Uploaded March 2026 | Updated September 2026, 3 weeks ago
IAS/Princeton/Montreal/Paris/Tel-Aviv Symplectic Geometry Zoominar
Topic: Higher-Dimensional Heegaard Floer Homology and Spectral Networks
Speaker: Ko Honda
Affiliation: UCLA
Date: March 27, 2026 9:15am
Remote Access
Let C be a closed surface and Σ⊂T*C a real exact Lagrangian surface associated to a spectral curve. In this talk we will first try to explain the context of this work (e.g., Higgs bundles and spectral curves). We then construct a homomorphism from the κ-strand braid skein algebra of C to the κ-strand matrix-valued braid skein algebra of Σ via higher-dimensional Heegaard Floer homology (HDHF). Finally we explore the adiabatic limit of this homomorphism, which yields a hybrid count of HDHF-type holomorphic curves coupled with certain Morse gradient graphs, called folded Morse trees. This is joint work with Tianyu Yuan and Yin Tian.
IAS/Princeton/Montreal/Paris/Tel-Aviv Symplectic Geometry Zoominar
Topic: Higher-Dimensional Heegaard Floer Homology and Spectral Networks
Speaker: Ko Honda
Affiliation: UCLA
Date: March 27, 2026 9:15am
Remote Access
Let C be a closed surface and Σ⊂T*C a real exact Lagrangian surface associated to a spectral curve. In this talk we will first try to explain the context of this work (e.g., Higgs bundles and spectral curves). We then construct a homomorphism from the κ-strand braid skein algebra of C to the κ-strand matrix-valued braid skein algebra of Σ via higher-dimensional Heegaard Floer homology (HDHF). Finally we explore the adiabatic limit of this homomorphism, which yields a hybrid count of HDHF-type holomorphic curves coupled with certain Morse gradient graphs, called folded Morse trees. This is joint work with Tianyu Yuan and Yin Tian.
