[1] K., Behrend. Donaldson-Thomas type invariants via microlocal geometry. Ann. of Math. (2), 170(3):1307–1338, 2009.Google Scholar

[2] A. A., Beïlinson, J., Bernstein, and P., Deligne. Faisceaux pervers. Analysis and topology on singular spaces, I (Luminy, 1981). Astérisque, 100:5–171, 1982.Google Scholar

[3] T., Bridgeland. Hall algebras and curve-counting invariants. J. Amer. Math. Soc., 24(4):969–998, 2011.Google Scholar

[4] J., Bryan and R., Pandharipande. The local Gromov-Witten theory of curves. J. Amer. Math. Soc., 21(1):101–136 (electronic), 2008. With an appendix by Bryan, C. Faber, A. Okounkov, and Pandharipande.

[5] W.-Y., Chuang, D.-E., Diaconescu, and G., Pan. Wallcrossing and cohomology of the moduli space of Hitchin pairs. Commun. Num. Theor. Phys., 5:1–56, 2011.Google Scholar

[6] W.-Y., Chuang, D.-E., Diaconescu, and G., Pan. Chamber structure and wallcrossing in the ADHM theory of curves II. J. Geom. Phys., 62(2):548–561, 2012.Google Scholar

[7] K., Corlette. Flat G-bundles with canonical metrics. J. Differ. Geom., 28(3):361–382, 1988.Google Scholar

[8] M., de Cataldo, T., Hausel, and L., Migliorini. Topology of Hitchin systems and Hodge theory of character varieties. Ann. of Math. (2), 175(3):1329–1407, 2012.Google Scholar

[9] M. A. A., de Cataldo and L., Migliorini. The decomposition theorem, perverse sheaves and the topology of algebraic maps. Bull. Amer. Math. Soc. (N.S.), 46(4):535–633, 2009.Google Scholar

[10] M. A. A., de Cataldo and L., Migliorini. The perverse filtration and the Lefschetz hyperplane theorem. Ann. of Math. (2), 171(3):2089–2113, 2010.Google Scholar

[11] F., Denef and G. W., Moore. Split states, entropy enigmas, holes and halos. JHEP, 1111:129, 2011.Google Scholar

[12] D. E., Diaconescu. Moduli of ADHM sheaves and local Donaldson-Thomas theory. J. Geom. Phys., 64(4):763–799.

[13] R., Dijkgraaf, C., Vafa, and E., Verlinde. M-theory and a topological string duality, hep-th/0602087, 2006.

[14] T., Dimofte and S., Gukov. Refined, motivic, and quantum. Lett. Math. Phys., 91:1, 2010.

[15] S. K., Donaldson. Twisted harmonic maps and the self-duality equations. Proc. London Math. Soc. (3), 55(1):127–131, 1987.Google Scholar

[16] T., Eguchi and H., Kanno. Five-dimensional gauge theories and local mirror symmetry. Nucl. Phys., B586:331–345, 2000.Google Scholar

[17] T., Eguchi and H., Kanno. Topological strings and Nekrasov's formulas. JHEP, 12:006, 2003.Google Scholar

[18] R., Gopakumar and C., Vafa. M theory and topological strings II. arXiv:9812127, 1998.

[19] T., Hausel and F., Rodriguez-Villegas. Mixed Hodge polynomials of character varieties. Invent. Math., 174(3):555–624, 2008. With an appendix by Nicholas M. Katz.Google Scholar

[20] N. J., Hitchin. The self-duality equations on a Riemann surface. Proc. London Math. Soc. (3), 55(1):59–126, 1987.Google Scholar

[21] T. J., Hollowood, A., Iqbal, and C., Vafa. Matrix models, geometric engineering and elliptic genera. JHEP, 03:069, 2008.Google Scholar

[22] S., Hosono, M.-H., Saito, and A., Takahashi. Relative Lefschetz action and BPS state counting. Internal Math. Res. Not. 2001(15):783–816, 2001.Google Scholar

[23] Z., Hua. Chern-Simons functions on toric Calabi-Yau threefolds and Donaldson-Thomas theory. arXiv:1103.1921, 2011.

[24] D., Huybrechts and M., Lehn. The Geometry of Moduli Spaces of Sheaves. Aspects of Mathematics, E31. Braunschweig: Friedrich Vieweg & Sohn, 1997.

