Research

Papers

• Lipshitz--Sarkar stable homotopy type for certain planar trivalent graphs with perfect matchings, 2025. arXiv:2508.12272

• Transverse invariant as Khovanov skein spectrum at its Extreme Alexander grading (with Adithyan Pandikkadan), 2025. arXiv:2507.12882

• Khovanov homology (Master’s thesis), 2020. http://210.212.36.82:8080/jspui/handle/123456789/1398

Website 

• Legendrian Knot Atlas - Classifed all Legendrian knots of grid index less than 11 (with Cyrus Cox, Justin Murray, Adithyan Pandikkadan, Shea Vela-Vick, Angela Wu), 2023. Legendrian knot atlas

This knot atlas is an online database extending Chongchitmate and Ng's previous work. 

Research Interests

• Low-dimensional topology: Khovanov stable homotopy type, knot Floer stable homotopy type 

Here are my notes on Khovanov stable homotopy type and Burnside category, Steenrod square on Khovanov homology.

• Contact geometry: Legendrian and transverse knots and their invariants, Lagrangian cobordisms

Here are my notes on contact geometry.

• Quantum topology: sl(2) and sl(3) link homologies

• Gauge theory: Seiberg-Witten and Gromov-Witten theory