I am a postdoc in the Geometry and Topology research group at the University of Waterloo. In the current semester, I am an associate postdoc at the Perimeter Institute for Theoretical Physics. Previously, I was a postdoc at the University of Alberta, supported by a PIMS postdoc fellowship (2021-2023) and the NSERC Discovery Grant (2021-2024). I received my PhD from the University of Illinois at Urbana-Champaign in August 2021.

I am a mathematician studying the algebra and geometry of Homological Mirror Symmetry (HMS). HMS emerged from string theory as a mathematical incarnation of the A/B-model duality.  It asserts that for a pair of mirror Calabi–Yau manifolds (X,Y), the category of B-branes (coherent sheaves) on X is equivalent to the category of A-branes (Lagrangian submanifolds with local systems) on Y. This correspondence exchanges complex moduli with Kähler moduli, holomorphic bundles with Lagrangian cycles, and extension groups with Floer cohomologies, providing a categorified form of superstring T-duality in the type II theories.

From the physical point of view, HMS captures how two apparently distinct quantum field theories - the topological A-model and B-model - encode equivalent information about the same underlying superstring background. Morphisms in these categories correspond to open-string states, and the compositions record worldsheet instanton corrections. Thus HMS is not merely a geometric coincidence but a precise mathematical realization of gauge/string duality in the BPS sector.

My research develops mathematical applications of this equivalence in settings where both sides can be computed explicitly, primarily for toric varieties.  Toric varieties admit combinatorial descriptions that render their mirrors accessible via Laurent polynomials, whose Fukaya categories can be modeled microlocally by constructible sheaves on real tori.  This makes it possible to realize D-brane gauge theories, wall-crossing phenomena, and noncommutative resolutions entirely within a unifying geometric framework. My current research program has two guiding aims:

• To solve concrete problems in algebraic and noncommutative geometry using HMS as a computational mechanism;

• To develop a combinatorial symplectic geometry framework for categorical wall-crossing and phase transitions of supersymmetric gauge theories.

Achieving these goals involves using the correct mirror-geometric constructions to identify meaningful algebraic structures of the coherent derived categories. I have studied how these ideas pan out concretely in the context of toric GIT wall-crossings using window categories. These categories correspond to different gauge theory sectors within a common ultraviolet category - each phase selects a subset of branes surviving under a particular stability condition. My work describes the geometry of the corresponding microlocal A-brane transports, and studies applications of this geometric description to problems in birational geometry and noncommutative algebra. 

My perspectives on the subject are heavily inspired by quiver gauge theory and brane tiling. 

Where to find me in Fall 2025:

Tue, Wed, Thu: MC. Mon, Fri: PI.