I am a mathematician interested in the algebra and geometry of homological mirror symmetry. I have been a postdoc at the University of Waterloo (2024-2026) and the University of Alberta (2021-2024). I received my PhD from the University of Illinois at Urbana-Champaign in 2021.

Homological Mirror Symmetry (HMS) emerged from string theory as a mathematical incarnation of the type IIA/IIB string duality.  It asserts that for a pair of mirror Calabi–Yau manifolds (X,Y), the category of topological B-branes (coherent sheaves) on X is equivalent to the category of topological 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. 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 string duality in the BPS sector. 

My past 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 make their mirrors accessible via Laurent polynomials, whose Fukaya categories can be modelled 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 commutative and noncommutative algebraic 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 constructions to identify meaningful algebraic properties of the coherent derived categories. I have studied how this works 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 infrared phase selects a subset of UV branes which survive under a particular stability condition and RG flow to that phase. My work uses symplectic and microlocal techniques to describe the geometry of the mirror A-brane transports and develop applications of this geometric description to problems in birational geometry and noncommutative algebra. 

My perspectives are heavily inspired by quiver gauge theory, brane tiling, and brane dynamics.