Tianyu Yuan

collaborators

3 papers

math.SG2026

Higher-dimensional Heegaard Floer homology and spectral networks

Ko Honda, Yin Tian, Tianyu Yuan

Given a closed surface $C$ and a real exact Lagrangian $Σ \subset T^{*} C$ associated to a spectral curve, we construct a homomorphism $\operatorname{BSk}_κ(C)\to\operatorname{Mat}(N^κ…

math.SG2025

Higher-dimensional Heegaard Floer homology and the polynomial representation of double affine Hecke algebras

Yuan Gao, Eilon Reisin-Tzur, Yin Tian +1

We show that the higher-dimensional Heegaard Floer homology between tuples of cotangent fibers and the conormal bundle of a homotopically nontrivial simple closed curve on $T^{2}$ re…

math.SG2025

Morse theory of loop spaces and Hecke algebras

Ko Honda, Roman Krutowski, Yin Tian +1

Given a smooth closed $n$ -manifold $M$ and a $κ$ -tuple of basepoints $q \subset M$ , we define a Morse-type $A_{\infty}$ -algebra $C M_{-*} (Ω (M, q))$ , called the…