Opers and Non-Abelian Hodge: Numerical Studies

References

• Acosta, J. A. (2016). Holonomy limits of cyclic opers. ProQuest LLC, Ph.D. thesis. Rice University, Ann Arbor, MI.
   Google Scholar
• Biquard, O., and Boalch, P. (2002). Wild nonabelian Hodge theory on curves. arXiv:math/0111098.
   Google Scholar
• Boalch, P. (2001). Symplectic manifolds and isomonodromic deformations. Adv. Math. 163(2):137–205.
   Web of Science ®Google Scholar
• Boalch, P. (2018). Wild character varieties, meromorphic Hitchin systems and Dynkin diagrams. In: Andrew Dancer, Jørgen Ellegaard Andersen, and Oscar García-Prada (Eds.), Geometry and Physics, Vol. II. Oxford: Oxford Univ. Press.
   Google Scholar
• Cecotti, S., Neitzke, A., and Vafa, C. (2010). R-twisting and 4d/2d correspondences. arXiv:1006.3435.
   Google Scholar
• Cecotti, S., and Vafa, C. (1991). Topological-antitopological fusion. Nucl. Phys. B. 367: 359–461. doi:10.1016/0550-3213(91)90021-O
   Web of Science ®Google Scholar
• Collier, B., and Wentworth, R. (2019). Conformal limits and the Białynicki-Birula stratification of the space of λ-connections. Adv. Math. 350: 1193–1225. arXiv:1808.01622.
   Web of Science ®Google Scholar
• Concus, P., and Golub, G. H. (1973). Use of fast direct methods for the efficient numerical solution of nonseparable elliptic equations. SIAM J. Numer. Anal. 10: 1103–1120. doi:10.1137/0710092
   Web of Science ®Google Scholar
• Dorey, P., Dunning, C., and Tateo, R. (2004). Aspects of the ODE/IM correspondence. arXiv:hep-th/0411069.
   Google Scholar
• Dorey, P., Dunning, C., and Tateo, R. (2007). The ODE/IM Correspondence. J. Phys. A40:R205. arXiv:hep-th/0703066. doi:10.1088/1751-8113/40/32/R01
   Google Scholar
• Dorey, P., and Tateo, R. (1999). Anharmonic oscillators, the thermodynamic Bethe ansatz, and nonlinear integral equations. J. Phys. A, 32:L419–L425. arXiv:hep-th/9812211.
   Google Scholar
• Dorey, P., and Tateo, R. (1999). On the relation between Stokes multipliers and the T-Q systems of conformal field theory. Nucl. Phys. B563: 573–602. arXiv:hep-th/9906219. doi:10.1016/S0550-3213(99)00609-4
   Web of Science ®Google Scholar
• Dorey, P., and Tateo, R. (2000). Differential equations and integrable models: the SU(3) case. Nucl. Phys. B 571(3): 583–606.
   Web of Science ®Google Scholar
• Dorey, P. E., Dunning, C., and Tateo, R. (2000). Ordinary differential equations and integrable models. POS, TMR2000:034, arXiv:hep-th/0010148.
   Google Scholar
• Dumas, D. (2017). Holonomy limits of complex projective structures. Adv. Math. 315: 427–473. doi:10.1016/j.aim.2017.05.021
   Web of Science ®Google Scholar
• Dumas, D., and Neitzke, A. Asymptotics of Hitchin’s metric on the Hitchin section. Comm. Math. Phys. (367): 127. arXiv:1802.07200v2. doi:10.1007/s00220-018-3216-7
   Google Scholar
• Dumas, D., and Neitzke, A. (2020). Replication Data for: Opers and nonabelian Hodge: numerical studies. doi:10.7910/DVN/W0V4D9.
   Google Scholar
• Dumas, D., and Neitzke, A. (2020). Stokes numerics. https://github.com/neitzke/stokes-numerics/.
   Google Scholar
• Dumas, D., and Wolf, M. (2015). Polynomial cubic differentials and convex polygons in the projective plane. Geom. Funct. Anal., 25(6):1734–1798.
   Web of Science ®Google Scholar
• Dumitrescu, O., Fredrickson, L., Kydonakis, G., Mazzeo, R., Mulase, M., and Neitzke, A. (2016). Opers versus nonabelian Hodge. July, arxiv:1607.02172. To appear in J. Diff. Geom.
   Google Scholar
• Fock, V., and Goncharov, A. (2006). Moduli spaces of local systems and higher Teichmüller theory. Publ. Math. Inst. Hautes Études Sci. (103): 1–211. arXiv:math/0311149. doi:10.1007/s10240-006-0039-4
   Google Scholar
• Fredrickson, L. (2019). Perspectives on the asymptotic geometry of the Hitchin moduli space. SIGMA Symmetry Integrability Geom. Methods Appl. 15. doi:10.3842/SIGMA.2019.018
   Web of Science ®Google Scholar
• Fredrickson, L. (2020). Exponential decay for the asymptotic geometry of the Hitchin metric. Comm. Math. Phys. 375(2): 1393–1426.
   Web of Science ®Google Scholar
• Fredrickson, L., and Neitzke, A. From S1-fixed points to W-algebra representations. arXiv:1709.06142v1.
   Google Scholar
• Gaiotto, D. (2014). Opers and TBA. March, arXiv:1403.6137.
   Google Scholar
• Gaiotto, D., Moore, G. W., and Neitzke, A. (2010). Four-dimensional wall-crossing via three-dimensional field theory. Commun. Math. Phys. 299: 163–224. arXiv:0807.4723. doi:10.1007/s00220-010-1071-2
   Web of Science ®Google Scholar
• Gaiotto, D., Moore, G. W., and Neitzke, A. (2012). Wall-crossing in coupled 2d-4d systems. JHEP, 12, arXiv:1103.2598.
