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Award ID contains: 1709877

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  1. ; (, Experimental Mathematics)
    We present numerical experiments that test the predictions of a conjecture of Gaiotto–Moore–Neitzke and Gaiotto concerning the monodromy map for opers, the non-Abelian Hodge correspondence, and the restriction of the hyperkähler L2 metric to the Hitchin section. These experiments are conducted in the setting of polynomial holomorphic differentials on the complex plane, where the predictions take the form of conjectural formulas for the Stokes data and the metric tensor. Overall, the results of our experiments support the conjecture. 
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  2. ; (, Geometric and Functional Analysis)
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  3. ; ; ; (, Forum of Mathematics, Sigma)
    We study the geometry of the Thurston metric on the Teichmüller space of hyperbolic structures on a surface $$S$$ . Some of our results on the coarse geometry of this metric apply to arbitrary surfaces $$S$$ of finite type; however, we focus particular attention on the case where the surface is a once-punctured torus. In that case, our results provide a detailed picture of the infinitesimal, local, and global behavior of the geodesics of the Thurston metric, as well as an analogue of Royden’s theorem. 
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  4. ; (, Communications in Mathematical Physics)
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  5. ; ; ; ; ; ; ; ; ; (, Notices of the American Mathematical Society)
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