Research

My research investigates low-dimensional topology using methods from gauge theory and symplectic geometry. In particular, my research investigates spaces by studying their character varieties, which is the space of representations of the fundamental group into some Lie group modulo conjugation. My thesis studies traceless SU(2) character varieties of tangles and how these can be used to learn about knots.

For a more in-depth description of my research, here is my research statement.

Papers

Perturbed Traceless SU(2) Character Varieties for Tangle Sums - In Preparation

A Practical Guide to Perturbation Curves for Tangles - In Preparation

Past Talks

• "Character Varieties of Tangles and Singular Instanton Homology" - MCM Geometry Summer School, September 2023

• "Character Varieties of Tangle Sums"  - AMS Spring Sectional, April 2023 (Slides)

• "Character Varieties of Tangles and Singular Instanton Homology" - CIRGET Junior, March 2023 (Slides)

• "Character Varieties of Tangles and Singular Instanton Homology"  - WHVSS, January 2023 (Video, Slides)

• "Character Varieties of Tangles and Singular Instanton Homology" - IU Topology Seminar, November 2022

• "Character Varieties of Tangles and Singular Instanton Homology" - Workshop in Geometric Topology, June 2022 (Video, Slides)

• "Pillowcase Homology and Singular Instanton Homology" - GTA: Philadelphia, May 2022 (Slides)

• "Pillowcase Homology and Character Varieties of Tangles" - GSTGC, April 2022 (Video, Slides)

• "Pillowcase Homology and Character Varieties of Tangles" (virtual lightning talk) - Tech Topology Conference 2021 (Video, Slides)

• "The Upsilon Invariant" - IU Graduate Student Topology/Geometry Seminar, October 2020 (Notes)

• "The s Invariant and the Conway Knot" - IU Graduate Student Topology/Geometry Seminar, August 2020 (Talk 1 Notes, Talk 2 Notes)

• "Khovanov Homology and the s Invariant" - IU Graduate Student Topology/Geometry Seminar, April 2020 (Slides)

Software

• pcase - This is a SageMath module built for computing and studying Lagrangians in the pillowcase.

Conferences/Workshops Attended

• Workshop in Geometric Topology - Texas Christian University, June 2022 (Virtual)

• GTA: Philadelphia - Temple University, May 2022

• GSTGC - Georgia Tech, April 2022

• Interactions of Gauge Theory with Contact and Symplectic Topology in Dimensions 3 and 4 - BIRS, March 2022 (Virtual)

• Perspectives on Quantum Link Homology Theories - University of Regensburg, August 2021 (Virtual)

• Tech Topology Conference - Georgia Tech, December 2021 (Virtual)

• Tech Topology Summer School - Georgia Tech, July 2021 (Virtual)

• GSTGC  - Indiana University, April 2021 (Virtual)

• Special Session on Knotted Surfaces and Concordance - AMS Fall Western Sectional, October 2020 (Virtual)

• GOATS #2 - UGA, June 2020 (Virtual)

• Current Progress in Low Dimensional Topology Workshop - UQAM, August 2019