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She calculates certain volumes in moduli space and then deduces the counting result for simple closed geodesics from this calculation.
On the structure of instability in moduli theory, arXiv preprint arXiv 1411.0627 (2014).
However, Mirzakhani et al have proved that complex geodesics and their closures in moduli space are in fact surprisingly regular, rather than irregular or fractal.
Andersen, J., Chekhov, L., Penner, R., Reidys, C. & Sulkowski, P. Topological recursion for chord diagrams, RNA complexes, and cells in moduli spaces.
Most recently, Mirzakhani, together with Alex Eskin and, in part, Amir Mohammadi, made a major breakthrough in understanding another dynamical system on moduli space that is related to the behavior of geodesics in moduli space.
Inspired by the work of Margulis, Mirzakhani and her co-workers have proved yet another analogue of the prime number theorem, in which they count closed geodesics in moduli space, rather than on a single surface.
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The reductions in the in-plane moduli were contained within 7 10%.
Using ABAQUS, a simplified damage model was combined with stress-based failure criteria and reduced in-plane moduli to predict CAI.
By contrast, no significant changes in the moduli were observed in the absence of cyclic compression or in deactivated, cell-free samples.
Recently, Darling et al. [ 38] demonstrated that, under spread conditions, cells were stiffer, with the osteoblasts showing the greatest increase in average moduli (1.5-fold increase in Eelastic) compared with other cell types.
The increases in the moduli were coincided with the increase in calcified area in the bone samples.
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