The ultimate goal of my research is to better understand the mathematics of quantum field theory and string theory. I am particularly interested in applying tools from low-dimensional geometry and topology to understand the abstract categorical structures used to formulate modern theories of mathematical physics. A detailed summary of some of my projects can be found in my research statement.
Monoidal categorification of genus zero skein algebras (with Hyun Kyu Kim and Peng Shan), 50 pages, arXiv:2505.13332.
Dualities of K-theoretic Coulomb branches from a once-punctured torus (with Peng Shan), 22 pages, arXiv:2411.17378.
Skein algebras and quantized Coulomb branches (with Peng Shan), 36 pages, arXiv:2401.06737.
Stability conditions and Teichmüller space, Mathematische Annalen, 390(2024), 3827–3890.
On the wall-crossing formula for quadratic differentials, International Mathematics Research Notices, 2023(2023), 8033–8077.
Stability conditions, cluster varieties, and Riemann-Hilbert problems from surfaces, Advances in Mathematics, 380(2021), 107610.
Categorified canonical bases and framed BPS states, Selecta Mathematica, 25(2019), 69.
Voros symbols as cluster coordinates, Journal of Topology, 12(2019), 1031–1068.
The monodromy of meromorphic projective structures (with Tom Bridgeland), Transactions of the AMS, 373(2020), 6321–6367.
Stability conditions and cluster varieties from quivers of type A, Advances in Mathematics, 337(2018), 260–293.
The geometry of cluster varieties from surfaces, Ph.D. thesis, Yale University (2016).
Quantization of canonical bases and the quantum symplectic double, Manuscripta Mathematica, 167(2022), 613–651.
A duality map for quantum cluster varieties from surfaces (with Hyun Kyu Kim), Advances in Mathematics, 306(2017), 1164–1208.
The cluster symplectic double and moduli spaces of local systems, Proceedings of the AMS, 145(2017), 5191–5204.
Laminations from the symplectic double, Geometriae Dedicata, 199(2019), 27–86.