Research Interests:
Quantum topology and hyperbolic geometry, especially
the asymptotic behavior of quantum invariants of links and 3-manifolds and their relationship with hyperbolic geometry;
the adjoint twisted Reidemeister torsion of hyperbolic 3-manifolds;
Teichmüller/ Virasoro TQFT
Publications:
(with Tian Yang),
On the Volume conjecture for hyperbolic Dehn-filled 3-manifolds along the figure eight knot
Quantum Topology (2025), Quantum Topol. 16 (2025), no. 3, pp. 419–491
(with Tian Yang),
Adjoint Twisted Reidemeister torsion and Gram matrices,
Advances in Mathematics 438 (2024) 109470.
(with Tian Yang),
Relative Reshetikhin-Turaev invariants, hyperbolic cone metrics and discrete Fourier transforms I,
Commun. Math. Phys. (2022). https://doi.org/10.1007/s00220-022-04613-5
(with Thomas Kwok-Keung Au)
Algebraic & Geometric Topology 22-1 (2022), 1-53. DOI 10.2140/agt.2022.22.1
Preprints:
Asymptotics aspects of Teichmüller TQFT for generalized FAMED semi-geometric triangulations
(with Fathi Ben Aribi, Antonin Guilloux),
FAMED by computer: proving the Andersen-Kashaev volume conjecture for 42,000 knots
(with Fathi Ben Aribi),
The Andersen-Kashaev volume conjecture for FAMED geometric triangulations
(with Tushar Pandey),
(with Tushar Pandey),
Geometry of fundamental shadow link complements and application to the 1-loop conjecture
(with Tushar Pandey),
(submitted to Quantum Topology).
(with Tian Yang),
Asymptotic expansion of relative quantum invariants
(with Tian Yang),
Relative Reshetikhin-Turaev invariants, hyperbolic cone metrics and discrete Fourier transforms II
Volume conjecture, geometric decomposition and deformation of hyperbolic structures
Asymptotics of some quantum invariants of the Whitehead chains
(with Thomas Kwok-Keung Au)
Asymptotic behavior of colored HOMFLY polynomials of figure eight knot