   Google Scholar
• Gaiotto, D., Moore, G. W., and Neitzke, A. (2013). Spectral networks. Annales Henri Poincaré, 14(7): 1643–1731, 11. arXiv:1204.4824.
   Web of Science ®Google Scholar
• Gaiotto, D., Moore, G. W., and Neitzke, A. (2013). Wall-crossing, Hitchin systems, and the WKB approximation. Adv. Math. 234: 239–403. arXiv:0907.3987.
   Web of Science ®Google Scholar
• Grassi, A., Gu, J., and Marino, M. Non-perturbative approaches to the quantum Seiberg-Witten curve. arXiv:1908.07065.
   Google Scholar
• Gupta, S. Harmonic maps and wild Teichmüller spaces. Journal of Topology and Analysis. arXiv:1708.04780v2.
   Web of Science ®Google Scholar
• Han, Z. -C., Tam, L. -F., Treibergs, A., and Wan, T. (1995). Harmonic maps from the complex plane into surfaces with nonpositive curvature. Comm. Anal. Geom. 3(1/2):85–114. doi:10.4310/CAG.1995.v3.n1.a3
   Google Scholar
• Hitchin, N. J. (1992). Lie groups and Teichmüller space. Topology, 31(3):449–473. doi:10.1016/0040-9383(92)90044-I
   Google Scholar
• Hitchin, N. J. (1987). The self-duality equations on a Riemann surface. Proc. London Math. Soc. (3), 55(1): 59–126. doi:10.1112/plms/s3-55.1.59
   Google Scholar
• Hollands, L., and Neitzke, A. Exact WKB and Abelianization for the T3 equation. arxiv:1906.04271v1.
   Google Scholar
• Ito, K., Mariño, M., and Shu, H. (2019). TBA equations and resurgent quantum mechanics. J. High Energy Phys. (1): 228, arXiv:1811.04812.
   Web of Science ®Google Scholar
• Katzarkov, L., Noll, A., Pandit, P., and Simpson, C. (2015), Harmonic maps to buildings and singular perturbation theory. Comm. Math. Phys. 336(2): 853–903. doi:10.1007/s00220-014-2276-6
   Web of Science ®Google Scholar
• Loftin, J. (2007). Flat metrics, cubic differentials and limits of projective holonomies. Geom. Dedicata, 128: 97–106.
   Web of Science ®Google Scholar
• Lukyanov, S. L., and Zamolodchikov, A. B. (2010). Quantum sine(h)-gordon model and classical integrable equations. J. High Energy Phys. 2010(7).
   Google Scholar
• Mazzeo, R., Swoboda, J., Weiss, H., and Witt, F. (2016). Ends of the moduli space of Higgs bundles. Duke Math. J. 165(12):2227–2271, arXiv:1405.5765.
   Web of Science ®Google Scholar
• Mazzeo, R., Swoboda, J., Weiss, H., and Witt, F. (2019). Asymptotic geometry of the Hitchin metric. Comm. Math. Phys., 367(1):151–191.
   Web of Science ®Google Scholar
• Mochizuki, T. (2011). Wild harmonic bundles and wild pure twistor D-modules. Astérisque, (340):607. arXiv:0803.1344.
   Web of Science ®Google Scholar
• Mochizuki, T. (2019). Good wild harmonic bundles and good filtered higgs bundles. arXiv:1902.08298.
   Google Scholar
• Neitzke, A. (2017). Integral iterations for harmonic maps, arXiv:1704.01522.
   Google Scholar
• Oberkampf, W. L., and Roy, C. J. (2010). Verification and Validation in Scientific Computing, 1st ed. Cambridge, MA: Cambridge University Press.
   Google Scholar
• Simpson, C. (1991). Asymptotic Behavior of Monodromy, volume 1502 of Lecture Notes in Mathematics. Berlin: Springer-Verlag. Singularly perturbed differential equations on a Riemann surface.
   Google Scholar
• Thomas, J. W. (1995). Numerical Partial Differential Equations: Finite Difference Methods, Volume 22 of Texts in Applied Mathematics. New York: Springer-Verlag.
   Google Scholar
• Wan, T. Y. -H., and Au, T. K. -K. (1994). Parabolic constant mean curvature spacelike surfaces. Proc. Amer. Math. Soc. 120(2): 559–564.
   Web of Science ®Google Scholar
• Wentworth, R. A. (2016). Higgs bundles and local systems on Riemann surfaces. In: Luis Alvarez Consul, Jørgen Ellegaard Andersen, Ignasi Mundet i Riera (Eds.), Geometry and quantization of moduli spaces, Adv. Courses Math. CRM Barcelona, pp. 165–219. Cham: Birkhäuser/Springer.
   Google Scholar
• Wilkinson, J. H. (1965). The Algebraic Eigenvalue Problem, Oxford: Clarendon Press.
   Google Scholar
• Wolf, M. (1991), High energy degeneration of harmonic maps between surfaces and rays in Teichmüller space. Topology, 30(4): 517–540. doi:10.1016/0040-9383(91)90037-5
   Google Scholar
• Zamolodchikov, A. B. (1990). Thermodynamic Bethe ansatz in relativistic models. Scaling three state Potts and Lee-Yang models. Nucl. Phys. B342: 695–720. doi:10.1016/0550-3213(90)90333-9
   Google Scholar