Oca. Ph.D., University of Oregon, 2020.
• Thesis: An odd analog of Plamenevskaya's invariant of transverse knots
• Currently on the job market.
• Champ Davis. Ph.D., University of Oregon, 2023.
• Thesis: Structures and computations in annular Khovanov homology.
• Currently a lecturer at CU Boulder.
• Gary Guth. Ph.D., University of Oregon, 2023.
• Thesis: Ribbons, satellites, and exotic phenomena in Heegaard Floer homology.
• Currently a Simons postdoc at Stanford University.

Current

• Neda Bagherifard (University of Oregon)
• Holt Bodish (University of Oregon).
• Jesse Cohen (University of Oregon).
• Siavash Jafarizadeh (University of Oregon).

Master's Students

• Jacqueline Stone, M.S., University of North Carolina, 2013.
• Master's project: Algebraic Topology from the Perspective of Morse Homology
• Currently an Adjunct Mathematics Instructor at New Jersey Institute of Technology.

Undergraduate Students

Senior theses

• Edward Trefts, "Knot Floer Homology and the Genera of Torus Knots." Senior thesis, Columbia University, April 2008.
• Emily Clader, "Homotopy Theory of Finite Topological Spaces." Senior thesis, Columbia University, April 2009.
• A condensed version of this paper is published as: Emily Clader, "Inverse limits of finite topological spaces." Homology, Homotopy and Applications, 11 (2009), no. 2, 223--227.
• Atanas Atanasov, "Knots in S³ and Bordered Heegaard Floer Homology." Senior thesis, Columbia University, April 2010.
• Kyler Siegel, "A Geometric Proof of a Faithful Linear-Categorical Surface Mapping Class Group Action." arXiv:1108.3676. Senior thesis, Columbia University, August 2011.
• Nathaniel Schieber, "A Computational Approach to Tangles." Senior thesis, University of Oregon, June 2018.

Summer research projects

Columbia Undergraduate Mathematics Research Program, 2007.

These projects were assisted by Thomas Peters.

• Jonathan Hales, Dmytro Karabash and Michael Lock, "A Modification of the Sarkar-Wang Algorithm and an Analysis of its Computational Complexity." August 2007; revised January 2008. arXiv:0711.4405.
• Yael Degany, Andrew Freimuth and Edward Trefts, "Some Computational Results about Grid Diagrams of Knots." August 2007; revised April 2008.

Columbia Undergraduate Mathematics Research Program, 2009.

This project was coadvised with Timothy Perutz, with assistance from Jonathan Bloom and Thomas Peters

• Jin Woo Jang, Rachel Vishnepolsky and Xuran Wang, "Computing Fixed Point Floer Homology via the Hochschild Homology of a Sequence of Curves." November 2009. Rose Hulmann Journal of Undergraduate Mathematics Volume 11, Issue 2, 2010.