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math.GT2026
On the length conjecture for twist knots
Samuel Panitch, Mauricio Romo
Using the newly developed d quantum trace map, we compile more evidence for the length conjecture, a refinement of the all-order volume conjecture that incorporates insertions o…
math.GT2025
Compatibility of quantum trace and UV-IR maps
Samuel Panitch, Sunghyuk Park
This paper studies the connection between the quantum trace map -- which maps the -skein module to the quantum Teichmüller space for surfaces and to the quantum gl…
math.GT2024
3d Quantum Trace Map
Samuel Panitch, Sunghyuk Park
We construct the 3d quantum trace map, a homomorphism from the Kauffman bracket skein module of an ideally triangulated 3-manifold to its (square root) quantum gluing module, there…