Hang Yuan

I am a tenure-track Assistant Professor at BIMSA.

Previously, I was a Boas Assistant Professor of Mathematics at Northwestern University, where I was mentored by Professor Eric Zaslow. I earned my Ph.D. from Stony Brook University under the supervision of Professor Kenji Fukaya.

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Research interests

My primary research aims to develop a precise mathematical formulation of the SYZ conjecture by utilizing methods from non-Archimedean analytic geometry, homotopy theory of $A_\infty$ structures, and family Floer theory for quantum correction.

I am also interested in topics in noncommutative geometry and algebraic topology, such as operads, Hochschild (co)homology, and loop spaces.

Papers

• Koszul duality and homotopy algebras for operads over quivers arXiv
• Family Floer SYZ mirror algorithm for the Grassmannian $Gr(2,4)$ (with Zekai Yu) arXiv
• Existence of pseudo-holomorphic disks via non-archimedean disk potentials arXiv slide
• Higher operad structure for Fukaya categories arXiv
• Open-Closed Hochschild Homology and the Relative Disk Mapping Space (with Yi Wang) arXiv slide
• Cyclic brace relation and BV structure on open-closed Hochschild cohomology arXiv
• An open-closed string analogue of Hochschild cohomology arXiv
• Non-archimedean analytic continuation of unobstructedness Quantum Topol. (2025) arXiv slide
• Family Floer SYZ conjecture for $A_n$ singularity Beijing J. Pure Appl. Math., 2026, 3(2): 417–489 arXiv slide
• Family Floer SYZ singularities for the conifold transition Accepted by Kyoto Journal of Mathematics arXiv slide
• Family Floer mirror space for local SYZ singularities Forum Math. Sigma (2024), Vol. 12: e119 1–37 arXiv slide 1, 2 · video 1, 2
• Family Floer superpotential’s critical values are eigenvalues of quantum product by $c_1$ Selecta Mathematica, 2025, 31(1): 13 arXiv slide
• Disk counting and wall-crossing phenomenon via family Floer theory J. Fixed Point Theory Appl., 2022, 24(4): 77 arXiv slide · video
• Family Floer program and non-archimedean SYZ mirror construction arXiv slide · video, thesis