3 papers
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.QA2025
A quantum N-dimer model
Daniel C. Douglas, Richard Kenyon, Nicholas Ovenhouse +2
We study a quantum version of the -dimer model from statistical mechanics, based on the formalism from quantum topology developed by Reshetikhin and Turaev (the latter which, in…
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…