New Identities for small hyperbolic surfaces

Luo and Tan gave a new identity for hyperbolic surfaces with/without geodesic boundary in terms of dilogarithms of the lengths of simple closed geodesics on embedded three-holed spheres or one-holed tori. However, the identity was trivial for a hyperbolic one-holed torus with geodesic boundary. In this paper we adapt the argument from Luo and Tan to give an identity for hyperbolic tori with one geodesic boundary or cusp in terms of dilogarithm functions on the set of lengths of simple closed geodesics on the torus. As a corollary, we are also able to express the Luo-Tan identity as a sum over all immersed three-holed spheres $P$ which are embeddings when restricted to the interior of $P$.Comment: 11 pages, 4 figure

Relationship Between Social Media Use and Social Anxiety Among Emerging Adults

LUO Remote Online Presenter Graduate Theoretical Proposa

Thermodynamics of a Trapped Unitary Fermi Gas

We present the first model-independent comparison of recent measurements of the entropy and of the critical temperature of a unitary Fermi gas, performed by Luo et al., with the most complete results currently available from finite temperature Monte Carlo calculations. The measurement of the critical temperature in a cold fermionic atomic cloud is consistent with a value $T_c=0.23(2)epsilon_F$ in the bulk, as predicted by the present authors in their Monte Carlo calculations.Comment: 5 pages, 4 figures, published versio