[25] K. A., Intriligator, D. R., Morrison, and N., Seiberg. Five-dimensional super-symmetric gauge theories and degenerations of Calabi-Yau spaces. Nucl. Phys., B497:56–100, 1997.Google Scholar

[26] A., Iqbal and A.-K., Kashani-Poor. Instanton counting and Chern-Simons theory. Adv. Theor. Math. Phys., 7:457–497, 2004.Google Scholar

[27] A., Iqbal and A.-K., Kashani-Poor. SU(N) geometries and topological string amplitudes. Adv. Theor. Math. Phys., 10:1–32, 2006.Google Scholar

[28] A., Iqbal, C., Kozcaz, and C., Vafa. The refined topological vertex. JHEP, 10:069, 2009.Google Scholar

[29] S., Katz, P., Mayr, and C., Vafa. Mirror symmetry and exact solution of 4-D N=2 gauge theories: 1. Adv. Theor. Math. Phys., 1:53–114, 1998.Google Scholar

[30] S. H., Katz, A., Klemm, and C., Vafa. M-theory, topological strings and spinning black holes. Adv. Theor. Math. Phys., 3:1445–1537, 1999.Google Scholar

[31] S. H., Katz and C., Vafa. Geometric engineering of N=1 quantum field theories. Nucl. Phys., B497:196–204, 1997.Google Scholar

[32] Y., Konishi. Topological strings, instantons and asymptotic forms of Gopakumar-Vafa invariants. hep-th/0312090, 2003.

[33] M., Kontsevich and Y., Soibelman. Stability structures, Donaldson-Thomas invariants and cluster transformations. arXiv.org:0811.2435, 2008.

[34] A. E., Lawrence and N., Nekrasov. Instanton sums and five-dimensional gauge theories. Nucl. Phys., B513:239–265, 1998.Google Scholar

[35] J., Li, K., Liu, and J., Zhou. Topological string partition functions as equivariant indices. Asian J. Math., 10(1):81–114, 2006.Google Scholar

[36] D., Maulik, N., Nekrasov, A., Okounkov, and R., Pandharipande. Gromov-Witten theory and Donaldson-Thomas theory. I. Compos. Math., 142(5):1263–1285, 2006.Google Scholar

[37] D., Maulik, R., Pandharipande, and R., Thomas. Curves on K3 surfaces and modular forms. J. Topology, 3(4):937–996, 2010.Google Scholar

[38] D., Maulik and Z., Yun. Macdonald formula for curves with planar singularities. arXiv:1107.2175.

[39] L., Migliorini and V., Shende. A support theorem for Hilbert schemes of planar curves. arXiv:1107.2355, 2011.

[40] D. R., Morrison and N., Seiberg. Extremal transitions and five-dimensional supersymmetric field theories. Nucl. Phys., B483:229–247, 1997.Google Scholar

[41] S., Mozgovoy. Solution of the motivic ADHM recursion formula. Math. Res. Not., 2012(18):4218–4244, 2012.Google Scholar

[42] N. A., Nekrasov. Seiberg-Witten prepotential from instanton counting. Adv. Theor. Math. Phys., 7:831–864, 2004.Google Scholar

[43] A., Okounkov and R., Pandharipande. The local Donaldson-Thomas theory of curves. Geom. Topol., 14:1503–1567, 2010.Google Scholar

[44] R., Pandharipande and R. P., Thomas. Curve counting via stable pairs in the derived category. Invent. Math., 178(2):407–447, 2009.Google Scholar

[45] R., Pandharipande and R. P., Thomas. Stable pairs and BPS invariants. J. Amer. Math. Soc., 23(1):267–297, 2010.Google Scholar

[46] C. T., Simpson. Higgs bundles and local systems. Inst. Hautes Études Sci. Publ. Math., 75(1):5–95, 1992.Google Scholar

[47] J., Stoppa and R. P., Thomas. Hilbert schemes and stable pairs: GIT and derived category wall crossings. Bull. Soc. Math. France, 139(3):297–339, 2011.Google Scholar

[48] Y., Toda. Curve counting theories via stable objects I. DT/PT correspondence. J. Amer. Math. Soc., 23(4):1119–1157, 2010.Google Scholar

[49] Y., Toda. Generating functions of stable pair invariants via wall-crossings in derived categories. In New Developments in Algebraic Geometry, Integrable Systems and Mirror Symmetry (RIMS, Kyoto, 2008), M.-H., Saito, S., Hosono, and K., Yoshioka, eds. Advanced Studies in Pure Mathematics 59. Tokyo: Mathematical Society of Japan, 2010, pp. 389–434.

[50] Y., Yuan. Determinant line bundles on moduli spaces of pure sheaves on rational surfaces and strange duality. Asian J. Math., 16(3):451–478, 2012.Google Scholar