Research
Research
My research focuses on ergodic geometry, where I use tools from dynamical systems to explore problems rooted in geometry and topology. I am particularly interested in the interplay between thermodynamic objects—such as entropy and equilibrium states—and the geometry of the ambient space, as well as their applications in differential geometry and deformation theory.
Correlation Number for Potentials with Entropy Gaps and Cusped Hitchin Representations.
Joint with Giuseppe Martone
[arXiv]
Pressure gaps, geometric potentials, and nonpositively curved manifolds.
Joint with Dong Chen and Kiho Park
Transactions of the American Mathematical Society, to appear, [arXiv]
Pressure Metrics for Cusped Hitchin Components.
Joint with Harry Bray, Dick Canary, and Giuseppe Martone
Advances in Mathematics, 435 (2023), 109352, [Journal] [arXiv]
Counting, Equidistribution and Entropy Gaps at Infinity with Applications to Cusped Hitchin Representations.
Joint with Harry Bray, Dick Canary, and Giuseppe Martone
Journal für die reine und angewandte Mathematik (Crelle's Journal), 791 (2022), 1-51, [Journal] [arXiv]
Entropy Rigidity, Pressure Metric, and Immersed Surfaces in Hyperbolic 3-Manifolds.
Lecture Notes in Mathematics Series, 2290 CIRM Jean-Morlet Chair Subseries, Springer, Cham. 2021, 351-393, [Book]
Pressure Metrics for Deformation Spaces of Quasifuchsian Groups with Parabolics.
Joint with Harry Bray and Dick Canary
Algebraic & Geometric Topology, 23 (2023), no. 8, 3615-3653 [Journal] [arXiv]
Properties of Equilibrium States for Geodesic Flows over Manifolds without Focal Points.
Joint with Dong Chen and Kiho Park
Advances in Mathematics, 380 (2021), 107564, [Journal] [arXiv]
Pressure Metrics and Manhattan Curves for Teichmüller Spaces of Punctured Surfaces.
Israel Journal of Mathematics, 240 (2020), no. 2, 567-602, [Journal] [arXiv]
Unique Equilibrium States for Geodesic Flows Over Surfaces without Focal Points.
Joint with Dong Chen and Kiho Park
Nonlinearity, 33 (2020), no. 3, 1118-1155, [Journal] [arXiv]
Manhattan Curves for Hyperbolic Surfaces with Cusps.
Ergodic Theory and Dynamical Systems, 40 (2020), no. 7, 1843–1874, [Journal] [arXiv ]
Pressure Type Metrics on Spaces of Metric Graphs.
Geometriae Dedicata, 187 (2017), 151–177, [Journal] [arXiv]
Entropy, Manhattan Curves and Immersed Surfaces in Hyperbolic 3-Manifolds.
[Preprint]
(Not for publication: The main result in this note was extended in "Entropy Rigidity, Pressure Metric, and Immersed Surfaces in Hyperbolic 3-Manifolds". )
The Tripod Configurations of Curves.
Joint with Ai-Nung Wang.
Journal of Geometry and Physics, 63 (2013), 1–5, [Journal] [Preprint]
The 2022 Abel Prize: Dennis Sullivan – A Pioneer Connecting Topology, Geometry, and Dynamical Systems.
The Scientific Monthly, 633 (2022). [In Traditional Chinese, Taiwan]