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Journals and Conferences
We generalize McShane’s identity for the length series of simple closed geodesics on a cusped hyperbolic surface  to a general identity for hyperbolic cone-surfaces (with all cone angles ≤ π), possibly with cusps and/or geodesic boundary. The general identity is obtained by studying gaps formed by simplenormal geodesics emanating from a distinguished… (More)
The Andreev-Thurston theorem states that for any triangulation of a closed orientable surface Σg of genus g which is covered by a simple graph in the universal cover, there exists a unique metric of curvature 1, 0 or −1 on the surface depending on whether g = 0, 1 or ≥ 2 such that the surface with this metric admits a circle packing with combinatorics given… (More)
This paper surveys our on-going study of the moduli space of pairs of a surface with a complex projective structure, on which the circle makes sense, and a circle packing on it whose combinatorics is fixed. A conjectural picture, the results obtained so far and a list of problems for further study are discussed.
Soybeans have been cultivated and consumed in Asia for many centuries. Soy products can be found in all households in Asian countries, and Asian children begin to consume soy formulas and soy products at a very young age. In a study of soy exposure in a group of healthy Singaporean children < 10 y of age, 70% had consumed soy products and of those > 95% had… (More)
Let Σg be a closed orientable surface of genus g ≥ 2 and τ a graph on Σg with one vertex which lifts to a triangulation of the universal cover. We have shown that the cross ratio parameter space Cτ associated with τ , which can be identified with the set of all pairs of a projective structure and a circle packing on it with nerve isotopic to τ , is… (More)
We establish an identity for compact hyperbolic surfaces with or without boundary whose terms depend on the dilogarithms of the lengths of simple closed geodesics in all 3-holed spheres and 1-holed tori in the surface.
In this note we announce several results concerning the SL(2,C) character variety X of a one-holed torus. We give a description of the largest open subset XBQ of X on which the mapping class group Γ acts properly discontinuously, in terms of two very simple conditions, and show that a series identity generalizing McShane’s identity for the punctured torus… (More)